text:
<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
         xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/maven-v4_0_0.xsd">
    <modelVersion>4.0.0</modelVersion>
    <groupId>com.zhangyifa</groupId>
    <artifactId>Seckill</artifactId>
    <packaging>war</packaging>
    <version>1.0-SNAPSHOT</version>
    <name>Seckill Maven Webapp</name>
    <url>http://maven.apache.org</url>
    <dependencies>
        <dependency>
            <groupId>junit</groupId>
            <artifactId>junit</artifactId>
            <version>4.12</version>
            <scope>test</scope>
        </dependency>

        <!-- 1.日记
          slf4j 是规范/接口
          日志实现 log4j,logback,common-logging
          使用 slf4j + logback
        -->
        <dependency>
            <groupId>org.slf4j</groupId>
            <artifactId>slf4j-api</artifactId>
            <version>1.7.5</version>
        </dependency>
        <dependency>
            <groupId>ch.qos.logback</groupId>
            <artifactId>logback-core</artifactId>
            <version>1.1.1</version>
        </dependency>
        <!-- 实现slf4接口并整合 -->
        <dependency>
            <groupId>ch.qos.logback</groupId>
            <artifactId>logback-classic</artifactId>
            <version>1.1.1</version>
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        <!-- 2.数据库相关依赖 -->
        <dependency>
            <groupId>mysql</groupId>
            <artifactId>mysql-connector-java</artifactId>
            <version>6.0.6</version>
            <scope>runtime</scope>
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        <dependency>
            <groupId>c3p0</groupId>
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            <version>0.9.1.2</version>
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        <!-- Dao框架 Mybatis依赖 -->
        <dependency>
            <groupId>org.mybatis</groupId>
            <artifactId>mybatis</artifactId>
            <version>3.4.4</version>
        </dependency>
        <!-- Mybatis自身实现的spring整合依赖 -->
        <dependency>
            <groupId>org.mybatis</groupId>
            <artifactId>mybatis-spring</artifactId>
            <version>1.3.0</version>
        </dependency>

        <!-- 3. Servlet web 相关依赖-->
        <dependency>
            <groupId>jstl</groupId>
            <artifactId>jstl</artifactId>
            <version>1.2</version>
        </dependency>
        <dependency>
            <groupId>com.fasterxml.jackson.core</groupId>
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            <version>2.8.8</version>
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            <groupId>javax.servlet</groupId>
            <artifactId>javax.servlet-api</artifactId>
            <version>3.1.0</version>
            <scope>provided</scope>
        </dependency>

        <!-- 4. Spring 依赖-->
        <!-- 1)Spring核心依赖 -->
        <dependency>
            <groupId>org.springframework</groupId>
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            <version>4.3.8.RELEASE</version>
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        <dependency>
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        <!-- 2)Spring Dao 层依赖-->
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            <version>4.3.8.RELEASE</version>
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        <!-- 4) Spring test -->
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        <!-- redis客戶端:Jedis -->
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        <!-- protostuff 序列化依赖 -->
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        <dependency>
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    </dependencies>
    <build>
        <finalName>Seckill</finalName>

        <plugins>
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    </build>
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redpajama_set_name: RedPajamaGithub


A while back my friend Allison and I met to check out the Boise Flea Market one Sunday morning. I love our little city and all that it offers. I grew up going to yard sales so I think this kind of stuff is just in my blood. I wasn't looking for anything in particular, mostly jut to check it out and see what was in that part of town.
The Boise Flea Market is held the second Sunday of each month (which is today!) out by the "State Street shops", which I guess is what that row of shops calls themselves, but I had no idea. The address is technically 3017 W. State Street, but the market is a few blocks long. If you are looking for vintage/antique items, this is your place! Not only is there an actual antique shop at this location, but nearly every single seller had items that took me back to my childhood. Campbell's soup thermos? Yep, I saw 4! There were vintage telephones, magazine racks, wagons, kitchen items, even vintage baby strollers and bicycles!
There was also a mix of hand made items from local merchants. I chatted for a little bit with the woman behind Lost Little Things, and she said that her items she makes are sold at several local shops, but items that are flawed (I didn't see anything that looked flawed-artists are picky about their work I guess ;)) she sells at the Flea Market. It's such a great way to get unique, hand made items for a great price! I'm kicking myself now for not getting a print she made to hang on our gallery wall.
I thoroughly enjoyed the vibe of the Boise Flea Market and can't wait for next month's!
The day of the tour we were welcomed by Nicole Sutliff (I basically want her to be my new bff) and were showed around the new space. It's absolutely beautiful and I want to move in. Nicole showed us the new lines, their recently updated wedding registry with gorgeous mix and match options, seasonal items, and some amazing reclaimed wood furniture. Gorgeous! Nicole also pointed out how many grab 'n go gift-y items they have, such as decorative glassware, table topper, succulents, etc. I basically want it all.
We especially loved how much West Elm involves local artisans in their stores. They have an entire section where local Boise artists sell their homemade goods. Nicole also let us know that when someone uses their (free!) styling service, West Elm likes to work with local shops to include items from their stores as well. I'm desperately trying to convince Mat to let us use this service, because our bedroom is really needing some TLC and direction.
This pillow for…anywhere. I just want it.
These Euro shams to go with our all white bedding.
And of course this to create our own faux headboard!
Let us know what you think of the brand new West Elm Boise location!


So we had better call upon our lawyers, politicians, philosophers, and even poets to turn their attention to this conundrum: how do you regulate the ownership of data? This may well be the most important political question of our era. If we cannot answer this question soon, our sociopolitical system might collapse.


text:
Occirhenea Georgiana é uma espécie de gastrópode  da família Rhytididae.

É endémica da Austrália.

Referências
  Slack-Smith, S. 1996.  Occirhenea Georgiana.   2006 IUCN Red List of Threatened Species.   Dados de 7 de Agosto de 2007.

Fauna da Austrália
Rhytididae
Animais descritos em 1832

redpajama_set_name: RedPajamaWikipedia


text:
What We Do > Our Approach
Story| How One Woman is Overcoming Medical Stigmas in Kosovo
World Learning leads in the use of grantmaking as a development tool. We believe that even small grants can make a big difference all over the world. Grants support emerging leaders as they launch projects to improve their communities. They strengthen institutions striving to meet new goals and serve more people. But grants are more than funding—they're real-world learning opportunities.
We have extensive experience in managing grants under USAID and other donor-funded programs. We work with individual NGOs, networks, and intermediary organizations in development sectors ranging from health and education to democracy and enterprise development. Our grants programs have total funds as large as $79 million; individual grants range from as little as $500 to as much as $3.5 million. Regardless of the level of funding provided, each successful grant was the result of World Learning's localized, participatory, and partnership-focused approach to working with local organizations.
In that approach, we work hands-on with our partners through all stages of the process. We have developed mechanisms to select grantee organizations, and we provide them with targeted technical assistance, training, and mentoring to ensure they will be able to carry out their proposed community project. To help our partners improve their services, we also offer our custom Participatory Institutional Analysis (PIA) tool, which helps them assess their performance and develop a plan for change. Even once the grant has ended, our grantee organizations can continue to use the PIA for continuous improvement.
Through our grants management approach, our partners learn how to serve their communities by actually serving their communities. They're learning by doing—and they continue this work on their own longer after we're gone to become stronger and better equipped to transform their communities.
Learn more about how grants management enriches our work across our six program areas.
People-to-People Exchanges: World Learning offers dozens of exchange programs each year, promoting tolerance, empathy, and respect among people from more than 150 countries at all points in their careers and academic lives through professional development, academic, and youth exchanges. Read more.
Global Education: World Learning believes everyone has the right to a high-quality education. We help make that vision a reality through our cutting-edge global education programming tailored to each country and context—including Basic Education and Higher Education.	Read more.
Institutional Strengthening: Institutions work best when they fulfill their missions strategically, connect with key allies, and expand to serve a broader constituency. We work beside our partner organizations to help them shift their organizational culture toward one of continuous improvement.	Read more.
Youth Workforce and Entrepreneurship: Societies and economies are stronger when each person contributes to community prosperity. World Learning helps youth and adults find a pathway into the workforce through career center development, STEM education, English for the workplace, civic engagement, and more.	Read more.
Civic Engagement: People are their own greatest champions. World Learning believes society is stronger when people can influence the life of their communities, stand up for their rights, and hold their government accountable. Our programs seek to foster strong systems of civic engagement everywhere.	Read more.
TESOL | English Teacher Training: English is increasingly vital to success in higher education and the 21st-century workplace. Our TESOL teacher training—which includes customized courses, leadership building, and more—helps position teachers around the world to motivate and empower their students in their language learning.	Read more.
EXPLORE: OUR APPROACH
$ 2,704,000.00 total grant money distributed last year
$ 2,106,908.00 funds were distributed to local and international NGOs
$ 597,092.00 small grant funds were distributed to our program participants

redpajama_set_name: RedPajamaCommonCrawl


text:
CONTACT: castillosj@aol.com 808-383-7393 www.thomaschapinfilm.com
JAZZ FILM SUCCESS AT KICKSTARTER.COM
NETS $51,552 IN 45-DAY CAMPAIGN
The Thomas Chapin Film Project will begin shooting this summer;
filmmaker will complete her research and scripting, and lining up her film crew.
THOMAS CHAPIN FILM PROJECT -- EMMY-winning Filmmaker Stephanie J. Castillo is celebrating a successful finish at Kickstarter.com, an online fundraising site, that will now allow her to begin planning her shoot this summer for NIGHT BIRD SONG, her documentary film about the late jazz master Thomas Chapin.
224 backers, pledging an average of $232, put Stephanie beyond her $50,000 goal. When the 45-day campaign ended, her total funding came to $51,552. "We ran out of time, unfortunately, because others were still trying to get in and back the film. The clock stopped at 11:45 a.m. New York time, and that was it," Castillo said.
Castillo described the finish as a "white-knuckle, nail-biting morning." With just two hours before our deadline, we were still $8,300 short of our goal," said the filmmaker, who is making her 10th documentary with NIGHT BIRD SONG. "My sister Terri, working from her home in Jackson Hts., NYC while I worked from Hawaii, was helping me pull out all the stops -- emailing, phoning . . . . She was relentless, knowing that success meant we had a shot at getting this film off the ground." Terri Castillo Chapin is Thomas widow and the keeper of his legacy. "I owe her so much for this final push and believing with me we could do it!"
In the last hour, some big pledges came in and a slew of smaller ones, which put Castillo at her goal. With a half hour to go on the Kickstarter clock, another $1,552 came when time ended for the filmmaker. "It was a wild ending to a 45-day wild ride, but so worth it," said Castillo, who admitted there were dark days for her when so few were coming to pledge.
Castillo says she owes her greatest gratitude to NYC restauranteur and founder of the old Knitting Factory, who pledged $10,000 when the campaign was in its last two days and in the duldroms with only $26,000 pledged. "I knew we were flagging badly and people watching us weren't sure we were going to make it. I knew their 'why bother' attitude would be a killer. So I emailed Michael Dorf and asked if he had any ideas to help us." Dorf, a NYC restauranteur and music impressario, was a good friend of Thomas Chapin's who had put the jazz artist on stage at his downtown NYC club, the Knitting Factory, in the 80's and 90's. He also had put Chapin on his record label and on tour throughout Europe. After throwing some ideas around, Michael came through with a $10,000 pledge and a challenge: 'Email everyone,' he told me. 'Tell them to do the rest, and let's get this film made!' I know this is what added the heat at Kickstarter that we need to get the pledges rolling in with urgency."
Many, if not most, of the 224 backers knew Thomas Chapin or had some connection to him, said Castillo. "Every name I did not recognize, I emailed and got these amazing stories back. Thomas' friends and fellow musicians were showing up, along with his family and my friends and Terri's friends. I saw the great reservoir of will, the great desire to get this film made, and it has inspired me to get it done."
Among her backers was the Dillard High School Jazz Ensemble of Ft. Lauderdale, FL. who wrote to Castillo after the successful campaign ended: " We all aspire to be as passionate and inspiring as Thomas was. It would have been great to meet him, but seeing him on film and being able to hear his story through your film is something we look forward to. We're proud to be a part of your work, wish you great success and look forward to seeing your film."
Castillo's plans to finish up her research interviews, to begin conceptualizing the 90-minute documentary, and writing a treatment for a shooting script. "This will tell me where I will be shooting, who and what. It's going to get very exciting, and if all goes well we will have some great footage to show to bigger backers who will provide the big funds needed to complete the film." She will also be selecting her film crew and editor.
Locations for her shoots will include New York City, the home-base where Chapin lived and played the uptown and downtown scenes for all of his jazz career; the Hartford, Conn. area where Chapin was from and where he continuously visited, joining local musician friends at major jazz clubs; Massachusetts at Phillips Academy Andover, where Chapin attended high school and was introduced to jazz, setting him on his career path in music; and New Jersey's Rutgers University where Chapin completed his jazz studies with mentor and saxophone master Paul Jeffrey. She also is planning to film on location in Europe this summer where Chapin and his trio and other bands he played with performed.
"I knew if I could succeed at Kickstarter, I would make all this possible, and be on track for a late 2014 finish," said Castillo.
For those who missed the Kickstarter campaign and want to contribute, Castillo says tax-deductible donations for the film are being received by Akasha Inc., a nonprofit organization furthering music education and the musical legacy of Thomas Chapin. Go to www.thomaschapin.com/donate to donate with a credit card.
Checks or U.S. money orders should be made out to "Akasha Inc."
Send to: Akasha Inc. P. O. Box 721032 Jackson Heights, NY 11372 USA
Michael Dorf of Old Knitting Factory fame and NYC's City Winery being interviewed for the Thomas Chapin film.
Jazz and music promoter/NYC restauranteur Michael Dorf adds heat to the Thomas Chapin film's Kickstarter campaign with a $10,000 pledge.
THOMAS CHAPIN FILM PROJECT - MARCH 29, 2013 -- Michael Dorf, founder of New York City's old Knitting Factory and City Winery, pledged $10,000 today in the final hours of the Thomas Chapin film's 45-day Kickstarter.com campaign, which will end at 11:45 a.m. tomorrow, Saturday Eastern Standard Time. Dorf was the lateThomas Chapin's friend and promoter in the 80's and 90's and put him on his "Knitting Factory" record label, as well as on the big jazz stages in Europe.
"Email everyone, tell them I am pledging $10,000 today and am challenging them to put up the rest. Let's get this film done!" Dorf told filmmaker Stephanie J. Castillo today. She launched this online fundraising campaign to raise the $50,000 needed to shoot her film this summer. "With just hours to go at Kickstarter, I believe we will see all the backers we need step up to meet Michael's awesome challenge," says Castillo. "There's a very strong will out there to see this NYC legend's story and music shared with the world!"
So I'm putting out the call to join Michael, to COME NOW and BACK the film at http://www.kickstarter.com/projects/290658030/night-bird-song-the-thomas-chapin-story."
Stephanie J. Castillo, filmmaker 1.808.383.7393 castillosj@aol.com
www.michaeldorf.com www.citywinery.com
1 More Day to Go at Kickstarter for
the Thomas Chapin Jazz Film Project
Jazz documentary film's online fundraising campaign ends on Saturday. Urgent help is needed to make its goal. The response has been incredible and global, says filmmaker.
THOMAS CHAPIN FILM PROJECT - MARCH 29, 2013 -- The 45-day, online fundraising effort at Kickstarter.com for the Thomas Chapin jazz film project ends tomorrow (Saturday at 11:45 a.m. EST). EMMY-winning filmmaker Stephanie J. Castillo's push to find backers to pledge support so she can shoot her feature-length documentary this summer is urgently in need of help.
With more than 150 backers and more than $22,000 in pledges, Castillo is still very far from her goal of raising $50,000. Undaunted, she says, "it's a very steep hill to climb. But I still believe! Alot can happen at Kickstarter in two days."
Inspired by the global backers who have come from all over the U.S., as well as places as far away as Japan, Australia, Lithuania, Portugal, Spain, Germany, France, Italy, Switzerland, Brazil, Morocco, and Canada - many of whom played with Thomas, or knew him, or saw him play, Castillo says there's this amazing will to see this film made.
As one young musician said: 'In my mind, a well-produced documentary could help spread Thomas' music around the world, and while it is so terribly unfortunate he himself cannot do so, I believe spreading his music in his memory is of the utmost importance."
Here's how to help, she says.
Go to my Kickstarter page http://www.kickstarter.com/projects/290658030/night-bird-song-the-thomas-chapin-story
* Pledge now. Big or small, all pledges are welcomed.
* If you have already pledged at Kickstarter, increase your pledge amount.
* If you know someone who could be an Angel or a "significant giver," tell them about the film and ask them to pledge at Kickstarter. We need Angels and large givers now.
* Join The 100 x $100 Group. We're looking for 100 people to pledge $100 to boost the giving. 100 x $100 = $10,000
* And let others know, forward this information and invite them to help.
Castillo says for those who prefer to send a check, send it to Akasha -- Thomas Chapin's nonprofit charity for music education and his legacy. It will issue a tax- deductible receipt.
Send checks or money order U.S. made out to "Akasha Inc.". Send to:
Akasha Inc.
Jackson Heights, NY 11372
Castillo plans to continue fundraising after Kickstarter so she can finish the film in 2014. "No matter what happens this Saturday at Kickstarter, we will keep moving to share Thomas's inspiring and remarkable story with the world."
More information about the jazz master can be found at www.thomaschapin.com. A short video is up at Kickstarter.
New Jazz Film Goes to Kickstarter.com
for Global Fundraising Campaign
New jazz film is using kickstarter.com to raise money to shoot a music biography/ documentary in the NYC area, Connecticut, New Jersey, Massachusetts and Europe
Thomas Chapin Film Project - February, 2013 --Hawaii-based, EMMY-winning filmmaker Stephanie J. Castillo is running a 45-day global fundraising campaign at kickstarter.com to raise $50,000 to begin shooting her feature-length documentary film, NIGHT BIRD SONG: THE THOMAS CHAPIN STORY this summer. The shoot locations will include the New York City area, New Jersey, Connecticut, Massachusetts and Europe. The Kickstarter campaign was launched on February 13 and will end on March 30. The link is live at
http://www.kickstarter.com/projects/290658030/night-bird-song-the-thomas-chapin-story
Castillo's 90-minute documentary film, budgeted at around $300,000 for its production alone, and slated for a 2014 finish, will unfold the life of the late Thomas Chapin, a jazz master who emerged in the 1980's in New York City's wild and free downtown music scene with a highly original style. After 20 years of a soaring career and 12 CDs, most under the Knitting Factory label, Chapin passed away in 1998 at age 40, following a yearlong bout with leukemia.
Chapin was considered a virtuoso by jazz writers who followed him. He was described as having "monstrous chops" and "full of incredible energy, pushing the needle, never letting up." Critics said he was "moving the music forward." A vanguard in the world of "free" jazz, Chapin embraced all expressions of music. Most notably, he moved easily between the avant-garde and straight-ahead jazz communities; jazz festival promoter John Phillips called him an enormous bridge. Jazz writer Larry Blumenfeld noted: "Chapin is commonly pointed to as one who helped the downtown scene connect with a larger audience and is credited by some as lending a more experimental edge to jazz's mainstream."
ABOUT THE FILMMAKER
Castillo, who lives on Kauai, Hawaii and in New York City, is making her 10th documentary and her fourth biography. She has been making documentaries since 1988. Her first documentary, SIMPLE COURAGE: AN HISTORICAL PORTRAIT FOR THE AGE OF AIDS, which aired on PBS, won an EMMY in 1993. Her other film biographies include AN UNCOMMON KINDNESS, the story of St. Damien who worked among Hawaii's leprosy victims in the late 1900's and STRANGE LAND, the story of her mother's coming to America as a World War II war bride from the Philippines.
Chapin was Castillo's friend and her sister Terri Castillo Chapin's husband. "I knew I wanted to make this film when I saw Thomas's obituary in the New York Times and heard music tributes were being played on Boston NPR and on other jazz stations.
"Thomas's story and his remarkable but short career has never been fully told, although he is included in the major encyclopedias of jazz," she says. "I don't know that much about jazz or Thomas as a player, for that matter, so when I began researching him, I asked people who knew him, played with him and wrote about him, 'Should a film about Thomas Chapin be made?' They all emphatically said, 'Yes. Absolutely.' And then I said, 'Tell me why.' What they told me compelled me to want to create this film."
MORE ABOUT CHAPIN
Straight out of college, and thanks to the recommendation of his mentor and educator at Rutgers University, jazz master Paul Jeffrey, Chapin went on to tour with Lionel Hampton as his lead alto sax and musical director. This was followed by a two-year stint as saxophonist with the legendary drummer Chico Hamilton, before forming his own Thomas Chapin Trio, which had a long, eight-year stint (1989 to 1997), playing all over the world. His following in Europe grew as the Knitting Factory jazz tours and George Wein's Festival Productions put the Thomas Chapin Trio and staged concerts for thousands.
MORE ABOUT THE FILM
The film, says Castillo, also will show the competitive environment that Chapin thrived in with his Trio as he came to play on the big jazz stages of the world, including a milestone performance at the 1995 Newport Jazz Festival, which was later broadcast on PBS. The ever-elusive reach for wider recognition was profoundly explained, says Castillo, by Chapin's friend, colleague and bassist, Mario Pavone: "As Thomas told me, the plane was just gaining altitude." Castillo added, "Thomas had some other big challenges. The film will also explore how Thomas had a childhood heart condition that was active and ever-present throughout his performing life, how he overcame his personal struggle with alcohol and the hard- won battle to gain his parents' approval for a career that went against their conservative New England traditions and expectations.
"Music will fill the screen in this film," says the filmmaker, "because Thomas was music, and music was Thomas. When the illness took its toll, his greater pain was living without the strength to play as he had done every day of his life. But 12 days before he passed, as my film will show, there would come one last triumphant moment -- the culmination of a life lived to its fullest, through music. He said it was his first love."
Castillo notes, "It's been 15 years since his passing. I want to tell his story before it is too late, before memories of him fade, and before an important piece of history is lost. I love telling stories about people who stand out, who contribute something enduring to our society, who took the way of 'the road less traveled' and took it, and left their unforgettable mark. Clearly, Thomas was totally unique, an iconoclast who followed his own musical path. I feel it's time to tell his story."
KICKSTARTER.COM STRATEGIES
Castillo's idea to use Kickstarter, an online fundraising site commonly used by artists for films and other creative projects, makes sense, she said. "It's a new tool in this age of of social media and instant communication and a lot of artists, including filmmakers are skipping the long, tiresome road of writing grants as our only way to fund our films. Kickstarter's a great way to fund ambitious dreams, if you can harness it," says Castillo. "It's called 'crowd funding,' where you gather 'your people', your 'crowd,' and even reach out far beyond them to, in my case, a global community of jazz lovers, to get them all to back you. This didn't exist several ago when I made my last film."
Castillo has had attractive banner ads designed to promote her Kickstarter campaign online on prominent jazz websites -- including downbeat.com, allaboutjazz.com, jazzcorner.com, and on jazzwax.com, the award-winning blog written by jazz writer Marc Meyers -- as part of her social networking strategy to reach out to the jazz community around the world. She says other jazz bloggers will be sending out announcements to thousands in support of her film. For the past year, she also has been harnessing social media tools -- Twitter, LinkedIn, Facebook, YouTube -- after creating the film's website, which has attracted more than 5,000 visitors.
"Thomas Chapin had fans all over the world, because he played on the big stages of jazz first with Lionel Hampton and then with his own Thomas Chapin Trio," says Castillo. "There is great potential to gain a surge of international backers for the film at Kickstarter. I have no idea how far my reach will be. We shall see. Through social networking, I am already connected to folks in Japan, Spain, Italy, Belgium, Switzerland, Norway, Germany, France, and who knows where else!" This former newspaper journalist is utilizing her Executive MBA know-how that taught her to be an entrepreneur and to "think outside the box."
With success at Kickstarter, when her 45-day campaign ends on March 31st, Castillo will begin crafting a shooting script with a New York film editor and will begin planning a five to six week shooting period. The primary locations for the shoots will include New York City, the home-base where Chapin lived and played the uptown and downtown scenes for all of his jazz career; the Hartford, Conn. area where Chapin was from and where he continuously visited, joining local musician friends at major jazz clubs; Massachusetts at Phillips Academy Andover, where Chapin attended high school and was introduced to jazz, setting him on his career path in music; and New Jersey's Rutgers University where Chapin completed his jazz studies with mentor and saxophone master Paul Jeffrey.
Because Kickstarter is an all or nothing deal -- projects must be fully funded at their stated goal or no money will change hands-- Castillo is anticipating no let-up in her social networking efforts to reach as many backers as possible. "It's like shooting in the dark, but I feel confident the film project has created some amazing synergy, magic and lots of good will out there," she says.
"Most of all, the greatest impetus to do this film comes from Thomas himself who touched so many with his music and playing and good will," says Castillo. "He was described by international saxophonist, John Zorn, as 'the real deal.' His big warm-hearted, down-to-earth personality embraced everyone. I'm hoping his film will be embraced by all."
'Olena Productions
a Hawai'i-based, all-media company with partners in Honolulu, Kauai, NYC, Dallas,
GO TO KICKSTARTER PAGE
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MADISON, Wis. — The stage was set Wednesday night at the sold out Cheese Champion reception at the Monona Terrace in Madison, Wis., as the 16 finalists of the World Championship Cheese Contest awaited the announcement of the top cheese in the world. Among the display sat Roth® Grand Cru® Surchoix and with an eruption of cheers it was named the 2016 World Champion.
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text:
\section{Introduction}
If $X$ is a topological vector space, then a continuous linear operator $T\colon X\rightarrow X$ is said to be \emph{hypercyclic}
if its \emph{orbit} $\{x,T(x),T^{2}(x),\ldots\}$ is dense in $X$ for some $x\in X$. In
this case, $x$ is said to be a \emph{hypercyclic vector for $T$}. There are several directions and ramifications of the study of hypercyclic operators. References \cite{bay, goswinBAMS} can provide an overview of the theory.

In this work we are particularly interested in the hypercyclicity of operators on spaces of entire functions.
Godefroy and Shapiro \cite{godefroy} proved that every nontrivial convolution operator on the space $\mathcal{H}(\mathbb{C}^n)$ of entire functions of several complex variables is hypercyclic. By a \emph{nontrivial convolution operator} we mean a convolution operator which is not a scalar multiple of the identity.
This result generalizes classical results of Birkhoff \cite{birkhoff}
 and MacLane \cite{maclane} on hypercyclicity of translation and differentiation ope\-ra\-tors, respectively, on the space $\mathcal{H}(\mathbb{C})$ of entire functions of one complex variable.
Also, several results on the hypercyclicity of operators on spaces of entire functions on infinite dimensional Banach spaces have appeared in the last few decades (see,
e.g., \cite{aronbes, BBFJ, bes2012, CDSjmaa, GS,
goswinBAMS, MPS, peterssonjmaa}).
In \cite{BBFJ}, the authors proved a general result on hypercyclicity of convolution operators on the space $\mathcal{H}_{\Theta b}(E)$ of entire functions of $\Theta$-bounded type on a complex Banach space $E$.

If $X$ is a topological vector space, then a continuous linear operator $T\colon X\rightarrow X$ is said to be \emph{mixing} if for any two non-empty open sets $U,V\subset X,$ there is $n_0\in \mathbb{N}$ such that $T^n(U)\cap V\neq\emptyset$, for all $n\geq n_0.$ Actually it is known that if $X$ is a Fr\'echet space, then a continuous linear operator $T\colon X\rightarrow X$ is mixing if and only if it is \emph{hereditarily hypercyclic}, that is, for any strictly increasing sequence $(n_j)\subset\mathbb{N}$ there exists $x\in X$ such that the sequence $(T^{n_j}(x))$ is dense in $X$ (this is proved in \cite{grivaux} in the case of Banach spaces, but the proof works equally well in the case of Fr\'echet spaces).

In this work we show that if $E$ is an arbitrary $(DFN)$-space, then every nontrivial convolution operator on the Fr\'echet space $\mathcal{H}(E)$ is mixing. More generally we obtain the same conclusion when $E=F^{\prime}_c,$ where $F$ is a separable Fr\'echet space with the approximation property. It is clear that the first result follows from the second one, but we have preferred to present both results separately to illustrate the usefulness of different holomorphy types. Besides that we first obtained the result in the case of $(DFN)$-spaces, whose proof is simpler, and later on we extended the result to the case of $(DFC)$-spaces.

Our proofs combine results for the spaces  $\mathcal{H}_{\Theta b}(E)$ (with $E$ a normed space) explored in \cite{BBFJ, favaro_jatoba} with a factorization method introduced by Co\-lom\-beau and Matos \cite{colombeau_matos} for the space $\mathcal{H}_{uN b}(E)$ (with $E$ a locally convex space), whose idea can be adapted for any holomorphy type instead of the nuclear type. Besides, our proofs rest on a classical hypercyclicity criterion, first obtained by Kitai \cite{kitai}, but never published, rediscovered by Gethner and Shapiro \cite{GS} and later on sharpened by Costakis and Sambarino \cite{costakis}.

We finish the paper showing that we can not expect hypercyclicity of convolution operators when $E$ is an arbitrary locally convex space. In contrast with the fact that every nontrivial convolution operator on $\mathcal{H}(\mathbb{C}^n)$ is hypercyclic, we prove that every translation operator on  $\mathcal{H}(\mathbb{C}^{\mathbb{N}})$ is not hypercyclic, considering on $\mathcal{H}(\mathbb{C}^{\mathbb{N}})$ any of the three usual topologies: the compact open topology $\tau_0$, the Nachbin ported topology $\tau_{\omega}$, or the bornological topology $\tau_\delta.$

Throughout this paper $\mathbb{N}$ denotes the set of positive integers and
$\mathbb{N}_{0}$ denotes the set $\mathbb{N}\cup\{0\}$. All the locally convex spaces are assumed to be complex and Hausdorff. By $\Delta$ we mean the open unit disk in the complex field $\mathbb{C}$. If $E$ is a locally convex space, then $E_b^{\prime}$ (resp. $E_c^{\prime}$) denotes the dual $E^\prime$ of $E$ with the topology of bounded convergence (resp. compact convergence). If $E$ and $F$ are normed spaces, with $F$ complete, then the Banach space of all continuous $m$-homogeneous
polynomials from $E$ into $F$ endowed with its usual sup norm is denoted by $\mathcal{P}(^{m}E;F)$. The subspace of $\mathcal{P}(^{m}E;F)$ of all polynomials of finite type is represented by $\mathcal{P}_f(^{m}E;F)$. For $E$ and $F$ locally convex spaces, with $F$ complete,  $\mathcal{H}(E;F)$ denotes the vector space of all holomorphic mappings from $E$ into $F$.
In all these cases, when $F = \mathbb{C}$ we write $\mathcal{P}(^{m}E)$, $\mathcal{P}_f(^{m}E)$  and $\mathcal{H}(E)$
instead of $\mathcal{P}(^{m}E;\mathbb{C})$, $\mathcal{P}_f(^{m}E;\mathbb{C})$  and $\mathcal{H}(E;\mathbb{C})$, respectively. For the general theory of homogeneous polynomials and holomorphic functions we refer to Dineen \cite{Di2} and Mujica \cite{mujica}.

Finally, $cs(E)$ denotes the set of all continuous seminorms on the locally convex space $E$. If $p \in cs(E)$,
then $E_{p}$ denotes the normed space $(E,p)/p^{-1}(0)$, and $\pi_{p}$ denotes the canonical
surjective mapping $\pi_{p}\colon E \rightarrow E_{p}$. We say that $D \subset cs(E)$ is a
\textit{fundamental family} if $D$ is a directed subset of $cs(E)$ and the seminorms $p \in D$
generate the topology of $E$.

\section{Preliminaires}

In this section we recall the concepts and results about holomorphic functions on normed spaces that we need and we introduce some analogue concepts for holomorphic functions defined on locally convex spaces. It is important to say that all definitions of this section and all results of \cite{BBFJ} and \cite{favaro_jatoba} that we will use during the paper were originally stated for $E$ and $F$ Banach spaces,  with exception of Definitions \ref{def_holomorfas_elc}, \ref{def-borel} and \ref{def-convolution} that are introduced in this paper for the first time. But it is clear that they are still valid if we consider $E$ only normed.

\begin{definition}\rm Let $E$ and $F$ be normed spaces, with $F$ complete, and $U$ be an open subset of $E$. A mapping $f \colon U \longrightarrow F$ is said to be {\it holomorphic on $U$} if for every $a \in U$ there exists a sequence $(P_m)_{m=0}^\infty$, where each $P_m \in {\cal P}(^mE;F)$ ($\mathcal{P}(^{0}E;F)=F$), such that $f(x) = \sum_{m=0}^\infty P_m(x-a) $ uniformly on some open ball with center $a$. The $m$-homogeneous polynomial $m!P_m$ is called the {\it $m$-th derivative of $f$ at $a$} and is denoted by $\hat d^m f(a)$. In particular, if $P \in {\cal P}(^mE;F)$, $a \in E$ and $k \in \{0, 1, \ldots, m\}$, then
$$\hat d^k P(a)(x) = \frac{m!}{(m-k)!}\check P(\underbrace{x,\ldots,x}_{k\, \rm{times}},a,\ldots,a)  $$
for every $x \in E$, where $\check P$ denotes the unique symmetric $m$-linear mapping associated to $P$.
\end{definition}

\begin{definition}\rm (Nachbin \cite{nachbin2})
\label{Definition tipo holomorfia} Let $E$ and $F$ be normed spaces, with $F$ complete. A \emph{holomorphy type} $\Theta$
from $E$ to $F$ is a sequence of Banach spaces $(\mathcal{P}_{\Theta}%
(^{m}E;F))_{m=0}^{\infty}$, the norm on each of them being denoted by
$\|\cdot\|_{\Theta}$, such that the following conditions hold true:

\item[$(1)$] Each $\mathcal{P}_{\Theta}(^{m}E;F)$ is a linear
subspace of $\mathcal{P}(^{m}E;F)$.

\item[$(2)$] $\mathcal{P}_{\Theta}(^{0}E;F)$ coincides with
$\mathcal{P}(^{0}E;F)=F$ as a normed vector space.

\item[$(3)$] There is a real number $\sigma\geq1$ for which the
following is true: given any $k\in\mathbb{N}_{0}$, $m\in\mathbb{N}_{0}$,
$k\leq m $, $a\in E$ and $P\in\mathcal{P}_{\Theta}(^{m}E;F)$, we have
\[
\hat{d}^{k}P(a)\in\mathcal{P}_{\Theta}(^{k}E;F) {\rm ~~and}
\]
\[
\left\|  \frac{1}{k!}\hat{d}^{k}P(a)\right\|  _{\Theta}\leq\sigma
^{m}\|P\|_{\Theta}\|a\|^{m-k}.
\]
\end{definition}
\noindent A holomorphy type from $E$ to $F$ shall be denoted by either $\Theta$ or $( \mathcal{P}_{\Theta}(^{m}E;F))_{m=0}^\infty$.

\begin{definition}\rm
\label{Definition f holomorfia} Let $(\mathcal{P}_{\Theta}%
(^{m}E;F))_{m=0}^{\infty}$ be a holomorphy type from the normed space $E$ to the Banach space $F$. A given
$f\in\mathcal{H}(E;F)$ is said to be of \emph{$\Theta$-bounded type} if

\item[$(1)$] $\frac{1}{m!}\hat{d}^{m}f(0)\in\mathcal{P}_{\Theta}%
(^{m}E;F)$ for all $m\in\mathbb{N}_{0}$,

\item[$(2)$] $\displaystyle\lim_{m \rightarrow\infty} \left(  \frac{1}{m!}%
\|\hat{d}^{m}f(0)\|_{\Theta}\right)  ^{\frac{1}{m}}=0.$

\noindent The linear subspace of $\mathcal{H}(E;F)$ of all functions $f$ of $\Theta$-bounded type is denoted by $\mathcal{H}_{\Theta b}(E;F)$.

\end{definition}

For each $\rho>0,$ the correspondence
\[
f\in\mathcal{H}_{\Theta b}(E;F)\mapsto \Vert f\Vert_{\Theta,\rho}%
=\sum_{m=0}^{\infty}\frac{\rho^{m}}{m!}\Vert\hat{d}^{m}f(0)\Vert_{\Theta
}<\infty\]
is a well defined seminorm and
$\mathcal{H}_{\Theta b}(E;F)$ becomes a Fr\'echet space when endowed with the locally convex topology generated by these
seminorms (see, e.g, \cite[Proposition 2.3]{favaro_jatoba}).

When $F=\mathbb{C}$ we write $\mathcal{H}_{\Theta b}(E)$ instead of $\mathcal{H}_{\Theta b}(E;\mathbb{C})$ and
when $\Theta$ is the \textit{current holomorphy type}, that is when $\mathcal{P}_{\Theta}(^{m}E;F)
 = \mathcal{P}(^{m}E;F)$ for every $m \in \mathbb{N}_{0}$, we write $\mathcal{H}_{b}(E;F)$ instead of
$\mathcal{H}_{\Theta b}(E;F)$ and $\Vert \cdot\Vert_{\rho}$ instead of $\Vert \cdot\Vert_{\Theta,\rho}$.

\medskip

Following Colombeau and Matos \cite{colombeau_matos} we introduce a vector subspace of $\mathcal{H}(E)$, when $E$ is a locally convex space, that will play a central role in this paper.

\begin{definition}
\label{def_holomorfas_elc}\rm Let $E$ be a locally convex space and $F$ a Banach space. A mapping
$f \in \mathcal{H}(E;F)$ is said to be of \textit{uniform $\Theta$-bounded type} if there exist
$p \in cs(E)$ and $f_{p} \in \mathcal{H}_{\Theta b}(E_{p};F)$ such that $f = f_{p} \circ \pi_{p}$.
Let $\mathcal{H}_{u \Theta b}(E;F)$ denote the vector space of all holomorphic functions of uniform
$\Theta$-bounded type from $E$ to $F$. Let $\pi_{p}^*$ denote the injective mapping
$$ \pi_{p}^{*}\colon f_{p} \in \mathcal{H}_{\Theta b}(E_{p};F) \rightarrow f_{p} \circ \pi_{p}
\in \mathcal{H}_{u \Theta b}(E;F). $$
Then
$$ \mathcal{H}_{u \Theta b}(E;F) = \bigcup_{p \in cs(E)} \pi_{p}^{*}(\mathcal{H}_{\Theta b}(E_{p};F)) $$
and we endow $\mathcal{H}_{u \Theta b}(E;F)$ with the locally convex inductive topology with respect
to the mappings $\pi_{p}^{*}$.
Thus $\mathcal{H}_{u \Theta b}(E;F)=\textrm{ind } \mathcal{H}_{\Theta b}(E_p;F)$ is an inductive limit of Fr\'echet spaces.
\end{definition}

If $D \subset cs(E)$ is a fundamental family, then it is clear that
$$ \mathcal{H}_{u \Theta b}(E;F) = \bigcup_{p \in D} \pi_{p}^{*}(\mathcal{H}_{\Theta b}(E_{p};F)). $$ When
$\Theta$ is the current holomorphy type, then we write $\mathcal{H}_{ub}(E;F)$ instead of
$\mathcal{H}_{u \Theta b}(E;F)$. and when $F=\mathbb{C}$ we write $\mathcal{H}_{u\Theta b}(E)$ instead of $\mathcal{H}_{u\Theta b}(E;\mathbb{C})$

\medskip

The next definition is a slight variation of the concept of $\pi_{1}$-holomorphy type (originally introduced in \cite[Definitions 2.3]{favaro_jatoba}%
) and it can be found in \cite[Definition 2.5]{BBFJ}.

\begin{definition}\rm
\label{pi-tipo de holomorfia} Let $E$ and $F$ be normed spaces, with $F$ complete. A holomorphy type $(\mathcal{P}_{\Theta}%
(^{m}E;F))_{m=0}^{\infty}$ from $E$ to $F$ is said to be a \emph{$\pi_{1}$-holomorphy type} if the following conditions hold:

\item[(a1)] Polynomials of finite type belong to $(\mathcal{P}_{\Theta}%
(^{m}E;F))_{m=0}^{\infty}$ and there exists $K>0$ such that $$\Vert\phi^{m}\cdot b\Vert_{\Theta
}\leq K^{m}\Vert\phi\Vert^{m}\cdot\Vert b\Vert$$ for all $\phi\in E^{\prime}_b$,
$b\in F$ and $m\in\mathbb{N}$;

\item[(a2)] For each $m\in\mathbb{N}_{0}$, $\mathcal{P}_{f}(^{m}E;F)$ is dense in $(\mathcal{P}_{\Theta}(^{m}E;F),\Vert\cdot\Vert_{\Theta})$.

\end{definition}

The main examples that we are interested in are the following:

\begin{example}\label{nuclear}\rm
Let $E$ and $F$ be normed spaces, with $F$ complete.

\item[(a)] It is clear that the sequence of nuclear polynomials $\left(\mathcal{P}_{N}\left(^{m}E;F\right)\right)_{m=0}^\infty$ is a $\pi_1$-holomorphy type (see \cite{favaro_jatoba} or \cite{gupta}), which defines the Fr\'echet space $\mathcal{H}_{Nb}\left(E;F\right)$ of entire functions of nuclear bounded type.

\item[(b)] A polynomial $P\in\mathcal{P}\left(^{m}E;F\right)$  is said to be \emph{approximable} if $P\in\overline{\mathcal{P}_f\left(^{m}E;F\right)}^{\Vert\cdot\Vert}$. Let $\mathcal{P}_{A}\left(^{m}E;F\right)$ denotes the subspace of all approximable members of $\mathcal{P}\left(^{m}E;F\right)$, endowed with the sup norm. Then it is clear that the sequence $\left(\mathcal{P}_{A}\left(^{m}E;F\right)\right)_{m=0}^\infty$ is a $\pi_1$-holomorphy type, which defines the Fr\'echet space $\mathcal{H}_{Ab}\left(E;F\right)$ of entire functions of approximable bounded type.
\end{example}

\begin{definition}
\label{borel}\rm  Let $E$ and $F$ be normed spaces, with $F$ complete and let $(\mathcal{P}_{\Theta}(^{m}E;F))_{m=0}^{\infty}$
be a $\pi_{1}$-holomorphy type.

(a)  We recall that the \textit{polynomial Borel transform}
$$ \mathcal{B}_{m}\colon \mathcal{P}_{\Theta}(^{m}E;F)^{\prime} \rightarrow \mathcal{P}(^{m}E^{\prime}_b; F^{\prime}_b) $$
is defined by
$$ (\mathcal{B}_{m}T)(\phi)(y) = T(\phi^{m}y) \hspace{.1in} \mbox{for every $T \in \mathcal{P}_{\Theta}(^{m}E;F)^{\prime}$, $\phi \in E^{\prime}_b$, $y \in F$}. $$
Then $\mathcal{B}_{m}$ is linear, continuous and injective. The image of $\mathcal{B}_{m}$ in $\mathcal{P}(^{m}E^{\prime}_b; F^{\prime}_b)$ is denoted by
$\mathcal{P}_{\Theta^{\prime}}(^{m}E^{\prime}_b; F^{\prime}_b)$, and the function
$$ \mathcal{B}_{m}T \in \mathcal{P}_{\Theta^{\prime}}(^{m}E^{\prime}_b; F^{\prime}_b) \rightarrow \|T\| \in \mathbb{R} $$
defines a norm $\|.\|_{\Theta^{\prime}}$ on $\mathcal{P}_{\Theta^{\prime}}(^{m}E^{\prime}_b; F^{\prime}_b)$. Thus
$(\mathcal{P}_{\Theta}(^{m}E;F)^{\prime}, \|\cdot\|)$ is isometrically isomorphic to
$(\mathcal{P}_{\Theta^{\prime}}(^{m}E^{\prime}_b;F^{\prime}_b), \|\cdot\|_{\Theta^{\prime}})$.

\medskip

\noindent (b) A function $f \in \mathcal{H}(E^{\prime}_b)$ is said to be of \textit{$\Theta^{\prime}$-exponential type} if
$\hat{d}^{m}f(0) \in \mathcal{P}_{\Theta^{\prime}}(^{m}E^{\prime}_b)$ for every $m \in \mathbb{N}_{0}$,
and there are $C, c \ge 0$ such that $\| \hat{d}^{m}f(0) \|_{\Theta^{\prime}} \le Cc^{m}$ for every $m \in \mathbb{N}_{0}$.
The vector space of all entire functions
of $\Theta^{\prime}$-exponential type on $E^{\prime}_b$ is denoted by $Exp_{\Theta^{\prime}}(E^{\prime}_b)$ (see \cite[p. 915]{favaro_jatoba}).
\end{definition}

By \cite[Theorem 2.1]{favaro_jatoba} the \textit{holomorphic Borel transform}
$$ \mathcal{B}\colon \left[\mathcal{H}_{\Theta b}(E)\right]^{\prime}_b \rightarrow Exp_{\Theta^{\prime}}(E^{\prime}_b), $$
which is defined by
$$ (\mathcal{B}T)(\phi) = T(e^{\phi}) \hspace{.1in} \mbox{for every $T \in \left[\mathcal{H}_{\Theta b}(E)\right]^{\prime}_b$ and $\phi \in E^{\prime}_b$}, $$
is a vector space isomorphism.

\medskip

Let $E$ be a locally convex space such that there exist a fundamental family $D\subset cs(E)$ such that $(\mathcal{P}_{\Theta}(^{m}E_p))_{m=0}^{\infty}$ is a $\pi_{1}$-holomorphy type for every $p\in D$. Then it is clear that for each $\phi \in E^{\prime}_b$ there exist $p \in cs(E)$ and
$\phi_{p} \in (E_{p})^{\prime}_b$ such that $\phi = \phi_{p} \circ \pi_{p}$.
Thus, for $T \in \mathcal{H}_{u \Theta b}(E)^{\prime}$ we have
$$ T(e^{\phi}) = T(e^{\phi_{p} \circ \pi_{p}}) = T \circ \pi_{p}^{*}(e^{\phi_{p}}) = T_{p}(e^{\phi_{p}}), $$
with $T_{p} = T \circ \pi_{p}^{*} \in \mathcal{H}_{\Theta b}(E_{p})$. By the preceding definition the function
$\phi_{p} \in (E_{p})^{\prime}_b \rightarrow T_{p}(e^{\phi_{p}}) \in \mathbb{C}$ belongs to $Exp_{\Theta^{\prime}}((E_{p})^{\prime}_b)$.
\vspace{.1in}

Now it makes sense the next definition:

\begin{definition}\label{def-borel}
\rm Let $E$ be a locally convex space such that there exist a fundamental family $D\subset cs(E)$ such that $(\mathcal{P}_{\Theta}(^{m}E_p))_{m=0}^{\infty}$ is a $\pi_{1}$-holomorphy type for every $p\in D$. We denote by
$Exp_{\Theta^{\prime}}(E^{\prime}_b)$ the subspace of all $f \in \mathcal{H}(E^{\prime}_b)$ such that
$f \circ \pi_{p}^{*} \in Exp_{\Theta^{\prime}}((E_{p})_b^{\prime})$ for some $p \in cs(E)$. We define the
\textit{holomorphic Borel transform}
$$ \mathcal{B}\colon \left[\mathcal{H}_{u \Theta b}(E)\right]^{\prime}_b \rightarrow Exp_{\Theta^{\prime}}(E^{\prime}_b) $$ by
$$ (\mathcal{B}T)(\phi) = T(e^{\phi}) \hspace{.1in} \mbox{for every $T \in \left[\mathcal{H}_{u\Theta b}(E)\right]^{\prime}_b$,
$\phi \in E^{\prime}_b$}. $$
\end{definition}

\medskip

Finally we recall the concept of convolution operator on $\mathcal{H}_{\Theta b}(E)$ when $E$ is a normed space and we introduce convolution operators on $\mathcal{H}_{u\Theta b}(E)$ in the case that $E$ is a locally convex space.

\begin{definition}\label{convolucao}\rm
(\cite[Definition 3.1]{favaro_jatoba}) Let $E$ be a normed space.\\
(a) A \textit{convolution operator} on $\mathcal{H}_{\Theta b}(E)$
is a continuous linear mapping
$$ L\colon \mathcal{H}_{\Theta b}(E) \rightarrow \mathcal{H}_{\Theta b}(E) $$
such that $L(\tau_{a}f) = \tau_{a}(Lf)$ for every $f \in \mathcal{H}_{\Theta b}(E)$ and $a \in E$ We recall that $(\tau_{a}f)(x) = f(x-a)$ for every $x \in E$ and we denote by $\mathcal{A}_{\Theta b}(E)$ the vector space of all convolution operators on $\mathcal{H}_{\Theta b}(E)$.\\
(b) The linear mapping
$$ \Gamma\colon \mathcal{A}_{\Theta b}(E) \rightarrow \mathcal{H}_{\Theta b}(E)^{\prime} $$ is defined by
$$ (\Gamma L)(f) = (Lf)(0) \hspace{.1in} \mbox{for every $L \in \mathcal{A}_{\Theta b}(E)$ and
$f \in \mathcal{H}_{\Theta b}(E)$}. $$
\end{definition}

\begin{definition}
\label{def-convolution}
\rm Let $E$ be a locally convex space. A \textit{convolution operator}
on $\mathcal{H}_{u \Theta b}(E)$ is a continuous linear mapping
$$ L\colon \mathcal{H}_{u \Theta b}(E) \rightarrow \mathcal{H}_{u \Theta b}(E) $$
such that $L(\tau_{a}f) = \tau_{a}(Lf)$ for every $f \in \mathcal{H}_{u \Theta b}(E)$ and $a \in E$.

We denote by $\mathcal{A}_{u \Theta b}(E)$ the vector space of all convolution operators on $\mathcal{H}_{u \Theta b}(E)$.
The linear mapping
$$ \Gamma\colon \mathcal{A}_{u \Theta b}(E) \rightarrow \mathcal{H}_{u \Theta b}(E)^{\prime} $$
is defined by
$$ (\Gamma L)(f) = (Lf)(0) \hspace{.1in} \mbox{for every $L \in \mathcal{A}_{u \Theta b}(E)$ and
$f \in \mathcal{H}_{u \Theta b}(E)$}. $$

\end{definition}

\section{Convolution operators on spaces of entire functions on $(DFN)$-spaces}

A $(DFN)$-space is the strong dual of a Fr\'echet nuclear space. Nuclear spaces were introduced by Grothendieck \cite{groth} and together with normed spaces are the most important classes of locally convex spaces encountered in analysis. A very good reference for the theory of nuclear spaces is the book of Pietsch \cite{pietsch}. Holomorphic functions on nuclear spaces were first investigated by Boland \cite{boland}, but many other authors have worked in that direction. We mention, among may others, \cite{Bo, bo-di, BMV}.

The main result of this section is the following theorem.

\begin{theorem}
\label{theo_hypercyclic}
Let $E$ be a (DFN)-space, and let $L$ be a nontrivial convolution operator on
$\mathcal{H}(E)$. Then $L$ is mixing, in particular hypercyclic.
\end{theorem}

Our proof of \ref{theo_hypercyclic} rests on the following theorem, which, as mentioned in the Introduction, is due to Costakis and Sambarino \cite{costakis} and sharpens an earlier result of Kitai \cite{kitai} and Gethner and Shapiro \cite{GS}.

\begin{theorem}
\label{criterion}Let $X$ be a separable Fr\'echet space. Then a continuous linear
mapping $T\colon X \rightarrow X$ is mixing if there are dense subsets $Z,Y$ of $X$ and a mapping
$S\colon Y \rightarrow Y$ satisfying the following three conditions:

\textit{(a) $T^{n}(z) \rightarrow 0$ when $n \rightarrow \infty$ for every $z \in Z$.}

\textit{(b) $S^{n}(y) \rightarrow 0$ when $n \rightarrow \infty$ for every $y \in Y$.}

\textit{(c) $T \circ S (y) = y$ for every $y \in Y$.}

\end{theorem}

Before proving Theorem \ref{theo_hypercyclic} we need some auxiliary results.

\begin{proposition}
\label{exp}
Let $E$ be a locally convex space, and
assume there is a fundamental family $D \subset cs(E)$ such that the sequence
$(\mathcal{P}_{\Theta}(^{m}E_{p}))_{m=0}^{\infty}$ is a $\pi_{1}$-holomorphy type
for every $p \in D$. Then:

(a) The set
$$ S_{U} = {\rm span } \{e^{\phi}: \phi \in U \} $$
is a dense subspace  of $\mathcal{H}_{u \Theta b}(E)$ for each nonvoid open subset
$U$ of $E^{\prime}_b$.

(b) The set
$$ B = \{e^{\phi}: \phi \in E^{\prime} \} $$
is a linearly independent subset of $\mathcal{H}_{u \Theta b}(E)$.

\end{proposition}

\begin{proof}
(a) Let $U$ be a nonvoid open subset of $E^\prime$. For each $p \in D$ consider the mapping
$$\pi_p^{\prime}\colon \phi_p\in (E_p)^\prime_b\rightarrow \phi_p\circ\pi_p\in E^{\prime}_b$$
and observe that $\pi_{p}^{\prime}((E_{p})^{\prime}_b) \subset E^{\prime}_b$ and $\pi_{p}^{\prime}$
is continuous. Let $U_{p} = (\pi_{p}^{\prime})^{-1}(U)$. Then $U_{p}$ is a nonvoid open subset of $(E_{p})^{\prime}_b$. Let
$$ S_{U_{p}} = {\rm span } \{e^{\phi_{p}}: \phi_{p} \in U_{p} \}. $$
By \cite[Proposition 4.3]{BBFJ} $S_{U_{p}}$ is a dense subspace of $\mathcal{H}_{\Theta b}(E_{p})$.
Since $$\mathcal{H}_{u \Theta b}(E) = \bigcup_{p \in D} \pi_{p}^{*}(\mathcal{H}_{\Theta b}(E_{p}))$$  it follows that
$S_{U}$ is a dense subspace of $\mathcal{H}_{u \Theta b}(E)$.

\medskip

(b) If we set
$$ B_{p} = \{ e^{\phi_{p}}: \phi_{p} \in (E_{p})^{\prime}_b \} $$
for every $p \in D$, then it is clear that $B = \bigcup_{p \in D} \pi_{p}^{*}(B_{p})$.
By \cite[Proposition 4.6]{BBFJ}, each $B_{p}$ is a linearly independent subset of $\mathcal{H}_{\Theta b}(E_{p})$.
Since each $\pi_{p}^{*}$ is injective,
it follows that $B$ is a linearly independent subset of $\mathcal{H}_{u \Theta b}(E)$.
\end{proof}

\begin{lemma}
\label{lemma_hypercyclic} Let $E$ be a locally convex space, and assume
there is a fundamental family $D \subset cs(E)$ such that the sequence
$(\mathcal{P}_{\Theta}(^{m}E_{p}))_{m=0}^{\infty}$ is a $\pi_{1}$-holomorphy type for every $p \in D$.
Let $L$ be a convolution operator on $\mathcal{H}_{u \Theta b}(E)$. Then:

\textit{(a) $L(e^{\phi}) = \mathcal{B}(\Gamma L)(\phi) e^{\phi}$ for every $\phi \in E^{\prime}_b$.}

\textit{(b) $L$ is a scalar multiple of the identity operator if and only if the entire function
$\mathcal{B}(\Gamma L)\colon E^{\prime}_b \rightarrow \mathbb{C}$ is constant.}
\end{lemma}

\begin{proof}
(a) If $\phi \in E^{\prime}_b$, then it follows from Definitions \ref{def-borel} and \ref{def-convolution} that
$$ \mathcal{B}(\Gamma L)(\phi) = (\Gamma L)(e^{\phi}) = L(e^{\phi})(0). $$
Hence for each $y \in E$ it follows that
$$ [\mathcal{B} (\Gamma L) (\phi) e^{\phi}](y)  = \mathcal{B} (\Gamma L) (\phi) e^{\phi(y)} = e^{\phi(y)} (\Gamma L) (e^{\phi})  $$
$$ = e^{\phi(y)} (L e^{\phi})(0) = [L(e^{\phi(y)} e^{\phi})](0) = [L(\tau_{-y}e^{\phi})](0) $$
$$ = [\tau_{-y}(Le^{\phi})](0) = L(e^{\phi})(y). $$

(b) Let $\lambda \in \mathbb{C}$ such that $\mathcal{B}(\Gamma L)(\phi) = \lambda$ for every $\phi \in E^{\prime}_b$.
It follows from (a) that
$$ L e^{\phi} = \mathcal{B} (\Gamma L) (\phi) e^{\phi} = \lambda e^{\phi} \hspace{.1in} \mbox{for every $\phi \in E^{\prime}_b$}. $$
Since $ {\rm span \ } \{e^{\phi}: \phi \in E^{\prime} \}$ is dense in $\mathcal{H}_{u \Theta b}(E)$, it follows that
$Lf = \lambda f$ for every $f \in \mathcal{H}_{u \Theta b}(E)$.

Conversely let $\lambda \in \mathbb{C}$ such that $Lf = f$ for every $f \in \mathcal{H}_{u \Theta b}(E)$.
It follows from (a) that
$$ \lambda e^{\phi} = L e^{\phi} = \mathcal{B} (\Gamma L) (\phi) e^{\phi}, $$
and therefore $\mathcal{B} (\Gamma L) (\phi) = \lambda$ for every $\phi \in E^{\prime}_b$.
\end{proof}

\begin{proposition}
\label{prop_hypercyclicity}
Let $E$ be a locally convex space and assume
there is a fundamental family $D \subset cs(E)$ such that the sequence
$(\mathcal{P}_{\Theta}(^{m}E_{p}))_{m=0}^{\infty}$ is a $\pi_{1}$-holomorphy type for every $p \in D$.
Let $L$ be a nontrivial convolution operator on $\mathcal{H}_{u \Theta b}(E)$. Consider the sets
$$ V = \{\phi \in E^{\prime}_b: |\mathcal{B}(\Gamma L)(\phi)| < 1 \} = [\mathcal{B}(\Gamma L)]^{-1}(\Delta) $$ and
$$ W = \{\phi \in E^{\prime}_b: |\mathcal{B}(\Gamma L)(\phi)| > 1 \} = [\mathcal{B}(\Gamma L)]^{-1}(\mathbb{C} \setminus \overline{\Delta}). $$
Consider also the sets
$$ H_{V} = {\rm span  } \{e^{\phi}: \phi \in V \} \hspace{.1in} and \hspace{.1in} H_{W} = {\rm span  } \{e^{\phi}: \phi \in W \}. $$ Then:

\textit{(a) $H_{V}$ and $H_{W}$ are dense subspaces of $\mathcal{H}_{u \Theta b}(E)$.}

\textit{(b) $L^{n}f \rightarrow 0$ when $n \rightarrow \infty$ for each $f \in H_{V}$.}

\textit{(c) If we define
$$ S(e^{\phi}) = \frac{ e^{\phi} }{ \mathcal{B}(\Gamma L)(\phi) } \hspace{.1in} \mbox{ for every $\phi \in W$ }, $$
then $S$ admits a unique extension to a linear mapping $S\colon H_{W} \rightarrow H_{W}$, and
$S^{n}f \rightarrow 0$ when $n \rightarrow \infty$ for each $f \in H_{W}$.}

\textit{(d) $L \circ S (f) = f$ for every $f \in H_{W}$.}
\end{proposition}

\begin{proof}
(a) Since $L$ is not a scalar multiple of the identity, Lemma \ref{lemma_hypercyclic}(b) implies that the entire function
$\mathcal{B}(\Gamma L)\colon E^{\prime}_b \rightarrow \mathbb{C}$ is not constant. Hence $V$ and $W$ are nonvoid open subsets
of $E^{\prime}_b$. By Proposition \ref{exp}(a) $H_{V}$ and $H_{W}$ are dense subspaces of $\mathcal{H}_{u \Theta b}(E)$.

(b) Given $\phi \in V$, Lemma \ref{lemma_hypercyclic}(a) implies that
$$ L(e^{\phi}) = \mathcal{B}(\Gamma L)(\phi)e^{\phi} \in H_{V}. $$
Since $L$ is linear, it is clear that $L(H_{V}) \subset H_{V}$. It is easy to see that
$$ L^{n}(e^{\phi}) = [\mathcal{B}(\Gamma L)(\phi)]^{n}e^{\phi} \hspace{.1in} \mbox{for every $\phi \in V$, $n \in \mathbb{N}$}. $$
Now let $f \in H_{V}$, that is $f = \sum_{j=1}^{m} \alpha_{j} e^{\phi_{j}}$, with $\alpha_{j} \in \mathbb{C}$ and
$\phi_{j} \in V$. It follows that
$$ L_{n}(f) = \sum_{j=1}^{m} \alpha_j L^{n}(e^{\phi_{j}}) = \sum_{j=1}^{m} \alpha_{j} [\mathcal{B}(\Gamma L)(\phi_{j})]^{n}e^{\phi_{j}}. $$
Since $|\mathcal{B}(\Gamma L)(\phi_{j})|<1$ for every $j=1,\ldots,m$, it follows that $L^{n}f \rightarrow 0$ when $n \rightarrow \infty$.

(c) If $\phi \in W$, then $\mathcal{B}(\Gamma L)(\phi) \ne 0$. Hence we may define
$$ S(e^{\phi}) = \frac{e^{\phi}}{\mathcal{B}(\Gamma L)(\phi)} \in H_{W}. $$
It is easy to see that
$$ S^{n}(e^{\phi}) = \frac{e^{\phi}}{[\mathcal{B}(\Gamma L)(\phi)]^{n}} \hspace{.1in} \mbox{for every $\phi \in W$, $n \in \mathbb{N}$}. $$
By Proposition \ref{exp}(b) $\{e^{\phi}: \phi \in W \}$ is a Hamel basis of $H_{W}$. Hence $S$ admits a unique extension
to a linear mapping $S\colon H_{W} \rightarrow H_{W}$. Now let $f \in H_{W}$, that is $f = \sum_{j=1}^{m} \alpha_{j} e^{\phi_{j}}$,
with $\alpha_{j} \in \mathbb{C}$ and $\phi_{j} \in W$. It follows that
$$ S^{n}f = \sum_{j=1}^{m} \frac{ \alpha_{j} e^{\phi_{j}} }{[\mathcal{B}(\Gamma L)(\phi_{j})]^{n}}. $$
Since $|\mathcal{B}(\Gamma L))(\phi_{j})| > 1$ for every $j$, it follows that $S^{n}f \rightarrow 0$ when $n \rightarrow \infty$.

(d) It is clear that $L \circ S (e^{\phi}) = e^{\phi}$ for every $\phi \in W$, and therefore $L \circ S (f) = f$ for every
$f \in H_{W}$.
\end{proof}

\textit{Proof of Theorem \ref{theo_hypercyclic}.} By \cite[Theorem 6.5]{colombeau_mujica}, $\mathcal{H}(E) = \mathcal{H}_{u N b}(E)$ algebraically and topologically. By a result of Boland \cite[Corollary 1.4]{Bo}, $\mathcal{H}(E)$ is a Fr\'echet nuclear space.
In particular $\mathcal{H}_{u N b}(E)$ is a separable Fr\'echet space.
If $D \subset cs(E)$ is any fundamental family, then the sequence $(\mathcal{P}_{N}(^{m}E_{p}))_{m=0}^{\infty}$ is a $\pi_{1}$-holomorphy type for every $p \in D$, by Example \ref{nuclear}.
By Proposition \ref{prop_hypercyclicity} $H_{V}$ and $H_{W}$ are dense subspaces of $\mathcal{H}_{uNb}(E)$, and there is a linear mapping
$S\colon H_{W} \rightarrow H_{W}$ such that

(a) $L^{n}f \rightarrow 0$ when $n \rightarrow \infty$ for every $f \in H_{V}$;

(b) $S^{n}f \rightarrow 0$ when $n \rightarrow \infty$ for every $f \in H_{W}$;

(c) $L \circ S (f) = f$ for every $f \in H_{W}$.

By Theorem \ref{criterion} the operator $L$ is mixing.   \hfill$\square$

\section{Convolution operators on spaces of entire functions on $(DFC)$-spaces}

A $(DFC)$-space is a locally convex space of the form $E=F_c^{\prime}$, where $F$ is a Fr\'echet space. $(DFC)$-spaces were first studied by Brauner \cite{brauner} and H\"ollstein \cite{holl1,holl2}. Holomorphic functions on $(DFC)$-spaces have been studied by Mujica \cite{mujica_dfc}, Valdivia \cite{valdivia}, Schottenloher \cite{schot}, Nachbin \cite{nachbin4}, Louren\c co \cite{lilian} and Galindo et al. \cite{GGM}.

The main result in this section is the following theorem.

\begin{theorem}
\label{theo_dfc}
Let $E = F^{\prime}_{c}$, where $F$ is a separable Fr\'echet space with the approximation property.
Let $L$ be a nontrivial convolution operator on $(\mathcal{H}(E), \tau_{0})$. Then $L$ is mixing, in particular hypercyclic.
\end{theorem}

The proof of Theorem \ref{theo_dfc} rests on Theorem \ref{criterion}, but before proving the theorem we need some auxiliary results.

\begin{proposition}
Let $E = F^{\prime}_{c}$, where $F$ is a Fr\'echet space. Then:

\textit{(a) $E$ is a semi-Montel, hemicompact k-space.}

\textit{(b) $(\mathcal{H}(E), \tau_{0})$ is a Fr\'echet space.} \vspace{.1in}
\end{proposition}

\begin{proof}
 (a) By \cite[Proposition 7.2]{mujica_dfc} $E$ is a semi-Montel, hemicompact space. By the Banach-Dieudonn\'e theorem
(see \cite[p. 245, Theorem 1]{horvath}) $E$ is a $k$-space. (b) follows at once from (a).
\end{proof}

If $E = F^{\prime}_{c}$, where $F$ is a Fr\'echet space, then a result of Schwartz guarantees that $F$ has the approximation property
if and only if $E$ has the approximation property (see \cite[Expos\'e $n^{0}$ 14, Th\'eor\`eme 2]{schwartz} or \cite[Corollary 1.3]{DiMu}).

\begin{proposition}
\label{HE_frechet}
 \textit{Let $E = F^{\prime}_{c}$, where $F$ is a separable Fr\'echet space with the approximation property.
Then $(\mathcal{H}(E), \tau_{0})$ is a separable Fr\'echet space.}
\end{proposition}

\begin{proof}
By considering the Taylor series we see that every $f \in \mathcal{H}(E)$ can be approximated, uniformly on compact sets,
by continuous polynomials on $E$. Since $E$ has the approximation property, it is clear that every continuous polynomial on $E$ can be approximated,
uniformly on compact sets, by continuous polynomials of finite type. By the Mackey-Arens theorem (see \cite[p. 205, Theorem 1]{horvath}) $E^{\prime}_{b} = E^{\prime}_{c} = F$ is separable, it follows that
$(\mathcal{P}_{f}(^{m}E), \tau_{0})$ is separable for every $m \in \mathbb{N}_{0}$. Hence it follows that $(\mathcal{H}(E), \tau_{0})$
is separable, as asserted.
\end{proof}

\begin{definition}\rm
Let $E$ and $F$ be normed spaces. An operator $T \in \mathcal{L}(E;F)$ is said to be \textit{approximable} if
$T \in \overline{E^{\prime} \otimes F}$.
\end{definition}

\begin{lemma} \textit{Let $E$, $F$ and $G$ be normed spaces, with $G$ complete, and let $T \in \mathcal{L}(F;E)$ be an approximable operator. Then
$f \circ T \in \mathcal{H}_{Ab}(F;G)$ for every $f \in \mathcal{H}_{b}(E;G)$, and the mapping
$$ f \in \mathcal{H}_{b}(E;G) \rightarrow f \circ T \in \mathcal{H}_{Ab}(F;G) $$ is linear and continuous.}
\end{lemma}

\begin{proof}
Let $\sum_{m=0}^{\infty} P_{m}(x)$ denote the Taylor series of $f$ at the origin. Then
$$ f \circ T(y) = \sum_{m=0}^{\infty} P_{m} \circ T(y) \hspace{.1in} \mbox{for every $y \in F$}. $$
Since $T$ is approximable, there is a sequence $(T_{n})_{n=1}^{\infty} \in F^{\prime} \otimes E$
such that $\|T-T_{n}\| \rightarrow 0$. Since $P_{m} \in \mathcal{P}(^{m}E)$ for every $m \in \mathbb{N}_{0}$, it is clear that
$P_{m} \circ T \in \mathcal{P}(^{m}F)$ and $\|P_{m} \circ T\| \le \|P_{m}\| \|T\|^{m}$ for every $m \in \mathbb{N}_{0}$.

Since $f \in \mathcal{H}_{b}(E;G)$, the Taylor series of $f$ at the origin has an infinite radius of convergence.
By the Cauchy-Hadamard formula (see \cite[Theorem 4.3]{mujica}),  $\|P_{m}\|^{1/m} \rightarrow 0$. Hence it follows that
$$ \|P_{m} \circ T\|^{1/m} \leq \|P_{m}\|^{1/m} \|T\| \rightarrow 0. $$
Hence the Taylor series of $f \circ T$ at the origin has also an infinite radius of convergence, and therefore
$f \circ T \in \mathcal{H}_{b}(F;G)$.

To show that $f \circ T \in \mathcal{H}_{Ab}(F;G)$ we have to prove that $P_{m} \circ T \in \mathcal{P}_{A}(F;G)$ for every
$m \in \mathbb{N}_{0}$. By the Newton binomial formula (see \cite[Corollary 1.9]{mujica}), for every $y \in F$ with $\|y\| \le 1$ it follows that
$$ \Vert P_{m} \circ T(y)-P_{m} \circ T_{n}(y)\Vert = \left\| \sum_{k=1}^{m}
\binom{m}{k} \check{P}_{m} (T_{n}y)^{m-k}(Ty-T_{n}y)^{k} \right\| $$
$$ \le \sum_{k=1}^{m} \binom{m}{k}  \|\check{P}_{m}\| \|T_{n}\|^{m-k}\|T-T_{n}\|^{k} $$
$$ \le e^{m} \|P_{m}\| \|T-T_{n}\| \sum_{k=1}^{m} \binom{m}{k}  c^{m-k} d^{k-1} $$
 for suitable positive constants $c$ and $d$. Therefore $\| P_{m} \circ T - P_{m} \circ T_{n} \| \rightarrow 0$.
Since $T_{n} \in F^{\prime} \otimes E$, it is clear that
$P_{m} \circ T_{n} \in \mathcal{P}_{f}(^{m}F)$, and therefore $P_{m} \circ T \in \mathcal{P}_{A}(^{m}F;G)$.

Finally it is clear that the mapping $f \in \mathcal{H}_{b}(E;G) \rightarrow f \circ T \in \mathcal{H}_{Ab}(F;G)$ is continuous, since
$$ \|f \circ T\|_{\rho} = \sum_{m=0}^{\infty} \|P_{m} \circ T\|\rho^{m} \le \sum_{m=0}^{\infty} \|P_{m}\| \|T\|^{m}\rho^{m} = \|f\|_{\|T\|\rho} $$
for every $\rho>0$.
\end{proof}

\begin{theorem}
\label{theo_Huab}
 \textit{Let $E$ be a (DFC)-space with the approximation property. Then
$\mathcal{H}_{uAb}(E) = \mathcal{H}_{ub}(E) = (\mathcal{H}(E), \tau_{0})$ algebraically and topologically.}
\end{theorem}

\begin{proof}
 We first establish the continuous inclusions
$$ \mathcal{H}_{uAb}(E) \hookrightarrow \mathcal{H}_{ub}(E) \hookrightarrow (\mathcal{H}(E), \tau_{0}). $$
Since
$$ \mathcal{H}_{uAb}(E) = \bigcup_{p \in cs(E)} \pi_{p}^{*}(\mathcal{H}_{Ab}(E_{p})) $$ and
$$ \mathcal{H}_{ub}(E) = \bigcup_{p \in cs(E)} \pi_{p}^{*}(\mathcal{H}_{b}(E_{p})), $$ it is clear that
$\mathcal{H}_{uAb}(E) \subset \mathcal{H}_{ub}(E)$, and the inclusion mapping is continuous.
Since the inclusion mapping
$\pi_{p}^{*}(\mathcal{H}_{b}(E_{p})) \hookrightarrow (\mathcal{H}(E), \tau_{0})$
is clearly continuous, we obtain the continuous inclusion
$\mathcal{H}_{ub}(E) \hookrightarrow (\mathcal{H}(E), \tau_{0})$.

We next show that $\mathcal{H}_{uAb}(E) = (\mathcal{H}(E), \tau_{0})$ algebraically and topologically.
We know that $\mathcal{H}_{uAb}(E)$ is bornological, and $(\mathcal{H}(E), \tau_{0})$ is a Fr\'echet space,
in particular bornological. Hence it suffices to show that each bounded subset of $(\mathcal{H}(E), \tau_{0})$
is contained and bounded in $\mathcal{H}_{uAb}(E)$. Let $\{f_{i}: i \in I\}$ be a bounded subset of
$(\mathcal{H}(E), \tau_{0})$. Let $f \in \mathcal{H}(E; \ell_{\infty}(I))$ be defined by
$f(x) = (f_{i}(x))_{i \in I}$ for every $x \in E$.  By a result of Galindo et al. (see \cite[Corollary 1]{GGM}),
$$ (\mathcal{H}(E; \ell_{\infty}(I)), \tau_{0}) = \mathcal{H}_{ub}(E; \ell_{\infty}(I)) $$
algebraically and topologically. In particular $ f \in \mathcal{H}_{ub}(E; \ell_{\infty}(I))$
and therefore there are $p \in cs(E)$ and $f_{p} \in \mathcal{H}_{b}(E; \ell_{\infty}(I))$ such that
$f = f_{p} \circ \pi_{p}$. By a result of Louren\c{c}o (see \cite[Lemma 2.2]{lilian}), there are $q \in cs(E)$, $q \ge p$
such that the canonical mapping $\pi_{pq}: E_{q} \rightarrow E_{p}$ is an approximate operator.
Let $f_{q} = f_{p} \circ \pi_{pq}$. By the preceding lemma $f_{q} \in \mathcal{H}_{Ab}(E_{q}; \ell_{\infty}(I))$
and
$$ f = f_{p} \circ \pi_{p} = f_{p} \circ \pi_{pq} \circ \pi_{q} = f_{q} \circ \pi_{q}. $$
Thus $f = (f_{i})_{i \in I} \in \mathcal{H}_{uAb}(E; \ell_{\infty}(I))$, and therefore $\{f_{i}: i \in I\}$
is a bounded subset of $\mathcal{H}_{uAb}(E)$, as asserted.
\end{proof}

\textit{Proof of Theorem \ref{theo_dfc}}. By Proposition \ref{HE_frechet} and Theorem \ref{theo_Huab} $\mathcal{H}_{uAb}(E) = (\mathcal{H}(E), \tau_{0})$
is a separable Fr\'echet space. If $D \subset cs(E)$ is any fundamental family, then it follows from Example \ref{nuclear} that $(\mathcal{P}_{A}(^{m}E_{p}))_{m=0}^{\infty}$
is a $\pi_{1}$-holomorphy type for every $p \in D$. By Proposition \ref{prop_hypercyclicity} there are dense subspaces $H_{V}$ and $H_{W}$ of $\mathcal{H}_{uAb}(E)$ and there is a linear mapping
$S\colon H_{W} \rightarrow H_{V}$ such that:

(a) $L^{n}f \rightarrow 0$ when $n \rightarrow \infty$ for every $f \in H_{V}$;

(b) $S^{n}f \rightarrow 0$ when $n \rightarrow \infty$ for every $f \in H_{W}$;

(c) $L \circ S (f) =f$ for every $f \in H_{W}$.

By Theorem \ref{criterion} the operator $L$ is mixing.     \hfill$\square$

\section{A counterexample}

We present a simple example of convolution operator which is not hypercyclic.
So far we have only considered the compact-open topology $\tau_{0}$ on the space $\mathcal{H}(E)$. But now we will also
consider the compact-ported topology $\tau_{\omega}$ introduced by Nachbin \cite{nachbin1}, and the bornological topology $\tau_{\delta}$ introduced
by Coeur\'e \cite{coeure} and Nachbin \cite{nachbin3}. For background information on these topologies we refer the reader to the book of Dineen \cite{Di2}.

\begin{theorem}

(a) $(\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau_{0}) = (\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau_{\omega}) \ne
(\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau_{\delta}) = \mathcal{H}_{ub}(\mathbb{C}^{\mathbb{N}})$.

(b) For each $a \in \mathbb{C}^{\mathbb{N}}$, the translation operator $\tau_{a}$ is a
convolution operator on $(\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau)$ which is not hypercyclic, for $\tau = \tau_{0}$,
$\tau_{\omega}$ and $\tau_{\delta}$.

\end{theorem}

\begin{proof} (a) By a result of Barroso (see \cite[p. 537, Teorema 2.2]{Ba}), $\tau_{0}=\tau_{\omega}$ on $\mathcal{H}(\mathbb{C}^{\mathbb{N}})$.
By a result of Dineen (see \cite[p. 45, Corollary 3.2]{Di1} or \cite[Example 3.24(a)]{Di2}) we have $\tau_{\omega} \ne \tau_{\delta}$ on
$\mathcal{H}(\mathbb{C}^{\mathbb{N}})$.

To see the connection with $\mathcal{H}_{ub}(\mathbb{C}^{\mathbb{N}})$, for each $n\in\mathbb{N}$ and for $\tau = \tau_{0}$, $\tau_{\omega}$ and $\tau_{\delta}$,
consider the canonical inclusion $J_{n}\colon \mathbb{C}^{n} \hookrightarrow \mathbb{C}^{\mathbb{N}}$,
the canonical projection $\pi_{n}\colon \mathbb{C}^{\mathbb{N}} \rightarrow \mathbb{C}^{n}$ and the
corresponding mappings
$$ J_{n}^{*}\colon f \in (\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau) \rightarrow f \circ J_{n} \in (\mathcal{H}(\mathbb{C}^{n}), \tau) $$ and
$$ \pi_{n}^{*}\colon f_{n} \in (\mathcal{H}(\mathbb{C}^{n}), \tau) \rightarrow f_{n} \circ \pi_{n} \in (\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau). $$
Since $J_{n}^{*} \circ \pi_{n}^{*} $ is the identity on $\mathcal{H}(\mathbb{C}^{n})$, it follows that $(\mathcal{H}(\mathbb{C}^{n}), \tau)$ is topologically isomorphic to a complemented subspace of
$(\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau)$. In particular
$\pi_n^*(\mathcal{H}(\mathbb{C}^{n}))$ is a proper closed subspace of ($\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau)$. By a result of Barroso (see \cite[p. 38, Corol\'ario]{Ba} or \cite[Proposition 1.1]{A})
$$ \mathcal{H}(\mathbb{C}^{\mathbb{N}}) = \bigcup_{n=1}^{\infty} \{ f_{n} \circ \pi_{n}\colon f_{n} \in \mathcal{H}(\mathbb{C}^{n}) \}
= \bigcup_{n=1}^{\infty} \pi_{n}^{*}(\mathcal{H}(\mathbb{C}^{n})). $$
If we define $p_{n} \in cs(\mathbb{C}^{\mathbb{N}})$ by
$$ p_{n}(x) = \sup_{j \le n} |\xi_{j}| \hspace{.1in} \mbox{for every $x = (\xi_{j})_{j=1}^{\infty} \in \mathbb{C}^{\mathbb{N}}$}, $$
then we can readily see that the normed space $(\mathbb{C}^{\mathbb{N}})_{p_{n}}$ is topologically isomorphic to $\mathbb{C}^{n}$,
and therefore
$$ \mathcal{H}_{ub}(\mathbb{C}^{\mathbb{N}}) = ind (\mathcal{H}((\mathbb{C}^{\mathbb{N}})_{p_{n}}, \tau_{0})
= ind (\mathcal{H}(\mathbb{C}^{n}), \tau_{0}). $$
By a result of Ansemil (see \cite[Proposition 1.3]{A})
$$ (\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau_{\delta}) = ind (\mathcal{H}(\mathbb{C}^{n}), \tau_{0}) = \mathcal{H}_{ub}(\mathbb{C}^{\mathbb{N}}). $$

(b) Let $a \in  \mathbb{C}^{\mathbb{N}}$ and assume that the translation operator
$$ \tau_{a}\colon (\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau_{0}) \rightarrow (\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau_{0}) $$
were hypercyclic. Then there would exist $f \in \mathcal{H}(\mathbb{C}^{\mathbb{N}})$ such that the set
$\{f, \tau_{a}f, \tau_{a}^{2}f, ... \}$
would be dense in $(\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau)$. Let $n\in\mathbb{N}$ be such that $f = f_{n} \circ \pi_{n}$, with $f_{n} \in \mathcal{H}(\mathbb{C}^{n})$.
Then
$$ \{f, \tau_{a}f, \tau_{a}^{2}f,\ldots\}  = \pi_{n}^{*}(\{f_{n}, \tau_{\pi_n(a)}f_{n}, \tau_{\pi_n(a)}^{2}f_{n},\ldots\} )
\subset \pi_{k}^{*}(\mathcal{H}(\mathbb{C}^{n})) , $$
a contradiction, since $\pi_{n}^{*}(\mathcal{H}(\mathbb{C}^{n}))$ is a proper closed subspace of $(\mathcal{H}(\mathbb{C}^{\mathbb{N}}), \tau)$.

\end{proof}

\begin{corollary}
For each $a \in \mathbb{C}^{\mathbb{N}}$, the translation operator $\tau_{a}$ is a
convolution operator on $\mathcal{H}_{u b} (\mathbb{C}^{\mathbb{N}})$ which is not hypercyclic.
\end{corollary}

redpajama_set_name: RedPajamaArXiv


text:
Indonesian president hosts kings, sultans
Politics, Asia - Pacific
Dozens of royal leaders gather at presidential palace in Java to meet Joko Widodo
Indonesian President Joko Widodo
By Erric Permana
BOGOR, Indonesia
Indonesian President Joko Widodo on Thursday invited kings and sultans from all over Indonesia to meet at the Bogor Palace in West Java.
Around 90 kings and sultans participated in the gathering where the president heard grievances, input, and suggestions from royal families across the country.
"I invite anyone who would like to convey any issues they are facing in their respective areas," President Widodo addressed the crowd.
The majority of them -- around 20 -- hailed from the island of Sumatera, while only two came from Papua.
The royals were decked out in traditional costumes and ranged from the heads of sultanates and kingdoms, as well princes and princesses.
Among them were Sultan Muhammad Putera Ferryandi from West Nusa Tenggara, King Leopold Nicholas Nisnoni of Kupang, and Commander Kapitan Muhammad Ali Alting of the Tidore Sultanate.
Alting asked the president to acknowledge various kingdoms and place their representatives in parliament.
"The sultanates across Indonesia have contributed to the country as well, so the president should appreciate that," he said.
His sentiments were echoed by King Jan Christofel Benjamin from the Baubau Kingdom in East Nusa Tenggara.
"We are very flattered by this special occasion. This gathering shows that the presidential palace cares about and respects the ancient kingdoms of Indonesia and the president is willing to listen to us," he said.
When the country gained independence in 1945, the sultans and kings of Indonesia were stripped of their powers. However, they continue to wield influence and have significant roles in the public life.
Royal courts still exist in Java, Bali, Sumatera, Papua and other islands where locals revere royal families.
Indonesia kings sultans
Indonesia passes law to move capital from Jakarta to Borneo


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A tribute: Ela Ramesh Bhatt, the gentle revolutionary
Dr Martha Chen
Ela Bhatt, homepage
by Dr Martha Chen
This tribute comes with the passing of Ela Bhatt, whose work created an employment support programme in India for women who live in poverty. Ela started a trade union Self-Employed Women's Association (SEWA) was established in 1972, the same year as BRAC.
Ela Ramesh Bhatt, the founder of the Self-Employed Women's Association (SEWA) of India, passed away on 2 November, 2022. Known as the 'gentle revolutionary', Ela-ben, as she is affectionately known, is recognised around the world for her Gandhian values, visionary ideals, pioneering work and quiet-centered humanity.
Ela Bhatt at a WIEGO Annual Meeting and Public Seminar Hosted by the International Development Research Centre (IDRC) at Ottawa, Ontario in April 1999.
Established in 1972, SEWA is the largest trade union in India and the largest union of informal workers in the world, with over two million women members from multiple trades.
It is also a sisterhood of institutions, including a cooperative bank, an insurance cooperative, and over 100 producer and service cooperatives. SWEA is world-renowned for its unique and effective blend of trade union activism and development interventions with, as its core function, the building of institutions owned and managed by working women living in poverty.
Ela Bhatt with Maureen O'Neil, President of International Development Research Centre (IDRC) in 1999.
Ela Bhatt was a member of the Indian Parliament and subsequently the Indian Planning Commission. She was a Member of the Elders and served as a trustee of the Rockefeller Foundation. She co-founded and served as chair of two global networks: Women's World Banking, and Women in Informal Employment: Globalizing and Organizing (WIEGO).
She was a pioneering leader of – and abiding inspiration to – four global movements: the women's movement, the microfinance movement, the labour movement and the movement of informal workers. She received many awards, including the Ramon Magsaysay Award and the Right Livelihoods Award, as well as honorary degrees from Harvard University, the University of KwaZulu Natal, Yale University and other academic institutions.
Pat Horn, Ela Bhatt and Andrea Singh in Ottawa, Ontario in 1999.
I had the deep privilege and joy of working closely with Ela-ben for 46 years.
She was my mentor, intellectual companion and comrade sister in the struggle for economic justice for the working poor in the informal economy – and the dearest of friends.
She was the moral compass – the North Star – of the global network WIEGO that we co-founded in 1997. I cannot imagine SEWA, WIEGO, my life – or the world – without her gentle moral presence.
Dr Martha Chen is Senior Advisor, Women's World Banking, and Women in Informal Employment: Globalizing and Organizing (WIEGO), a Lecturer in Urban Planning and Design, Harvard Graduate School of Design, and Chair of BRAC's Global Board.
Jamdani and Aarong: A love affair spanning half a century
From Sulla to the world: Happy birthday, Abed bhai
She was the heart and soul of BRAC


Another month, another selection of the best of the output of Leeds based label Dance to the Radio, whose 4X12" series each select a single by four bands expected to make a stir over the coming months. Within this, they have tried to showcase a diversity too of output quite different from what would be expected from many labels.
This is no different on this, the third release, with opening track by metal doers Chickenhawk coming thundering in with high tempo drums, bass and guitar crescendoing into singer Paulk Astick's screaming vocals. The song continues in a similar vein, with the occasional breakdown for a very solid and together three minutes that makes it an enjoyable listen even for those less inclined towards such heavy material.
The sharp contrast favoured by DttR is then rapidly shown as the tempo switches down to a clip of a 1940's BBC presenter-style talking about x-rays. This slowly leads into gentle synths and the haunting voice of Esben & The Witch's singer Rachel. This is complimented throughout with further lengthy samples talking about the subject matter. This song is a slow burner and all the more beautiful for it as repeated ideas continually mesh, seperate and crescendo.
"Husk" by Olfar brings us back to much more standard radio friendly fare. Whilst this is in no way a bad thing in itself, little evidence is on display that radio will want to fall in love with Olfar. The chorus is pretty and the verses lead nicely into it, but the subject matter doesn't come across as particularly heartfelt and little is done to distinguish this from the myriads of bands doing the same things and doing it better.
The closing act, Airship, is one such band. Whilst at first listen they don't seem to offering much more than Olfar in terms of structure or content, apart from a slightly more dreamy edge to their output, a proper listen displays a breadth of ideas that means "Spirit Party" is a truly well constructed song. Drum shifts and uninterested vocals that manage to still complement the central theme make this a song with much to offer.


text:
require 'test_helper'

class ParticipantTest < ActiveSupport::TestCase

  def setup
    @participant = participants :santa
    @event = events :empty
    @other_event = events :thesupersecretsanta
  end

  test "should be valid" do
    assert @participant.valid?
    assert @event.valid?
  end

  test "create participant with invalid name" do
    @participant.name = ''
    assert_not @participant.valid?
  end

  test "create participant with empty email" do
    @participant.email = ''
    assert_not @participant.valid?
  end

  test "create participant with invalid email" do
    @participant.email = 'foo'
    assert_not @participant.valid?
  end

  test "events are created with 0 participant" do
    assert_equal 0, @event.participants.size
  end

  test "add a participant" do
    assert_difference '@event.participants.size', 1 do
      @event.participants << @participant
    end
  end

  test "Participant names should be unique" do
    p1 = Participant.new(name: 'Bobby', email: 'bobby@example.com')
    p2 = Participant.new(name: 'Bobby', email: 'other_bobby@example.com')
    assert p1.valid?
    assert p2.valid?
    @event.participants << p1
    @event.participants << p2
    assert p1.valid?
    assert_not p2.valid?

    p3 = Participant.new(name: 'Bobby', email: 'yet_another_bobby@example.com')
    assert p3.valid?
    @other_event.participants << p3
    assert p3.valid?
  end

  test "Several participants can have the same email" do
    p1 = Participant.new(name: 'Jimmy', email: 'contact-ledzep@example.com')
    p2 = Participant.new(name: 'Robert', email: 'contact-ledzep@example.com')
    @event.participants << p1
    @event.participants << p2
    assert p1.valid?
    assert p2.valid?
  end
end


Transfer files from PC to Phone, Shareit is the app which you can transfer photos, videos, music, contacts, apps and some more data from one device to the other device without USB cable and with the help of Wi-Fi compatible it is too much easy and fast to share your data between your friends.
Thies application is from Lenovo that allows Windows, Windows Phone, Android, and iOS devices to share their data from one device to many devices, and now it is available in 39 languages which include English, French, Spanish, Russian, Arabic, Chinese and some more.
Shareit The Transfer/Sharing Tool between PC and Mobile Phones.
Here is the official website of shareit from you can download the file for your device.
1. First, download the app setup for you PC latest version from the link from the above text.
2. Open the app setup.
3. You will see some information about the app read and press Accept button.
4. Now you can change the installation place for the app by clicking on the Browse button then after choosing the place press the Next button on the screen.
5. Now you will get a new page, click Next and then it will be installed on your PC.
6. You can click on the empty box and open the app now and then click Finish button.
7. Now you have installed Shareit successfully on your PC and now you can open it and use it.
How to use Shareit on Mobile Devices.
2. Connect both devices which you want to share files between in one Wi-Fi or you can use hotspot of your mobile phone.
3. Now open it on your device and click on the send or receive button on the top of the screen of your device.
4. Now choose what you want to share with your friends.
5. Now if you both are connected to one Wi-Fi then you will get the other device Icone on the radar of your screen.
6. Click on the Icone and now your data is transferring to the other device which you selected.
Thier is the easiest way to Transfer files from PC to Phone without any internet or any USB cable.
Install it on your PC (like I show the way of installing it in the above texts) and mobile device, and you must connect both PC and your mobile in one Wi-Fi device.
1. Open the app on your PC and the mobile device both.
2. Now click on the Show Qr Code on your PC screen.
3. And open shareit on your mobile phone and click on the receive or send button.
4. Now select the data which you want to share it and then click on the down left side of the screen to scan the Qr Code.
5. Now your data is going to transfer to the other device which you selected.
Relative: Click Here to Get More Information About Related To Shareit.


These charts show the average base salary (core compensation), as well as the average total compensation for the job of Marketing Manager in Wilmington, NC. The base salary for Marketing Manager ranges from $80,494 to $108,764 with the average base salary of $92,381. The total compensation, which includes bonus, health and retirement, can vary anywhere from $85,354 to $120,421 with the average total compensation of $98,648.


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Rural Northland transgender couple to tell their story at NZ Fringe
By MiNDFOOD	| February 17, 2020
A transgender couple from Northland are set to delve deep into their story of hormonal gender transition.
As a transgender couple leading a provincial life in rural Northland, Willow and Ren Lunicke have been somewhat "small-town famous".
Their long-term relationship took an exciting new direction when they simultaneously began to undergo gender-affirming hormone therapy.
On their journey they encountered not just physical changes, but unexpected shifts in their internal worlds that impacted how they relate to their community, themselves and each other.
Their story is told in SHE + THEY, a show with a live Q&A that will debut at the New Zealand Fringe Festival in March.
It's an autobiographical, dramatic and comedic depiction of the journey undertaken by Willow (SHE) and Ren (THEY) and the discoveries they make as they undergo hormonal gender transition together.
The audience is encouraged to arrive early to write down their questions to be answered by Willow and Ren during the show.
Ren is an award-winning performer and producer, and for this production they are joined by muse Willow in the pair's first collaboration.
SHE + THEY is Ren's fifth autobiographical show.
SHE + THEY
Aunty Dana's Op Shop, Wellington
https://www.fringe.co.nz/show/43782
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Join the Kappa Beta Delta Honor Society (1/22/2020)
Welcoming the World to Campus (1/7/2020)
Manufacturing Gets Modern (1/2/2020)
Trading Places (12/30/2019)
200 Hour Yoga Teacher Training Classes Start Mid-January (11/8/2019)
Starting Fresh at Saint Paul College
For Eloisa Segura, Saint Paul College represented a chance to reinvent herself as a stand-out student and community leader.
From the start, the odds seemed stacked against Eloisa Segura. "My mother immigrated to the United States to work as a nanny and housekeeper – she was a woman with only a ninth-grade education who did not speak English, and who had no family in the U.S.," says Segura. "I was born into a Spanish-speaking single-parent household with a family income far below the poverty line. As you can imagine, the circumstances I was born into did not set me up for success."
A Rocky Beginning
Due to these challenges, as a high schooler, Segura found herself just scraping by. "I never played a sport, an instrument, or got involved in extracurricular activities – in part because of the costs," she says. "I didn't take ACT prep classes, I didn't try hard in school, and to be honest I almost didn't graduate high school."
When senior year came Segura was surrounded by the buzz of college tours, applications, and acceptance letters; she got caught up in the excitement and decided she wanted to go to college, too. Segura chose a small Catholic college in Iowa, where she was excited to join the cheerleading team. She was accepted, however when her financial aid letter came, reality hit.
"I hadn't prepared to go to college and I wasn't a strong applicant," says Segura. "I wouldn't get an academic scholarship because I hadn't demonstrated that I was capable of doing the work. I wasn't worth investing in."
Opening to Opportunity
Rallying from her disappointment, Segura soon realized Saint Paul College could offer her the affordability she needed and the fresh start she wanted. "My mom dropped me off on my first day, and I was ready to start a new path and fully dedicate myself to doing my absolute best," says Segura.
Looking back, Segura believes Saint Paul College was the perfect place for her. "My classes were interesting and manageable, and the instructors were flexible, caring, and understanding. There were no surprises, so you could take charge of your own education by planning ahead and keeping your own commitments in mind."
She soon began taking advantage of the many opportunities available to Saint Paul College students, including earning a lead role as Millie in the Saint Paul College production of Picnic and serving as a Saint Paul College Student Ambassador.
"Eloisa was an excellent student who was committed to the process of creating our production of Picnic," says theater instructor James LeDuc. "She was a leader in the cast, and through her hard work and dedication, she was able to create a wonderful character."
"As a Student Ambassador Eloisa was always eager to represent our college on tours and at off-campus events, and was a very confident public speaker," adds Dave Mogren, a former advisor for the Student Ambassador program. "Eloisa is a great example of how valuable networking within the college can be – her constant participation was noticed by everyone, including our college president, who invited Eloisa to speak in front of visiting groups on several occasions."
"Ms. Segura's openness, choices and determination have made her story remarkable and inspiring. It shows just how transformative believing in yourself and being involved in your college community can be."
-Rassoul Dastmozd, President/CEO
Finding Success
Segura's academic efforts and enthusiasm paid off quickly with a scholarship to attend Saint Paul College for a second year. After meeting her would be husband, she set her sights on a closer Catholic college, St. Thomas, to complete her four-year degree.
"When I received my acceptance letter from St. Thomas it included an academic transfer scholarship for over half my tuition, and I could afford to finance the rest with federal student loans," says Segura. "I went on to become part of St. Thomas' honor society, as well as my department's honor society."
Segura graduated cum laude from the University of St. Thomas in 2016 with a major in Spanish linguistics and a minor in business. Today, she works as a commercial insurance analyst for a national commercial real estate capital solutions provider and has paid off all her student loans. "I am a success story, however, none of this would have been possible without the existence of Saint Paul College and the opportunity it presented," says Segura.
This article originally appeared in our College Magazine - Spring 2019. Download a free copy to read more stories like this one.