text:
'Mad Max: Fury Road' May Return to Theaters – In Black and White
Mad Max: Fury Road wasn't the biggest hit of the year, but it is one of the few summer blockbusters that is getting a lot of awards season buzz and several critics awards for Best Film of the Year. Now typically, when a movie released early in the year has a chance to win prizes in the Hollywood derby, it gets a proforma theatrical re-release, and rumors are circling that maybe Fury Road will be seen in cinemas again in the new year. The twist: it may be a black and white version of the film that George Miller apparently always wanted to make.
In a profile for ScreenDaily, Fury Road producer Doug Mitchell dropped the hint about the possible "special edition" release of the film.
In 2016, there might also be a black-and-white version of the film, which Miller confirms was his original intent. A greyscale and silent version was leaked online in September, although it has since been removed. Mitchell says that an official version exists and could yet receive a theatrical release.
I didn't know that Fury Road was supposed to be in black-and-white. I'm not sure how going monochrome was meant to help the film, the colors in it were filled with vibrant reds, oranges and yellows making it a veritable technicolor feast on screen. Perhaps the tone of a black-and-white Fury Road will feel different, perhaps it will be a bit more solemn and a little less zany. It will be interesting to see, if the black-and-white version of the film ever comes about.
Of course, Mad Max: Fury Road would not be the first color film in recent memory to get a black-and-white release. There was an official version of The Mist released on DVD in a black-and-white rendition after director Frank Darabont revealed that he originally wanted to release that film with our color. I can see why that would be appealing for The Mist with its Twilight Zone influence, but for Mad Max? I think at this point we have to assume that Miller knows what he's doing.
We'll let you know when and if Mad Max: Fury Road is coming back to a theater near you.
Source: The Mary Sue
Category: Film
Tags: George Miller, Mad Max Fury Road, re-release


text:
Ferries to Lanzarote
Home / Europe / Lanzarote / Arrecife / Ferry from Santa Cruz de La Palma to Arrecife
Popular Ferry Operators for Santa Cruz de La Palma - Arrecife
View Naviera Armas information
View Trasmediterranea information
Santa Cruz de La Palma - Arrecife is one of our busiest routes - sailings regularly sell out at busy periods
Tips & Information for Santa Cruz de La Palma - Arrecife
Latest offers for Santa Cruz de La Palma - Arrecife
Ferry from Santa Cruz de La Palma to Arrecife
The Santa Cruz de La Palma Arrecife ferry route connects La Palma with Lanzarote and is currently operated by 2 ferry companies. The Naviera Armas service runs up to 1 times per week with a sailing duration of around 30 hours while the Trasmediterranea service runs up to 1 times per week with a duration from 30 hours.
So that's a combined 2 sailings on offer per week on the Santa Cruz de La Palma Arrecife route between La Palma and Lanzarote. Compare now and get the best fare at the time that you want to travel.
For more information, please visit our Ferries from La Palma to Lanzarote page.
How long is the ferry from Santa Cruz de La Palma to Arrecife?
The typical crossing time for ferries from Santa Cruz de La Palma to Arrecife is approximately 30h. However, please keep in mind that sailing duration might change depending on what season you choose to travel.
How much is the ferry from Santa Cruz de La Palma to Arrecife?
The average price of a ferry from Santa Cruz de La Palma to Arrecife is approximately 150 €. However, please remember that the price of a ferry from Santa Cruz de La Palma to Arrecife can differ depending on the season.
Which ferry companies operate between Santa Cruz de La Palma to Arrecife?
There are currently 2 popular ferry operators travelling from Santa Cruz de La Palma to Arrecife. The following operators that provide this service are
How can I book ferry tickets from Santa Cruz de La Palma to Arrecife?
Ferries from Santa Cruz de La Palma to Arrecife are available for booking through our deal finder. Please also visit our offers page to stay updated with all the latest ferry offers on this route.
Can you travel as a foot passenger on the ferry from [Portfrom] to Arrecife?
Yes, you can currently travel as a foot passenger onboard the ferries from Santa Cruz de La Palma to Arrecife with
Can you take your car on the ferry from Santa Cruz de La Palma to Arrecife?
Yes, you can travel with a vehicle from Santa Cruz de La Palma to Arrecife with the following operators
Can you bring dogs on the ferry from [Portfrom] to Arrecife?
Yes, passengers are allowed to bring their dogs onboard this ferry service. However, you may require a pet passport and other documentation to take your furry companion with you. The following operators currently allow dogs on their ferries
What is the distance from Santa Cruz de La Palma to Arrecife?
Santa Cruz de La Palma to Arrecife is approximately 255 nautical miles distance apart.
Santa Cruz de La Palma Guide
The Spanish city of Santa Cruz de la Palma is located on the east coast of the island of La Palma, one of the Canary Islands. It is the island's second largest city, after Los Llanos de Aridane, but it is the island's capital. The city was founded by 1493 by Alonso Fernandez de Lugo and was located next to a river that was situated by a cave named Tedote (now Cueva de Carla) to the north of the city. The city's original name was called Villa del Apuron and its port connected routes to the Americas, from which goods from the island were exported. The city is characterised by its cobbled streets, timber balconies and ancient buildings and is just a short stroll from the holiday resort of Los Cancajos. For passengers disembarking at the city's port, the town centre is just across the road from the harbour's entrance.
Santa Cruz de la Palma has the only major port in the island, serving ferry routes to Cádiz in Spain, as well as to Tenerife, Gran Canaria and Lanzarote. The main ferry operators in the port are Naviera Armas and Fred Olsen Express. Many cruise line firms also operate from the port.
Arrecife Guide
The Spanish city and port of Arrecife is located on the island of Lanzarote which forms part of the Canary Islands. The town lies on the island's east coast and is a city full to the brim with culture and history. Arrecife's name is derived from the Spanish for reef and is a reference to the volcanic rock formations that lie out to sea and protect the pretty harbour.
The city can trace its origins back to the 15th century where it began as a small fishing village. Over the next 300 years or so, the settlement grew and eventually became the island's capital in 1852. Today, the city is adorned with boutiques, high end shops selling designer labels and is a popular destination for shoppers. The city also has its own beach, Playa del Reducto, that has lovely golden sand and warm, calm waters to bathe in. There is also a lovely promenade that runs from Playa del Reducto to the city's second beach, Playa del Cable, which is around 2 km to the west.
From the city's port, ferries depart to the other islands in the Canaries and also to other destinations in Europe and Africa.
Onboard the ferries
Albayzin

redpajama_set_name: RedPajamaCommonCrawl


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The Launch of Jamie Coulter Ministries
Jamie Coulter
announcements/news
By Lorraine Walker / June 8, 2016
(Hamburg, AR)– June 1, 2016 – Meet Jamie Coulter, also known as "The Little Giant of Gospel Music", who is known for his love for spreading the Gospel of Jesus Christ through ministry and song, and his heart for the lost. His ministry is located in Hamburg, Arkansas. When asked about what ministry meant to him, Jamie shared, "Ministry is all about carrying the gospel of Jesus Christ to a lost and dying world."
He has appeared on stage with many Southern Gospel artists down through the years such as The Hinsons, Kevin Spencer Family, The Whisnants, The Singing Cookes, Wendy Bagwell and The Sonliters, and The Hoppers.
While listening to his latest project Why I Do What I Do, you will find great songs such as, "A Little Faith", "The Lighthouse", "He's All I Need", and "When Jesus Walked." You will find that as you listen to this album, that the Holy Spirit begins to come and minister to you. But not only that, you will begin to lift up your hands in a sign of surrender and praise, thanking God for what He has brought you from and the trials He has brought you through.
To find out more information about Jamie and his ministries, you can visit his website, http://www.jamiecoulterministries.com. For booking inquiries, you can give him a call at (870)-500-4122.
For media inquiries and interviews:
Andrew B. Brunet
Lighthouse Media Group
Artist Bio:
Meet Jamie Coulter, the "little giant of Gospel Music", located in the heart of Hamburg, Arkansas. Throughout the years of Southern Gospel ministry, you will find that Jamie has shared the stage with countless artists such as The Hinsons, The Kevin Spencer Family, The Whisnants, The Singing Cookes, Wendy Bagwell and Sonlighters, and The Hoppers. Many of you have probably heard his song "Crippled Boy's Prayer", which he performed at the age of 6 on Weekend with the Stars Telethon. His recent release "Why I Do What I Do" is available for purchase via his website, where you can also find more information about his ministry, http://www.jamiecoulterministries.com
For more Southern Gospel news click here.
Tags: Jamie Coulter
LAKESIDE SIGNS WITH MORNING GLORY MUSIC, A DIVISION OF MOUNTAIN FEVER RECORDS
By Lorraine Walker / May 6, 2019
Cindy Hughlett Records 10th Album With Legendary Producer Ron Oates
By Rob Patz / May 6, 2019
Wilburn & Wilburn Set To Return with New Album
Sacred Harmony- Great Things Happening!
By Rob Patz / April 30, 2019
Bridge of Grace from Merced CA.
Pruitt Family Highly Anticipated Album Releases Today
Bill Griffin: The Influence and Reach of a Gospel Music Promoter


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Things To Do in Hartford, CT
Matrix Gallery
Hartford, CT Local Resources
in Hartford, CT
Did you know that there are approximately 850 million visits to museums every year in America? They contribute $50 billion to the U.S. economy each year. If you think about how marvelous museums are, these numbers make sense. Museums can transport you to old worlds, future worlds, worlds you never thought you could be a part of.
If you're looking to add some of those unknown worlds to your day, check out our list of museums in the area. They are all within driving distance and offer a variety of topics that will enchant every member of the family.
Hartford, CT 06106 Directions
History buffs, lifelong residents or just naturally curious minds will enjoy visiting the Connecticut State Library and State Archives. This facility is an Executive Branch agency of the State of Connecticut and provides a variety of information that includes historical documents and information, public records, and administrative services. There is also a moderately-sized but largely interesting museum in the building that does an impressive job of spotlighting all things Connecticut.
77 Forest St
Hartford resident Harriet Beecher Stowe attracted plenty of attention when she published her anti-slavery novel Uncle Tom's Cabin. Her outspoken nature and desire to champion issues like human dignity and equality were hallmarks of not only her work, but of the woman herself. You can learn more about her and her various campaigns to end racism when you visit the Harriet Beecher Stowe Center. The center and museum of sorts hosts various exhibits that stand alongside Stowe's personal effects that all work together to tell the story of this courageously outspoken author whose battle is still being fought today. The center spotlights current projects that are still being implemented in Stowe's honor.
Mark Twain House & Museum
351 Farmington Ave
Even if you've read Huckleberry Finn or Tom Sawyer several times, you still may not really know much about the man who created these timeless works of American literature. A visit to Hartford's Mark Twain House & Museum will change all that in a truly dramatic fashion. The historic home has been meticulously preserved and treats visitors to the sight of various personal items that belonged to Twain, who made his home here before and after he met with his staggering success. Among the most striking pieces at this house museum are his writing desk, eyeglasses and other personal curiosities, and various first editions of his most famous books.
The kids will love exploring the world of art that is presented at the Wadsworth Atheneum Museum of Art. Multimedia pieces, paintings and various collections feature the best of European art as well as several visually challenging works that range from the modern to the impressionistic. In addition to the many exhibits and attractions throughout the various galleries, the museum features an impressive schedule of events that include poetry readings, musical performances and much more.
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In our first April team building question, you are encouraged to consider the question - "What related disciplines and areas are important to learn from, to help you do your work more effectively". In today's business context, cross-sectoral knowledge, or multi-disciplinary thought, can be very important. The ongoing changes and innovations required, can often benefit from ideas and practices from related fields.
As a team, consider what are the related fields you can be learning from? What are the challenges you are facing that other teams might have already experienced? Who on your team might already have some different thinking on this?
Yesterday as I was working on research for my next book, one of the books I encountered was related to this topic - The Silo Effect: The Peril of Expertise and the Promise of Breaking Down Barriers.


For just 25,00 Euros per person per day you can spend your vacation in our vacation homes.
The prices are meant for a booking including 2 people in the flat Veilchen or Annemone for a minimum of 3 days and for a booking including 3 people in the flat Enzian or Edelweiß for a minimum of 3 days.
Children between 3-15 years old only pay half-price.
(Cribs and highchair are available for you).
Your four-legged family member stays for free.
Deposit: We welcome written reservations via e-mail. The reservation becomes binding once the deposit is paid by 50 € per week.
Surcharge for breakfast: For bed & breakfast we charge 7 € per person and children up to 14 years 5 €.
The final cleaning, the electricity and the heating are included in the price.
Please understand that in case of late cancellations (4 weeks prior to the start of your holiday) we will retain the deposit and in case of a late arrival or early departure we will charge 100% of the booked price.
We are looking forward to your visit. You may cancel your reservation until 3 months prior to arrival without any cancellation fee. From 3 months to 4 weeks before arrival we charge 3 days of the price. In the last 4 weeks before arrival the cancellation fee is 70 % of the price. However, we recommend that together with the booking of your stay you close a "Cancellation Insurance".
Check premiums and book at Europäische Reiseversicherung.
For the purposes of the GDPR, we inform you that your data will be used and saved exclusively for processing your application and will not be disclosed or distributed to third parties. Regarding data processing, you are entitled to all rights according to the GDPR. The holder of the rights is Paul Kruselburger – For more information about your rights, please visit here .


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Broadway Goes Eighties with Rock of Ages
Ashley Niro
Former American Idol contestant Constantine Maroulis has brought his rock edge from the TV screen to the Broadway stage in the new musical Rock of Ages. It is a comical love story told through popular 1980s songs by Styx, Journey, Bon Jovi, Twisted Sister, Pat Benatar, Poison and more. Maroulis stars as big dreamer Drew aka Wolfgang Von Colt who hopes to become a famous rock star. It is love at first sight on California's Sunset Strip when Drew meets Sherrie, a small town Kansas girl dreaming of being an actress. Drew and Sherrie's attempt to move past their friendship becomes complicated when pompous rock star Stacee Jaxx takes a short-lived interest in Sherrie. Meanwhile, more trouble strikes the Strip when a German businessman and his quirky son Franz scheme to industrialize the cultural landmark. It's all up to a passionate activist Regina, the Bourbon Room rock club owner Dennis, and the narrator Lonny to save the beloved Sunset Strip.
Rock of Ages on Broadway
While discovering the fate of the characters, the audience gets very involved in the musical by singing along to old favorites, rocking out during guitar solos, or waving plastic imitation lighters in the air during some of the slower rock songs—these plastic lighters are given to every member of the audience when they enter the theatre.
The wild hair, the colorful leather-friendly rock apparel, the rock club atmosphere, and famous rock songs that are recognizable to any generation all successfully bring the culture of the 1980s to the modern day world. Beneath all of the humorous innuendos and witty dialogue there are also life lessons that can be learned: follow your heart, fight for what is right, and most of all "Don't Stop Believin" in your dreams. Rock of Ages will definitely not disappoint music lovers of any age. This Broadway rock concert is sure to leave every member of the audience with a new appreciation for the '80s. For more information visit RockOfAgesMusical.com.
Women's basketball wins defensive battle vs. Saint Michael's
Caribbean Student Association gears up for their spring Fashion Show
The most wonderful time of the year at the university
Football falls to No. 11 Shepherd in NCAA Playoffs
Five field hockey players earn conference honors
Local bands shake the ground at Fall Fest
Charger Bulletin News 4/22/2022
'Precipice of Extinction' gallery show encourages student action for environmental change
Students attend first in-person Career Fair since COVID-19
Myatt Center encourages students to seek efforts of diversity and inclusion on campus


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Matador Gored to Death By Bull After Making Fatal Misstep In Ring
Ivan Fandino is the first performer to die in a French ring in nearly 100 years.
By The Editors of Men's Health
youtube/Azby59
Celebrated Basque matador Ivan Fandino died Saturday after being fatally gored through the chest by a bull. He was 36. (Fandino isn't the only matador to suffer a serious bullfighting accident this year, either; this man lost his glass eye in the ring.) Fandino was performing at the Aire-sur-l'Adour bullfighting festival near Pau in southern France when the bull, Burp, appeared to catch him in the side during a pass. While attempting to flee, Fandino became entangled in his cape and fell to the ground, where the bull set upon him with its horns. Other matadors were able to distract the animal before carrying Fandino from the ring.
However, on the way to the hospital, Fandino suffered two heart attacks, according to Agence France Press. He is survived by a wife and daughter. The bull was put down.
It was not the first time Fandino was injured in the bullfighting ring. In 2015, a bull sent him airborne in Pamplona, and in 2014 he was knocked unconscious in a bullfight in France. The sport of bullfighting at-large is popular in France and Spain, with some 1,800 events occurring each year in the latter country.
It is thought this event will renew debate over the merits of bullfighting as a sport and spectacle. Close to 1,000 bulls are killed for sport each year in France, and though Fandino is the first matador killed in France in nearly 100 years, it is possible activists will seek to overturn the country's 2012 legalization of the sport.
Below is footage of the fatal incident. The video is graphic.
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For the original Time article and video click here.
(MICHIGAN CITY, Ind.) — For the second time in five months, an infant has been left in a baby box at a northwestern Indiana volunteer fire station.
Lt. Chuck Kohler says he was on scene tending to the baby girl less than a minute after receiving a page Sunday night.
The page alerted him that alarms had been triggered on the Safe Haven Baby Box at the Coolspring Township Volunteer Fire Department, near Michigan City. Kohler says everything worked as planned.
The padded, climate-controlled box was installed about two years ago. The program allows a mother to relinquish her newborn anonymously, without fear of prosecution.
Another baby girl was safely rescued after being left in the box on Nov. 7.


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Richard Tofel, President of ProPublica, Joins Denver Frederick
by Denver Frederick | Sep 5, 2017 | Guest Interview
The following is a conversation between Richard Tofel, President of ProPublica, and Denver Frederick, Host of The Business of Giving on AM 970 The Answer in New York City. Denver: There have been few industries that have been disrupted more in recent years than have...
Jacob Harold, President and CEO of GuideStar, Joins Denver Frederick
GuideStar is the largest platform of information about data for nonprofits. In this segment, Jacob Harold, President and CEO of GuideStar, talks about how both individual donors and nonprofit executives leverage the data that GuideStar curates. He also discusses...
Kate Roberts of Maverick Collective and the Women-Centric Model of Philanthropy
by Denver Frederick | Aug 24, 2016 | Guest Interview
"Money doesn't solve problems. People do!" says Kate Roberts, co-founder of the Maverick Collective, an organization that aims to redefine what it means to be a philanthropist....
Perla Ni, CEO and Founder of Great Nonprofits
by Denver Frederick | Aug 9, 2016 | Guest Interview
In this podcast, Perla Ni, the founder and CEO of GreatNonprofits speaks about her background and how it inspired her to build the organization. She discusses the importance of "beneficiary feedback" and how those served by nonprofits are sometimes best able to...
Mark Tercek and His Views On True Philanthropy and Nature Protection
Mark Tercek talks about the Nature Conservancy's collaborative, science-grounded approach to land, water, and climate issues — embedded in the nonprofit's DNA when it was founded 65 years ago to purchase and protect the Mianus River Gorge in upstate New York....


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Daily Market Review > News > The Crown Season 5: Imelda Staunton to Portray the Character of Queen Elizabeth
Posted by Vijayalakshmi Devanathan December 12, 2020
The Crown is a Netflix drama based on an acclaimed play called "The Audience", by Peter Morgan. With it being renewed for a brand new season, here is everything you need to know:
The first season of The Crown dropped on Netflix in 2016, and it has garnered a good fan following since then. The series deals with the life and times of Queen Elizabeth II and has fictionalized it to some extent.
Season 1 through 4 deals starts off with her wedding in 1947, with Winston Churchill's resignation as Prime Minister, takes a look at her period of reign between 1964 and 1977, and finally comes to a stop at Margaret Thatcher's premiership where Prince William and Princess Diana are introduced. Season 4 left off at Thatcher leaving office, and we believe that this is exactly where the next season would take off. The fourth season has given us a glimpse of the period between 1977 and 1990. For season 5 of The Crown, it is speculated that the series will deal with the early 1990s, ending with Princess Diana's tragic death in 1997. With the 6th season being the final one, we hope to see the next installment bring a lot of important details to light – for it all to come together in the end.
The Crown Season 5: who is involved, and when will we get to see it?
The Crown is created by the original writer of the play mentioned above, Peter Morgan, along with Amy Jenkins, James Graham, Tom Edge, and David Hancock.
In Season 5 of The Crown, fans will see Imelda Staunton, most famous for her role as Professor Umbridge in Harry Potter, playing the Queen's role. Apart from this, we will also see Elizabeth Debicki as Princess Diana, Jonathan Pryce as Prince Philip and Lesley Manville as Princess Margaret. The rest of the cast will feature stars that have already appeared in the previous seasons and some that are new to the series.
Imelda Staunton to play Queen Elizabeth
The show's cast is one that keeps changing due to the changes that one would see in the different time periods that the show covers. This has led the audience to have a more wholesome experience, with new stars being presented to them every season. Although they might sometimes end up growing attached to a certain cast member, it makes more sense to keep the dice rolling.
The Crown Season 5: what to expect?
The Crown has always managed to deliver when it comes to what the audience expects of it. In fact, it is being rumored that the fourth season of the show garnered more views than the actual wedding of Prince Charles and Princess Diana. This shows the series' immense popularity amongst the crowd. People from all walks of life tune in to watch The Crown because it has multiple entertainment layers and does not focus on one very saturated point throughout its airtime.
If what we guess is right, we would potentially see a lot of high-intensity drama in the next season as the show is heading towards the end of its time. We already know that fans would turn up in large numbers online to stream it, which already makes it a huge success from this side of the discussion.
Read More: Euphoria Season 2: What to expect from the return of Rue and Jules in the upcoming season?
Vijayalakshmi Devanathan December 12, 2020
Previous Article RWBY Volume 8 Announced its Mid-Season Break – To Continue Till 2021
Next Article Cobra Kai Season 3: Will Ali return in the upcoming season?
Atypical Season 4: Will the Casey-Izzie ship survive?


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\section{Introduction} \label{intro}

The Riemann zeta function is defined for $s=\sigma+it$ by
\begin{equation}\label{dirichlet def}
\zeta(s) := \sum_{n=1}^{\infty} n^{-s}, \qquad \sigma>1.
\end{equation}
It can be analytically continued everywhere
except for a simple pole at $s=1$.
A well-known problem in number theory is to bound the growth rate
of zeta on the critical line $\sigma = 1/2$.
This problem has led to deep
ideas in the theory of exponential sums. In
particular, the method of exponent pairs (see \cite{graham-kolesnik},
\cite[page 116]{titchmarsh}), and the Bombieri-Iwaniec
method~\cite{bombieri-iwaniec-1,bombieri-iwaniec-2}.

Since $|\zeta(\sigma+it)| = |\zeta(\sigma-it)|$,
 we can suppose that $t\ge 0$.
Starting with the series \eqref{dirichlet def},
it follows by the Euler-Maclaurin formula that $\zeta(1/2+it) \ll t^{1/2}$
for large enough $t$.
This can be improved substantially
by appealing to the Riemann--Siegel formula, which gives
 $\zeta(1/2+it)\ll t^{1/4}$.
The Weyl-Hardy-Littlewood method (see
\cite[section 5.3]{titchmarsh}) detects
a certain amount of cancellation in
the main sum of the Riemann--Siegel formula,
further improving the bound to $\zeta(1/2+it)\ll
t^{1/6}\log^{3/2} t$.
The van der Corput method (e.g.\ \cite{corput-koksma,corput-1929})
removes an extra $\sqrt{\log t}$ factor,
which sharpens the estimate to
\begin{equation}\label{corput estimate 1}
\zeta(1/2+it)\ll t^{1/6}\log t.
\end{equation}

The exponent $1/6$ in estimate \eqref{corput estimate 1} is hard to improve.
The sharpest result so far is due to Huxley~\cite{huxley},
who proved that $\zeta(1/2+it)\ll t^{32/205}\log^{\gamma} t$ for some constant
$\gamma$. Note $32/205 = 0.15609\ldots$. (See also the recent result in \cite{bourgain}.)
Assuming the Riemann hypothesis, one can show
that $\zeta(1/2+it)\ll \exp (A\log t/\log \log t)$
for some constant $A$; see \cite[\textsection{14.4}]{titchmarsh}.
Hence,
$\zeta(1/2+it)$ is conjectured to grow slower than any fixed power of $t$.

In this article, we
obtain an explicit bound of the van der Corput type \eqref{corput estimate 1}.
That is, we compute constants $C_1$ and $C_2$ such that
$|\zeta(1/2+it)| \le C_1 t^{1/6}\log t$ for $t \ge C_2$.
This is part of our work in progress about subconvexity
bounds for zeta. We are
 also motivated by the following computational considerations where
the simplicity of an explicit van der Corput estimate is
particularly attractive.

Specifically, in numerical tests of the growth rate of $\zeta(1/2+it)$,
 it is necessary to have explicit bounds. For one usually cannot distinguish
a small power of $t$ from a logarithm or a subexponential factor
unless $t$ is prohibitively large. An explicit bound offers
an unconditional measure
against which one can compare
large values of $|\zeta(1/2+it)|$
found by special numerical searches, such as those in \cite{zeta-comp}.

Another motivation comes from
the algorithms in \cite{hiary}
which employ a Taylor expansion
to express zeta as a sum
of low degree exponential sums
and their derivatives.
The size of the remainder term in these algorithms
is bounded by the highest order derivative used  and
the maximal size of a certain subdivision of the main
sum of zeta.
In this context, an improved and simple method to obtain
an explicit bound is of value as it enables reducing
the number of derivatives needed to guarantee a given error tolerance.
This in turn will improve the running time appreciably.

Explicit bounds for zeta were obtained by
Cheng and Graham \cite{cheng-graham}, and
recently by Platt and Trudgian \cite{platt-trudgian} who proved
that
\begin{equation}\label{pt est}
|\zeta(1/2+it)|\le 0.732 t^{1/6}\log t, \qquad (t\ge 2).
\end{equation}
We improve the leading constant in \eqref{pt est} by 14\%.
\begin{theorem}\label{zeta bound}
If $0\le t \le 3$, then $|\zeta(1/2+it)| \le 1.461$.
If $t \ge 3$, then
\begin{equation}\label{zeta bound eq}
|\zeta(1/2+it)| \le 0.63\, t^{1/6}\log t.
\end{equation}
\end{theorem}
A numerical computation reveals that
$\max_{t\ge 3} |\zeta(1/2+it)|/t^{1/6}\log t > 0.507$.
So, a priori, the leading constant in \eqref{zeta bound eq} cannot
be reduced below $0.507$ without an additional assumption on the size of $t$.
In fact, if one employs the Riemann--Siegel--Lehman bound
$|\zeta(1/2+it)|\le 4(t/(2\pi)^{1/4}-2.08$
from Lemma~\ref{trivial bound lemma}
for any range of $t$ at all, then the leading constant
cannot break $0.541$, as a numerical computation shows that
\begin{equation}\label{riemann siegel barrier}
\min_{t\ge 3} \frac{4(t/(2\pi)^{1/4}-2.08}{t^{1/6}\log t} > 0.541.
\end{equation}

Our proof of Theorem~\ref{zeta bound} uses a
subdivision of the Riemann--Siegel
main sum different than \cite{cheng-graham,platt-trudgian},
giving rise to a simpler optimization problem.
In particular, we divide the main sum into short
pieces of length $\approx t^{1/3}$ (which appears to be a new, and natural, subdivision;
c.f.\ Weyl's method in \cite[Section 5.3]{titchmarsh} which divides the main sum
into pieces of length $\lesssim t^{1/6}$).
This subdivision enables better control of the oscillations
in each piece
via Lemma~\ref{corput lemma} since the range of
$f'''(x)$  for us will be more restricted.
\begin{lemma}\label{corput lemma}
Let $f(x)$ be a real-valued function with three continuous derivatives on
$[N+1,N+L]$. Suppose there are $W > 1$ and $\lambda \ge 1$ such that
$\frac{1}{W} \le |f'''(x)| \le \frac{\lambda}{W}$
for $N+1\le x \le N+L$. If $\eta>0$, then
\begin{equation}
\Big|\sum_{n=N+1}^{N+L} e^{2\pi i f(n)} \Big|^2 \le
(L W^{-1/3} +\eta)
(\alpha L + \beta W^{2/3}),
\end{equation}
where
\begin{equation}\label{alpha beta formula}
\begin{split}
\alpha  &:=\alpha(W,\lambda,\eta)=
 \frac{1}{\eta} +\frac{64\lambda}{75} \sqrt{\eta+W^{-1/3}}+
\frac{\lambda \eta}{W^{1/3}}+  \frac{\lambda}{W^{2/3}},\\
\beta &:=\beta(W,\eta)= \frac{64}{15}\frac{1}{\sqrt{\eta}} + \frac{3}{W^{1/3}}.
\end{split}
\end{equation}
\end{lemma}

\begin{remark}
Lemma~\ref{corput lemma} is proved in \textsection{\ref{lemma proof}}.
This lemma is an explicit version of the process
$AB$ in the method of exponent pairs.
The condition
$W>1$ in the lemma can be relaxed to $W> 2/\pi$.
The number
$\eta$ will be chosen of size $\approx 1$
in our application, Theorem~\ref{zeta bound}.
\end{remark}

The proof of Theorem~\ref{zeta bound} completely overlooks cancellation
among the $\approx t^{1/6}$ pieces where Lemma~\ref{corput lemma} is applied.
This is the main source of inefficiency in our proof.
As far as we know, there is
no definitive mechanism to take advantage of this cancellation.
 Instead,
one works with longer pieces,
and tries to prove
cancellation within each one.

Of course, the bound \eqref{zeta bound eq} is asymptotically
 far from the truth.
And even for moderately large values of $t$, this bound
is still probably a
substantial overestimate.
Evidence for this comes from computations by J.~W.\ Bober
and the author, some of which are summarized in \cite{zeta-comp}.
In these computations, several hundred large values of zeta
were recorded by
computing $\zeta(1/2+it)$ at certain special points.
The largest value found this way was
\begin{equation}\label{largest value}
|\zeta(1/2+iT_0)| = 16244.86526\ldots,
\end{equation}
where $T_0=39246764589894309155251169284104.050622\ldots$,
so $T_0\approx 3.9\times 10^{31}$.
(To our knowledge, \eqref{largest value} is the largest value of zeta
computed so far.)
In comparison, the bound \eqref{zeta bound eq} gives
$|\zeta(1/2+iT_0)| \le 8448744$, which is about $521$ times larger
than \eqref{largest value}.
Alternatively, one can use the
van der Corput bound \eqref{vdc bound} directly.
This gives a bound that is about $507$ times larger
than our computed value.
It should be stressed, though, that \eqref{largest value}
was found by searching  a thin set of special points,
not by an exhaustive search, and so
only provides a lower bound for $\max_{t\in [0,T_0]} |\zeta(1/2+it)|$.

\section{Proof of Theorem~\ref{zeta bound}}

For the remainder of the paper, we set
\begin{equation}
c_0 :=0.63,\qquad t_0 := 9.3\times 10^7.
\end{equation}

\begin{proof}
We consider $t$ over three ranges.
In the range $0\le t \le 200$, we use the computational bound
from Lemma~\ref{computational bound lemma}.
In the intermediate range
$200\le t \le t_0$ we use the Riemann--Siegel--Lehman bound supplied by
Lemma~\ref{trivial bound lemma}.
And in the last range $t\ge t_0$ we use the van der Corput bound
supplied by  Lemma~\ref{corput bound lemma}.
\end{proof}

To handle the intermediate and last ranges of $t$, we rely on
 Lemma~\ref{riemann siegel lemma},
which is consequence of the Riemann--Siegel formula.
This lemma requires $t\ge 200$, which is the reason we treat
the initial range $t\in[0, 200]$ separately.
\begin{lemma}\label{riemann siegel lemma}
If $t \ge 200$ and $n_1=\lfloor \sqrt{t/(2\pi)}\rfloor$, then
\begin{equation}\label{rs lemma}
|\zeta(1/2+it)| \le 2|\sum_{n=1}^{n_1} n^{-1/2+it}|
+\mathcal{R}(t).
\end{equation}
where $\mathcal{R}(t):= 1.48 t^{-1/4}  + 0.127 t^{-3/4}$.
\end{lemma}
\begin{proof}
The lemma gives a small improvement on \cite[Lemma 3]{platt-trudgian}.
The improvement is that the inequality for $\mathcal{R}(t)$ is
tighter if $t\ge 200$. The lemma is stated separately for emphasis,
as it is an essential first step in all that follows.

We apply the triangle inequality to
the Riemann--Siegel formula in \cite[page 9]{gabcke-thesis} to obtain
\begin{equation} \label{eq:rsform}
|\zeta(1/2+it)| \le 2 \left|\sum_{n=1}^{n_1}
\frac{\cos(t\log n-\theta(t))}{\sqrt{n}}\right|
+ \beta \left(\frac{2\pi}{t}\right)^{1/4}
+ |R_0(t)|,
\end{equation}
where $n_1=\lfloor \sqrt{t/2\pi}\rfloor$, $|R_0(t)| < 0.127 t^{-3/4}$ for $t \ge 200$, and
\begin{equation}
\beta = \max_{0\le z\le 1}
\left|\frac{\cos \frac{\pi}{2}(z^2+3/4)}{\cos \pi z}\right|.
\end{equation}
By \cite[page 65]{gabcke-thesis}, we have $\beta < 0.93$ (more precisely,
$\beta = \cos (\pi/8)$).
The lemma now follows from the inequality
$\beta (2\pi)^{1/4}< 1.48$, and using
\begin{equation}
\begin{split}
\left|\sum_{n=1}^{n_1}
 \frac{\cos(t\log n-\theta(t))}{\sqrt{n}}\right|
 &\le  \frac{1}{2}\left|\sum_{n=1}^{n_1}
  \frac{e^{it\log n-i\theta(t)}}{\sqrt{n}}\right| +
\frac{1}{2} \left|\sum_{n=1}^{n_1} \frac{e^{i\theta(t)-it\log n}}{\sqrt{n}}\right|\\
&= \left|\sum_{n=1}^{n_1} n^{-1/2+it}\right|.
\end{split}
\end{equation}
\end{proof}

In choosing the cutoff point
for the intermediate range, we computed an approximation,
call it $t_1$, for the largest $t \ge 200$ such that
the Riemann--Siegel--Lehman bound \eqref{rs bound}
beats the van der Corput bound \eqref{vdc bound}.
This gave $t_1\approx t_0$.
To decide the leading constant in Theorem~\ref{zeta bound}, we
computed an approximation, call it $c_1$, for the smallest
$c > 0$ such that the
Riemann--Siegel--Lehman bound evaluated
at $t_1$ is smaller than $c t_1^{1/6}\log t_1$. This
gave $c_1\approx c_0$.

The computational bound in Lemma~\ref{computational bound lemma} was verified
using interval arithmetic, which is also the method used
in \cite{platt-trudgian}.

\begin{lemma}[Computational bound] \label{computational bound lemma}
If $0\le t\le 3$, then $|\zeta(1/2+it)|\le 1.461$. If $3\le t \le 200$, then
$|\zeta(1/2+it)| \le c_0\, t^{1/6}\log t$.
\end{lemma}
\begin{proof}
We implemented
the Euler-Maclaurin formula (see \cite{odlyzko-schonhage-algorithm,rubinstein-computational-methods})
using interval arithmetic.
We remark that a substantial loss is incurred in
the upper bound (and computational speed) due to the
use of interval arithmetic, but this loss is still tolerable for our purposes.

We used a main sum of length $\lceil 2 t\rceil$ terms
in the Euler-Maclaurin formula with a single correction term.
Given an interval $[a_0,b_0]$,
our program
computed an enveloping interval
$I_{out}=[a_1,b_1]$ such that
$\{|\zeta(1/2+it)|: t\in [a,b]\} \subset I_{out}$. Hence,
\begin{equation}\label{interval bound}
\max_{t\in [a_0,b_0]}|\zeta(1/2+it)| \le \max_{t\in I_{out}} |t|=b_1.
\end{equation}
With this in mind,
we partitioned the interval $[3,200]$ into consecutive subintervals
$I_q:=[q/Q,(q+1)/Q]$, where $q=3Q,\ldots,200Q-1$ and $Q=2^7$.
For each $I_q$, our program returned an enveloping interval $I_{q,out}$
which we used in
 \eqref{interval bound} to verify that
\begin{equation}\label{check est}
\frac{\max_{t\in I_q}|\zeta(1/2+it)|}{(q/Q)^{1/6}\log(q/Q)}\le c_0.
\end{equation}
The estimate \eqref{check est} held for all relevant $q$, in fact, with a
smaller constant of $0.595$.

To verify the bound $|\zeta(1/2+it)|\le 1.461$
for $t \in [0,3]$, one could prove that $|\zeta(1/2+it)|$, $0\le t\le 3$,
attains its maximum at $t=0$.
However, this seemed unduly complicated. Instead,
we fell back on
our interval arithmetic program after modifying some its
parameters. Specifically, we used the Euler-Maclaurin formula
with a main sum of $\lceil 60(t+1)\rceil$ terms, which is much longer than
before.
We kept a single correction term, and
also used a finer partition with $Q=2^{14}$.
The longer main sum
for  $0\le t\le 3$ ensured that the error in the the Euler-Maclaurin
formula was sufficiently small. Given this, we
were able to verify the claimed bound.
\end{proof}

\begin{lemma}[Riemann--Siegel--Lehman bound] \label{trivial bound lemma}
If $t \ge 200$, then
\begin{equation}\label{rs bound}
|\zeta(1/2+it)| \le \frac{4t^{1/4}}{(2\pi)^{1/4}} - 2.08.
\end{equation}
In particular, for $200\le t\le t_0$, we have
$|\zeta(1/2+it)| \le c_0\, t^{1/6}\log t$.
\end{lemma}
\begin{proof}
This lemma gives a small improvement on the Lehman bound in \cite[Lemma
2]{lehman}. The improvement is in the term $-2.08$, which is significant if $t$
is not too large.

We start with the bound furnished by the Riemann--Siegel Lemma~\ref{riemann siegel lemma}.
To bound the main sum there, we employ the estimate
\begin{equation}\label{integration step}
\begin{split}
2\Big|\sum_{n=1}^{n_1} \frac{e^{it\log n}}{\sqrt{n}}\Big| &\le
2\sum_{n=1}^5 \frac{1}{\sqrt{n}}+ 2\int_5^{n_1}
\frac{1}{\sqrt{x}}\,dx\\
&= 2\sum_{n=1}^5 \frac{1}{\sqrt{n}}+ 4\sqrt{n_1}-4\sqrt{5}.
\end{split}
\end{equation}
Note that $n_1=\lfloor \sqrt{t/(2\pi)}\rfloor \ge 5$ for $t\ge 200$, so
the integration step in \eqref{integration step} makes sense.
Also, we have
$2\sum_{n=1}^5 n^{-1/2} - 4\sqrt{5} < -2.48$.
To bound the remainder term $\mathcal{R}(t)$ in the Riemann--Siegel Lemma~\ref{riemann siegel
lemma}, we employ the estimate
\begin{equation}\label{rem step}
\mathcal{R}(t)\le 1.48(200)^{-1/4} + 0.127(200)^{-3/4} < 0.4,\qquad (t\ge 200).
\end{equation}
The first part of the lemma now follows on
substituting \eqref{integration step} and \eqref{rem step} back
into \eqref{rs lemma}, and noting that $\sqrt{n_1}\le
\big(t/2\pi\big)^{1/4}$.

To prove the second part of the lemma, we use \verb!Mathematica! to
verify that
there is no solution to the equation
\begin{equation}
\frac{4t^{1/4}}{(2\pi)^{1/4}} - 2.08 = c_0\, t^{1/6}\log t,\qquad
(200\le t\le t_0),
\end{equation}
and that the l.h.s of the equation is smaller than
the r.h.s. at $t=200$,
and therefore throughout the range $t\in [200,t_0]$.
\end{proof}

\begin{lemma}[Van der Corput bound] \label{corput bound lemma}
If $t \ge t_0$, then
\begin{equation}\label{vdc bound}
|\zeta(1/2+it)| \le
a_1 t^{1/6}\log t + a_2 t^{1/6}+ a_3
\end{equation}
where
$a_1:=0.6058490462530$,
$a_2:=0.5743984045897$,
and $a_3:= -2.884626766806$.
In particular, for $t\ge t_0$, we have $|\zeta(1/2+it)|\le c_0 t^{1/6}\log t$.
\end{lemma}
\begin{proof}
We plan to divide the main sum in the Riemann--Siegel
Lemma~\ref{riemann siegel lemma} into pieces of length $\approx t^{1/3}$,
then apply the van der Corput
Lemma~\ref{corput lemma} to each piece.
To this end, let
$K =\lceil t^{1/3}\rceil$
and $R = \lfloor n_1/K\rfloor$,
where, as before, $n_1=\lfloor \sqrt{t/2\pi}\rfloor$.
Here, $K$ is the length of each piece (except possibly the last one, which
can be shorter), and $R+1$ is
the total number of pieces.

The remainder term
$\mathcal{R}(t):=1.48 t^{-1/4}  + 0.127 t^{-3/4}$
in the Riemann--Siegel Lemma~\ref{riemann siegel lemma}
satisfies
$\mathcal{R}\le \mathcal{R}(t_0)$ for $t\ge t_0$.
Thus, carrying out the aforementioned subdivision,
and using the triangle inequality, we obtain
\begin{equation}\label{main sum division}
\begin{split}
|\zeta(1/2+it)| \le&  2\sum_{n=1}^{r_0 K-1} \frac{1}{\sqrt{n}}+2\sum_{r=r_0}^{R-1}
\Big|\sum_{n=rK}^{(r+1)K-1} \frac{e^{it\log n}}{\sqrt{n}} \Big|\\
&+2\Big|\sum_{RK}^{n_1} \frac{e^{it\log n}}{\sqrt{n}}\Big|+\mathcal{R}(t_0).
\end{split}
\end{equation}
Here, we trivially estimated the part of the
main sum with $n<r_0K$,
where $r_0$ is a positive integer to be chosen later.
Also, we used $R>0$, which is due to $t\ge t_0$.

To bound the first sum in \eqref{main sum division},
we note that
$r_0K\ge \lceil r_0 t_0^{1/3}\rceil$.
So, proceeding as in \eqref{integration step}, we obtain
\begin{equation}
 2\sum_{n=1}^{r_0 K-1}  \frac{1}{\sqrt{n}}
 \le
 4\sqrt{r_0K}+ \mathcal{I}(r_0,t_0),
\end{equation}
where
\begin{equation}
\mathcal{I}(r_0,t_0) :=
2\sum_{n=1}^{\lceil r_0 t_0^{1/3}\rceil-1} \frac{1}{\sqrt{n}}
 -4\sqrt{\lceil r_0 t_0^{1/3}\rceil-1}.
\end{equation}
To bound the remaining sums in \eqref{main sum division},
we use partial summation~\cite[(5.2.1)]{titchmarsh}.
Put together, if we let
\begin{equation}
S:=2\sum_{r=r_0}^R \frac{1}{\sqrt{rK}} \max_{\Delta \le K}
\Big|\sum_{k =0}^{\Delta-1} e^{it\log (rK+k)}\Big|,
\end{equation}
then we obtain
\begin{equation}\label{zeta bound 0}
|\zeta(1/2+it)| \le S+ 4\sqrt{r_0K} +
\mathcal{I}(r_0,t_0)+\mathcal{R}(t_0).
\end{equation}

In order to bound the inner sum of $S$,
we employ the van der Corput Lemma~\ref{corput lemma}.
Setting
\begin{equation}
f(x) := \frac{t}{2\pi}\log(rK+x), \qquad (0\le x \le \Delta-1),
\end{equation}
then
\begin{equation}
f'''(x) = \frac{t}{\pi (rK + x)^3}, \qquad (0\le x\le \Delta -1).
\end{equation}
So, on defining
\begin{equation}\label{W lambda def}
W :=W_r=\frac{\pi (r+1)^3K^3}{t},\qquad \lambda:=\lambda_r =\frac{(r+1)^3}{r^3},
\end{equation}
and noting that $\Delta \le K$, we obtain
\begin{equation}
\frac{1}{W} \le |f'''(y)|\le \frac{\lambda}{W},\qquad (0\le y\le K).
\end{equation}
We apply Lemma~\ref{corput lemma}
with $L=K$, $\alpha_r:=\alpha(W_r,\lambda_r,\eta)$,
$\beta_r:=\beta(W_r,\eta)$, and with $\eta >0$ to be chosen later.
 This yields
\begin{equation}
S \le  2\sum_{r=r_0}^{R} \frac{1}{\sqrt{rK}}
\sqrt{\alpha_r K^2 W_r^{-1/3} + \eta \alpha_r K + \beta_r K W_r^{1/3}
+\eta\beta_rW_r^{2/3}}.
\end{equation}
We factor out $K^2W_r^{-1/3} = \frac{K t^{1/3}}{\pi^{1/3}(r+1)}$ from under the
square-root. This gives
\begin{equation}\label{S bound CalB}
S\le  \frac{2 t^{1/6}}{\pi^{1/6}}\sum_{r=r_0}^{R} \sqrt{\frac{\mathcal{B}_r}{r(r+1)}},
\end{equation}
where
\begin{equation}
\mathcal{B}_r :=\alpha_r+\frac{\eta \alpha_r W_r^{1/3}}{K} + \frac{\beta_r W_r^{2/3}}{K}+\frac{\eta \beta_r W_r}{K^2}.
\end{equation}
Since $K< t^{1/3}+1$ and $R \le t^{1/6}/\sqrt{2\pi}$,
we have
\begin{equation}
W_r \le \pi (R+1)^3 (1+t^{-1/3})^3\le \frac{\sqrt{t}\rho^3}{2^{3/2}\sqrt{\pi}},\qquad
\rho := \Big(1+\frac{1}{R}\Big)\Big(1+\frac{1}{t^{1/3}}\Big).
\end{equation}
In addition, $K\ge t^{1/3}$, so put together we obtain
\begin{equation}\label{CalB}
\mathcal{B}_r \le \alpha_r+\frac{\eta\alpha_r \rho}{\sqrt{2}\pi^{1/6} t^{1/6}} +
\frac{\beta_r\rho^2}{2\pi^{1/3}} + \frac{\eta \beta_r\rho^3}{2^{3/2}\sqrt{\pi}t^{1/6}}.
\end{equation}
At this point, we make several observations.
First, $W_r$ is monotonically increasing in $r$, and $\lambda_r$
is monotonically decreasing in $r$.
Hence, by the definitions of $\alpha_r$ and $\beta_r$, we see that
they monotonically decrease with $r$.
So $\alpha_r \le \alpha_{r_0}$ and
$\beta_r\le \beta_{r_0}$ for $r\ge r_0$.
Second, we fix $\eta = \eta_0:= (75/64)^{2/3}$, which is to help balance the leading two terms in the formula for $\alpha_r$ in
\eqref{alpha beta formula}.
Third, if we define
\begin{equation}
R_0 := \left\lceil \frac{\sqrt{t_0/(2\pi)}-1}{t_0^{1/3}+1}-1\right\rceil,
\end{equation}
then $R\ge R_0$, and therefore
\begin{equation}\label{rho max}
\rho \le \rho_0 := \Big(1+\frac{1}{R_0}\Big)\Big(1+\frac{1}{t_0^{1/3}}\Big).
\end{equation}
Assembling these estimates into \eqref{S bound CalB}, and using
\begin{equation}
\sum_{r=r_0}^R\frac{1}{\sqrt{r(r+1)}}\le \log \frac{R}{r_0-1},
\end{equation}
together with the inequality $t\ge t_0$ to bound the denominators
in \eqref{CalB} from below,
we obtain
\begin{equation}\label{S estimates fin}
S \le \frac{2t^{1/6}}{\pi^{1/6}}\sqrt{\alpha_{r_0}
+ \frac{\eta_0 \alpha_{r_0} \rho_0}{\sqrt{2}\pi^{1/6} t_0^{1/6}}
+\frac{\beta_{r_0}\rho_0^2}{2\pi^{1/3}}
+  \frac{\eta_0 \beta_{r_0} \rho_0^3}{2^{3/2} \sqrt{\pi}
t_0^{1/6}}} \log \frac{R}{r_0-1}.
\end{equation}
We substitute \eqref{S estimates fin} back
into \eqref{zeta
bound 0}, use the inequality $W_{r_0}\ge \pi(r_0+1)^3$
to simplify the bounds for $\alpha_{r_0}$ and $\beta_{r_0}$,
and choose $r_0=5$ which is suggested by
numerical experimentation.
Then, we combine the resulting expression with the bounds
\begin{equation}
4\sqrt{r_0K}\le 4\sqrt{r_0(1+t_0^{-1/3})}t^{1/6},\qquad
R \le t^{1/6}/\sqrt{2\pi},
\end{equation}
and numerically evaluate the resulting constants
using \verb!Mathematica!.
On completion, this yields the first part of the lemma.

To prove the second part of the lemma, denote the r.h.s.\ of \eqref{vdc bound} by
$(*)$, and consider the equation $(*) = c_0\, t^{1/6}\log t$.
Using \verb!Mathematica!,
we find that there is no solution $t\ge
t_0$ to this equation,
and that $(*)$ is smaller than the $c_0\, t^{1/6}\log t$ at $t=t_0$,
and therefore for all $t\ge t_0$.
\end{proof}

\begin{remark}
The reason we restrict $t \ge t_0$ in Lemma~\ref{corput bound lemma}
is that the Riemann--Siegel--Lehman  bound from Lemma~\ref{trivial bound lemma}
is tighter for $t < t_0$.
So we may as well take $t\ge t_0$, which
 gives marginally better constants.
\end{remark}

\section{Proof of Lemma~\ref{corput lemma}}\label{lemma proof}

\begin{proof}
We use the Weyl-van der Corput
Lemma in \cite[Lemma 5]{cheng-graham}, but in the more precise form presented at the bottom of
page 1273.
Also, we incorporate a refinement pointed out by Platt and Trudgian
in \cite[Lemma 2]{platt-trudgian}
that allows writing the leading term in \eqref{A process}
as $L+M-1$ instead of $L+M$.
Put together, if $M$ is a positive integer, then
\begin{equation}\label{A process}
\begin{split}
\Big|\sum_{n=N+1}^{N+L} e^{2\pi i f(n)} \Big|^2 \le &  (L+M-1)\Big(
\frac{L}{M}+\frac{2}{M}\sum_{m=1}^M \left(1-\frac{m}{M}\right)|S_m'(L)|\Big),
\end{split}
\end{equation}
where
\begin{equation}
S_m'(L) := \sum_{r = N+1}^{N+L-m} e^{2\pi i (f(r+m) - f(r))}.
\end{equation}
Henceforth, we may assume that $m< L$
and $L> 1$. Otherwise, the sum
$S_m'$ is empty,
and so it does not contribute to the upper bound in \eqref{A process}.

Let $g(x) := f(x+m) - f(x)$,  where $N+1\le x\le  N+L-m$.
Then, $g''(x) = f''(x+m)-f''(x)$.
Therefore, by the mean-value theorem,
  $g''(x) = m f'''(\xi^*)$
for some $\xi^* \in (x, x + m)$.
Since we assumed that $1\le m<L$ and $L>1$ then
$(x,x+m)\subset [N+1,N+L]$.
So, given our bound on $f'''$, we deduce that
\begin{equation}
\frac{m}{W} \le |g''(x)| \le \frac{m\lambda}{W},\qquad
(N+1\le x\le N+L-m).
\end{equation}
Applying the van der Corput Lemma in
\cite[Lemma 3]{cheng-graham} to $S_m'(L)$
 thus yields
\begin{equation}\label{corput second der}
|S_m'(L)| \le
\frac{8\lambda L\sqrt{m/W}}{5}
+ \frac{3 \lambda L m }{W}+ \frac{8\sqrt{W/m}}{5}
+3.
\end{equation}
We substitute \eqref{corput second der} into \eqref{A process}, then execute
the summation over $m$ using the estimates
that appear after \cite[Lemma 7]{cheng-graham}; namely,
\begin{equation}\label{trapz rule}
\sum_{m=1}^M \left(1-\frac{m}{M}\right)\sqrt{m} \le \frac{4M^{3/2}}{15},
\qquad
\sum_{m=1}^M \left(1-\frac{m}{M}\right)\frac{1}{\sqrt{m}} \le
\frac{4\sqrt{M}}{3},
\end{equation}
as well as the Euler-Maclaurin summation estimates
\begin{equation}
\sum_{m=1}^M \left(1-\frac{m}{M}\right)
<\frac{M}{2},\qquad
\sum_{m=1}^M \left(1-\frac{m}{M}\right)m < \frac{M^2}{6}.
\end{equation}
From this, we conclude that
\begin{equation}\label{corput S' estimate}
\sum_{m=1}^M \left(1-\frac{m}{M}\right)|S_m'(L)| \le
\frac{32\lambda L M^{3/2}}{75\sqrt{W}}
+ \frac{\lambda L M^2}{2W}
+ \frac{32\sqrt{WM}}{15}
+ \frac{3M}{2}.
\end{equation}
In particular,
 substituting \eqref{corput S' estimate} back into \eqref{A process},
we obtain
\begin{equation*}
\Big|\sum_{n=N+1}^{N+L} e^{2\pi i f(n)} \Big|^2 \le  (L+M-1)\left(
\frac{L}{M}+\frac{64\lambda L}{75}\sqrt{\frac{M}{W}}
+ \frac{\lambda L M}{W}
+ \frac{64}{15}\sqrt{\frac{W}{M}}
+ 3
\right).
\end{equation*}
We choose $M=\lceil \eta W^{1/3}\rceil$
for some free parameter $\eta >0$ that can be optimized
(usually, $\eta$ will be around $1$).
This choice is in order to balance the first two
terms on the r.h.s.\ as they typically dominate
in our application.
So, now, appealing to the inequality $\eta W^{1/3} \le
M\le \eta W^{1/3} + 1$, we deduce that
\begin{equation}
\begin{split}
\Big|\sum_{n=N+1}^{N+L} e^{2\pi i f(n)} \Big|^2 \le&
(L+\eta W^{1/3})\Big(\frac{L}{\eta W^{1/3}}+
\frac{64\lambda L}{75}\sqrt{\frac{\eta W^{1/3}+1}{W}}\\
&+\frac{\lambda L (\eta W^{1/3}+1)}{W}+
\frac{64}{15}\sqrt{\frac{W}{\eta W^{1/3}}}+
3\Big).
\end{split}
\end{equation}
We factor out $LW^{-1/3}$ from the first three terms in the second bracket,
and $W^{1/3}$ from the last two terms. This gives
\begin{equation*}\label{fin estimate}
\begin{split}
\Big|\sum_{n=N+1}^{N+L} e^{2\pi i f(n)} \Big|^2
\le& (L+ \eta W^{1/3})
\frac{L}{W^{1/3}}\Big(\frac{1}{\eta}+\frac{64\lambda}{75} \sqrt{\eta +W^{-1/3}}\\
&+\frac{\lambda (\eta+W^{-1/3})}{W^{1/3}}\Big)
+  (L+ \eta W^{1/3})W^{1/3}\Big(\frac{64}{15\sqrt{\eta}}
+3W^{-1/3}\Big).
\end{split}
\end{equation*}
Last, the lemma follows on recalling the definitions of $\alpha$ and $\beta$ in
\eqref{alpha beta formula}.
\end{proof}

\bibliographystyle{amsplain}

redpajama_set_name: RedPajamaArXiv


Fitness trackers cannot tell us what to do, they can only recap the exercise we have performed. This may help or as many are finding it can prove to be irrelevant as fitness or cardiovascular fitness to be exact is only one part of the many facets that make up peak physical conditioning. Over training in one of these facets can actually lead to fitness related illness.
The body works on many different levels to adjust to the lifestyle we present it with. It will strengthen, increase oxygen capacity, become more flexible, fast, agile and powerful. This can either be through the work we do, the sporting activities or the exercise stresses we place our body under.
Functional fitness is a good indicator of our bodies ability to perform at its peak depending on the activity. Functional fitness is also impossible for fitness trackers to calculate or standardise. We have to listen to our body and target our exercise specifically to achieve true fitness functionality.
The Rooboard was designed for the best fitness and body shaping results in the shortest possible time span. This small piece of fitness equipment has been designed to enhance body weight training and isolate specific muscle groups.
Exercises can be performed as specific muscle group routines or as high intensity interval workouts(HIIT). The beauty of this product is in its small size, adaptability and durability. It has been designed for total body training and is expected to be one of the top selling exercise products in 2015.


text:
Seth Macfarlane >
Seth MacFarlane Pulls Brakes On Live-Action 'Flintstones' Project
By Daniel Falconer in Movies / TV / Theatre on 18 September 2017
Follow Seth Macfarlane
The actor admits he struggled to find differences between Fred Flintstone and Peter Griffin.
Having created huge animated successes 'Family Guy' and 'American Dad', as well as debuting his new sci-fi comedy series 'The Orville' earlier this month, Seth Macfarlane looks to be riding an incredible wave of success that shows no signs of breaking any time soon.
Seth MacFarlane promotes his new series 'The Orville'
One of his many other projects that were said to be in the pipeline was a live-action 'Flintstones' television series, which would bring the Hanna-Barbera characters to the small screen in a way like never before. Unfortunately, for fans of the franchise and of MacFarlane, he doesn't seem to be feeling very passionate about the project at all as of late.
Speaking during a Reddit AMA, the actor and creator was asked if his live-action 'Flintstones' project would ever happen, to which he replied: "As of now, probably not. Honestly I couldn't figure out a way to find enough differentiation between modern-day Fred Flintstone and... Peter Griffin."
Despite the initial disappointment, it's refreshing to find such honesty from someone like MacFarlane, who's in the easy enough position to say he will still be working on something and that he hopes he can bring it to viewers in the near future. Instead, in allowing us all in on what's been happening behind-the-scenes with just a few words, he's not giving any false hope.
If he changes his mind in the future, there are plenty of places he could go to find inspiration, including DC Comics' launch of a string of new books that focused on the 'Flintstones', bringing a grittier, darker tone to proceedings.
Whatever the case may be, we at least know now not to get excited about any immediate 'Flintstones' prospects. That is of course unless somebody else expresses an interest in working with the brand! We'll see how this all goes down...
More: Seth MacFarlane Teases Unique New Sci-Fi Series 'The Orville'
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I know your birthday is not until May, but you have done so many things lately that I am so proud of. In August, you went through a huuuge puddle from a tropical storm. I was worried we wouldn't make it through, but I should have known better. You're a survivor. You showed that puddle who was boss, unlike the little white car that succumbed to the water in front of us.
Then in September, there was a bug inside of you and you didn't freak out. I freaked out, but you stayed calm. You did not even seem to mind my screaming. I don't know where the bug went, but I am sure you took care of him (read: destroyed him) because you and your 5-star safety rating are my protector.
Even this morning you were there for me. When we were at the stoplight, and a man got out of the car in front of us, and he was holding a sledgehammer – you did not falter. I know that you would have run him over to save me if I had asked you to. The man just hit his own car a couple times, which was weird. You should never have to see vehicular violence like that. Please know that I would never, ever hit you.
Have fun with the other cars in the parking lot. I will see you at 5:00.


text:
Album News, Tour Dates, Tracklist — September 8, 2011 at 7:40 am
The Fall to release 'Ersatz G.B.' — 29th studio album — in November, embark on U.K. tour
Manchester-bred post-punk legends The Fall will release their 29th studio album in 35 years — a 10-track collection called Ersatz G.B. — in November, when they'll also embark on an nine-date tour of their native U.K. to mark the record's arrival.
The album is set to be released on CD, LP and as a digital download on Nov. 14 by Cherry Red Records; the label also has announced it plans to precede the record with a yet-to-be-announced 7-inch single featuring an exclusive B-side.
Billed by Cherry Red as "retain(ing) many of their most distinctive elements whilst offering a fresh take on Mark E. Smith's familiar style and subject matter," the new album finds band mastermind Smith accompanied once again by the same relatively stable Fall lineup that recorded last year's Your Future Our Clutter and the 2008 release Imperial Wax Solvent: Smith's wife Elena Poulou on keyboards, Dave "The Eagle" Spurr on bass, Peter "P.P." Greenway on guitar and Keiron Melding on drums.
Tracklist: The Fall, Ersatz G.B.
1. "Cosmos 7"
2. "Taking Off"
3. "Kennedy"
4. "Mask Search"
5. "Greenway"
6. "Happy Song"
7. "Monocard"
8. "Laptop"
9. "I've Seen Them"
10. "Change"
The Fall tour dates:
Sept. 11: The Electric Frog, Glasgow, U.K.
Sept. 19: Incubate Festival, Tillburg, The Netherlands
Oct. 22: SWN Festival, Great Hall, Cardiff University, U.K.
Nov. 2: Stylus, Leeds, U.K.
Nov. 3: HMV Picture House, Edinburgh, U.K.
Nov. 4: Riverside, Newcastle, U.K.
Nov. 5: Fibbers, York, U.K.
Nov. 15: The Junction, Cambridge, U.K.
Nov. 17: Concorde 2, Brighton, U.K.
Nov. 18: The Auditorium, Leicester, U.K.
Nov. 24: indigO2, North Greenwich, London, U.K.
Nov. 26: Mr Kyps, Poole, U.K.
Dec. 2-4: All Tomorrow's Parties, Minehead, U.K.
Milestones: Mark E. Smith is 54 today; watch complete BBC documentary on The Fall
The Fall's 3CD 'This Nation's Saving Grace: Omnibus Edition' set for January release
Beggars preps 'Wonderful and Frightening World of the Fall' 'Omnibus Edition'
The Fall to release 'Your Future Our Clutter' next month, tour the U.K.
Beggars prepping 3CD 'Omnibus' reissue of The Fall's 'This Nation's Saving Grace'
Bauhaus, The Fall up for 'Omnibus' reissues from new Beggars Archive imprint
Tags Cherry Red Records Ersatz G.B. Imperial Wax Solvent Mark E. Smith The Fall Your Future Our Clutter
Jim McCabe
September 8, 2011 at 6:16 pm · Reply
How about a trip to the colonies, Mark?
Mike Hawk
September 9, 2011 at 5:25 am · Reply
Mark-uh, Adelaide-uh Australia needs you-uh. Maybe part-uh of the annual-uh Fringe Festival-uh (2nd biggest-uh in the world-uh behind Edinburgh-uh)to really put-uh the wind-uh up the masses-uh!


My order for black forest was delivered on time. The cake was fresh and taste beyond my expectation.
Blackforest cake in Oyc is so delicious and it looked so great too. Love this delivery service.
Being a crazy lover of black forest cakes, I would say this is really the delicious black forest cake I've ever tasted. Glad that I could order this anytime in online.
A sudden plan to cut the cake was made and one of my friend got the cake from OYC !!

 The cake was a Black Forest and was really nice and lovely .
Many thanks for making sure that my son gets the birthday cake well in time.

 I understand that the cake was very good!!

 Many thanks for this great experience.


text:
Enlarged to Show Detail 2 (full title: 311: Enlarged to Show Detail 2, a.k.a. E.T.S.D.2) is the second documentary created by the Multi-genred band 311 in 2001. This is their second video documenting their experiences as a band promoting what they consider to be peace and a positive outlook on life.  The video carries a Parental Advisory due to explicit lyrics and large display of adult content.

Enlarged to Show Detail 2 was certified as a Gold selling video by the RIAA.

 Format: Explicit Lyrics
 Rated: NR
 Studio: Bmg/Volcano/Capricorn
 DVD Release Date: December 11, 2001
 DVD Features:
 Number of discs: 2

Track listings

Disc 1 (DVD)
Intro 	2:25
3-11 Day 	6:00
The Hive 	1:56
Tim Mahoney 	2:03
311 in Japan 	3:23
Nick Hexum 	2:44
311 Milk Challenge 	4:05
Old School 	1:41
SA Martinez 	6:58
Tolerance 	7:24
Halloween 	1:38
Chad Sexton 	2:40
Weenie Roast 	3:21
P-Nut 	3:39
Small Venues 	7:28
The Fans 	1:50
Management & Crew 	7:39

Disc 2 (Bonus CD EP)

Dancehall
Bomb the Town
Will The World (Instrumental)
We Do It Like This
Dreamland (Instrumental)
I'll Be Here Awhile (Acoustic Version)

Track Listing info from MusicMoz

External links

Documentary films about rock music and musicians
311 video albums
2001 video albums
2001 live albums
2001 EPs
Live video albums
2000s English-language films

redpajama_set_name: RedPajamaWikipedia


text:
Why the Choking Game Is Extremely Dangerous for Teens
Mental Health A-Z
Race and Identity
Sleep and Dreaming
The Verywell Mind Podcast
Mental Health Tracker
The Breakout Issue
Verywell Mind's content is for informational and educational purposes only. Our website is not intended to be a substitute for professional medical advice, diagnosis, or treatment.
Jennifer O'Donnell
Jennifer O'Donnell holds a BA in English and has training in specific areas regarding tweens, covering parenting for over 8 years.
Verywell Mind content is rigorously reviewed by a team of qualified and experienced fact checkers. Fact checkers review articles for factual accuracy, relevance, and timeliness. We rely on the most current and reputable sources, which are cited in the text and listed at the bottom of each article. Content is fact checked after it has been edited and before publication. Learn more.
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Fact checked by Adah Chung
Adah Chung is a fact checker, writer, researcher, and occupational therapist.
Be sure you talk to your child about the dangers of the choking game, and answer any questions your tween might have. Photo: APatterson, freeimages.com
The choking game is a dangerous practice of tweens and teens in which they self-strangulate in order to achieve a brief high. The high is the result of oxygen rushing back to the brain after breathing is cut off by the practice of strangulation.
The choking game (also known as space monkey) is very dangerous and can easily lead to accidental death.
Why Kids Play the Choking Game
Pass-out or fainting games have been around for generations, but there is renewed concern in the era of social media and YouTube videos, which can increase peer pressure and make them seem like a normal way to pursue a high without drugs or alcohol.
In order to achieve a high, children may use ropes, scarves, or other items to strangle themselves, either alone or within a group. The game is more likely to be deadly when such items are used, and when practiced alone rather than with a friend or group.
Prevalence of the Choking Game
According to the Centers for Disease Control (CDC), there were more than 80 deaths due to self-strangulation in children aged 6 to 19 from 1995-2007. That estimate, according to parents and advocacy groups, doesn't accurately represent how widespread the problem is. Instead, they say that the choking game claims more than 100 lives per year, but many of these are incorrectly attributed to suicide.
A review of studies on choking behavior found that 7.4% of young people had engaged in this behavior up to the age of 20. Boys are more likely to die from the choking game, but the behavior is a danger to both boys and girls.
Youths who participate in the choking game are more likely to participate in other risk-taking behavior as well.
Signs Your Child Is Participating in the Choking Game
Children who participate in the choking game may exhibit physical and behavioral symptoms or behaviors:
Marks or bruises on the neck
Bloodshot eyes
Confusion or disorientation after being alone for a period of time
The presence of unusual items such as dog leashes, ropes, scarves, bungee cords, and belts
Bleeding under the skin of the face and eyelids
Other signs may include:
Wear marks on furniture (bedposts, doorknobs, etc.)
Linens or ropes tied around doorknobs or furniture or in closets
The frequent need for privacy
Be familiar with the different names given to the choking game that you may overhear in conversation or see in your child's communications. It's also known as the pass-out game, space monkey, the fainting game, scarf game, space cowboy, California choke, the dream game, cloud nine, and purple hazing.
How to Talk to Your Child About the Choking Game
If you suspect your child has engaged in this dangerous behavior, or if you hear that children at your child's school have engaged in this practice, you need to take quick action. Talk to your child about the real dangers of the choking game, including death, memory loss, seizures, concussions, hemorrhage of the eye, stroke, and brain damage.
Also, be sure there isn't anything going on with your child that could cause depression, anxiety, or desperate practices like the choking game. Try to get to the root of your child's problems, and if necessary, enlist the help of a professional counselor.
In addition, alert your child's school and other parents should you discover that children in your area are in danger of engaging in the choking game. Above all, help your child learn how to resist peer pressure, enjoy interests and passions, and make sure your child understands that you are always available to talk should they need a good listener.
Learn the best ways to manage stress and negativity in your life.
Verywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read our editorial process to learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.
Centers for Disease Control and Prevention. Unintentional Strangulation Deaths from the "Choking Game" Among Youths Aged 6-19 Years—United States, 1995-2007.
Busse H, Harrop T, Gunnell D, Kipping R. Prevalence and associated harm of engagement in self-asphyxial behaviours ('choking game') in young people: a systematic review. Arch Dis Child. 2015;100(12):1106-1114. doi:10.1136/archdischild-2015-308187
Korioth T. Children accidentally choking themselves for a brief 'high'. AAP News. 2014;35(10):44. doi:10.1542/aapnews.20143510-44d
Bernacki JM, Davies WH. Prevention of the Choking Game: Parent Perspectives. J Inj Violence Res. 2012;4(2):73-78. doi:10.5249/jivr.v4i2.119
Defenderfer EK, Austin JE, Davies WH. The Choking Game on YouTube: An Update. Glob Pediatr Health. 2016;3:2333794X16651782. doi:10.1177/2333794X15622333
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How Sex, Drug Use, and Teen Suicide Are Connected
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Think Your Child Has ADHD? Here's a Checklist of ADHD Symptoms in Kids
Why People Do the Milk Crate Challenge and Other Risky Stunts
Playing Sports as a Child Could Prevent Mental Illness Later On
Why Do People Commit Suicide?
What Is the Cotton Ball Diet?
The Link Between Asphyxiation and Drug or Sex Addiction
The Warning Signs of Schizophrenia in Children
How Individuation Helps People Develop a Sense of Self
Is Anxiety Medication Safe for Teens?
What Is Pica?
Understanding Teens Dealing With ADD/ADHD
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text:
Ford is developing an escape room game for the Ford Mustang Mach-E
In recent years, escape room games have become more popular than they used to be. These are teams or individuals who have to figure out hidden clues and solve puzzles to get out of a virtual room and get out of the game. Ford has taken this idea and used it to make the Mustang Mach-E electric SUV, which has a lot of technical parts that make it fun to play games.
The concept escape room game from the spy genre sends players on a secret mission to deliver a very important package. The car's speaker system is used to give out directions to people. In addition, some things are turned on or used during the game. These include electric seats, automatic tailgate, air conditioning, and lights.
Except for the heater and the speaker, no game functions can be controlled while the Ford Mustang Mach-E electric SUV is in motion. As a result, players can leave the vehicle at any time and not lose the levels they have already reached. This is different from most escape room games, usually only played on a computer screen. First, the computer game is installed on an iOS device connected to the car through Apple CarPlay. Then, the game is played on an iOS device.
Because it shows what electric cars can do with the technology we have now, it is both fun and essential. Carsten Starke, a technical expert in interior materials and customer experience at Ford Research & Advanced Engineering in Europe, says it is both fun and necessary. Fun interactions between the driver and car could lead to new ideas for the future, like an interactive operating manual or even driver coaching.
The game is presently a functional concept being created by Ford Europe in conjunction with the company's Emerging Technology & Innovation group and the IOT group based in Palo Alto, California. It wants to show how games can help people learn more about how their cars work. The game also gives a glimpse into the future of possible applications. For example, the escape room game can be used to keep drivers and passengers entertained while they wait at charging stations.
Watch the video here: https://youtu.be/Q9m6AO-xMpY.
By adruby, 28 January, 2022
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text:
Home Community Insights Coscharis Group Unveils a N12 Billion Farm, Rice Mill in Anambra State
Coscharis Group Unveils a N12 Billion Farm, Rice Mill in Anambra State
November 12, 2019 | by Samuel Nwite | 1
Cosmas Maduka, the founder and chairman of Coscharis Group, has unveiled a N12 billion rice farm and processing plant in Anambra State. The unveiling event took place on the 3rd of November, and was graced by the Central Bank Governor, Godwin Emefiele, Anambra State Governor, Wilie Obiano, his Kebbi State counterpart, Alhaji Abubakar Bagudu, the Minister of State for Agriculture and Rural development, Mustapha Shehuri, among others, This Day reported.
Rice has become a big subject in Nigeria since 2015, when the President Muhammadu Buhari's administration partially banned the importation. The government said the decision to restrict rice import was in a bid to diversify the economy and move concentration away from oil to agriculture.
But the ban has resulted in hunger and economic hardship because many businesses thrived on rice importation, and locally produced rice was not sufficient to bridge the demand gap.
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Nigeria consumes more than 7 million tons of rice annually, and according to the U.S Department of Agriculture, World Markets and Trade, Nigerian farmers can only produce 3.7 million tons of rice presently. That leaves a wide number of empty stomachs to be filled.
The CBN has introduced policies to facilitate private partnership in its commitment to develop the agricultural sector of the economy. Based on the agricultural facilitation policies of the CBN, many private companies are embracing the partnership.
According to Emefiele, Coscharis rice plant is evidence that the efforts of Buhari's administration in diversifying the economy and creating jobs through focused intervention in critical areas are yielding results.
"We must also commend the determination and doggedness of Coscharis Farms to establish not only its Rice Farms but also the Processing Mill which will process not only its paddy rice, but also those paddies produced by local small holder farmers under our Anchor Borrowers Programme (ABP)," he said.
Commenting at the event, Maduka said he had the vision for farming a long time ago, but in 2015, saw "the need to develop Nigeria's agricultural sector" in line with Buhari's vision, as a reason to make the vision a reality.
"We started with a land in Anaku that was abandoned for so many years because of the peculiar terrain which is prone to flooding. Despite challenges in mechanized farm development, I can tell you today that we will soon cover the entire about 3000 hectares of land that Coscharis Farms Limited currently owns in Anaku.
"We also have plans for smallholder farmers in our surrounding communities to provide training, inputs under the out-grower scheme in cooperation with NIRSAL and other agencies.
"The plan to build a rice processing mill is motivated by our desire to fix a problem. We want to create more jobs and also want to build skills in the region.
"We want to process paddy harvested from our farm in Anaku into best quality rice. We want to contribute significantly to the government's efforts to ensure food sufficiency through local production of rice. In addition, we want to set the pace for production of best quality local rice that will cause our people to change their milled rice which is known to be rich with important nutrients.
"Rice is the most popular staple food consumed by every household in Nigeria and the country is the highest consumer of rice in the West African sub region and the second largest importer in the world, buying at least 2 million metric tons per annum. Today, we have commenced the journey to accomplish these goals.
"Coscharis Rice Processing Mill, Igbariam is a 120, 000 MT modular ultra-modern Rice Mill this is the first phase with 40, 000 MT per annum capacity. The processing mill has come to stay in order to improve the quality of life of Ndi Anambra as well as the economy of the state and Nigeria in general. The next phase of 80, 000 MT per annum will come on stream before the end of next year," he said.
The Coscharis Group is not the only conglomerate in Nigeria to embrace farming in such a large way. In 2014, the Dangote Group pledged to invest $1 billion in rice farming to reduce the import quantity of rice and to create jobs.
The group said a few days ago, that "Nigeria will soon be exporting rice," as there has been a tremendous increase in their farming activities recently. The farms, covering 150, 000 hectares across Jigawa, Kano, Kebbi, Nasarawa, Niger, Sokoto, and Zamfara states, are expected to be producing millions of tons of rice daily. The Dangote Group said it's also establishing rice mills across the country for processing.
However, the impact of these developments is yet to be felt as the price of rice keeps going higher, and more Nigerians are complaining of hunger as a result of the Nigerian closed borders. The federal government has been urged to take on the challenges stymieing farming in Nigeria, by providing the infrastructure that farmers need to improve their agricultural activities.
One thought on "Coscharis Group Unveils a N12 Billion Farm, Rice Mill in Anambra State"
Francis Oguaju November 12, 2019 at 8:23 AM · Edit
It's a good one, and it also throws up some interesting insights. According to the report, the plant would start with 40K metric tonnes (800K bags of 50kg rice) per annum capacity, to grow to 120k metric tonnes (2.4m bags of 50kg rice) by end of next year. And by the time Dangote releases capacities of milling plants it's building in about five States, we will know how close we are to bridging the gap on self-sufficiency in rice.
This is very important, because when politicians shout about how wonderfully we are doing, with no data supporting those wild claims, it keeps creating the impression that we are productive, when the reality is different. So it will still take couple of years for us to be self-sufficient in rice production, that is the reality.
Another thing is yield per hectare, currently what Egypt achieves per hectare takes almost six hectares to achieve same here. If we do not address this massive disparity, we could turn all the lands here into farmlands, just to produce food; and that would create another problem for us. The population is still growing, while available land is shrinking.
Mr Emefiele cannot be a spokesman for Buhari's administration, anything outside monetary policy is not for him to say. From Finance minister to that of Information, or any political appointee of the government can do that job, but certainly not the CBN governor. His office is independent from the political theatre, so his comments must always reflect such.


text:
It's very rewarding to see the patients succeed after surgery.
– Allan D. Kirk, MD, PhD
Allan D. Kirk, MD, PhD
Kidney/Pancreas Transplant Surgeon, Pediatric Kidney Transplant Surgeon
American Board of Surgery, General Surgery
Duke Kidney/Pancreas Transplant Clinic - Clinic 2B/2C - Durham, NC
Clinical Focus and Research
Duke Kidney/Pancreas Transplant Clinic - Clinic 2B/2C
40 Duke Medicine Cir
I am a transplant surgeon specializing in kidney transplants. Kidney transplantation is unique in surgery because you're providing a cure for a disease. It's very rewarding to see the patients succeed after surgery; the donors also make my practice very special. We can't do a transplant without them providing this wonderful gift. Duke has been performing kidney transplants for 50+ years – since the very beginnings of the field. In fact, the process of how we match tissues for transplants was started at Duke. We've done thousands of kidney transplants here, so it's great to be a part of a program with such a rich history. I'm also the chairman of the Department of Surgery and the surgeon-in-chief for the Duke University Health System, where we perform all types of transplants.
School of Medicine Department
School of Medicine Division
Abdominal Transplant Surgery
Multi-Organ Transplantation, University of Wisconsin, 1995-1997
Surgery, Duke University Hospital, 1987-1989
Research Fellow, Surgery, Duke University Hospital, 1989-1992
Senior Resident, Surgery, Duke University Hospital, 1992-1994 (Chief Resident, 1994-1995)
MD, Duke University School of Medicine, 1987
PhD, Immunology, Duke University, 1992
My Research Interests
My particular area of interest is learning how to manipulate people's immune systems so that they don't reject their organ, but can still reject bacteria, viruses and things along those lines. We're now at the point where in selected cases we can transplant a kidney from one person to another and keep that kidney working with only one medication, once a month. I also work with the Military to help develop better was of managing people who have been critically injured. That work is particularly rewarding and is taking some of the same principles we are learning from my transplant research and using them to improve the outcome after trauma and severe illness.
Viela Bio (Kidney Transplant)
IRB# PRO00103332 , NCT# NCT04046549
View my publications on PubMed
This faculty member (or a member of their immediate family) has reported outside activities with the companies or institutions listed below. This information has been reported to the health system leadership and, when appropriate, management plans are in place to address potential conflicts of interest.
MedBlue
MedBlue Data
Semma Therapeutics


Well, we had a few days of warm weather. The cool, wet weather is slowing things down again. Nonetheless, there is still a decent harvest coming in. The June berries are here and you'll find Hoods, Totems and Shuksans available this week. Early raspberries will be available too. You'll also find lettuce, carrots, radishes, turnips, potatoes, kale, chard and onions.
Little Pots and Pans quickly sold out of their new Strawberry Basil Goat Cheese Tart on Tuesday. They will be bringing a lot more tomorrow. The Hummus Stop will have several flavors of hummus, pita, pita chips, tabouli, artichoke salad and other savory items. Amaranth of Ammie's Goodies will be back with a wide variety of gluten-free items. Full of Life Farm will have a variety of beef cuts and chicken. They also will be taking orders if you are interested in stocking your freezer. They are also taking turkey orders for Thanksgiving. (It may seem too soon but a few farms have already pre-sold all their birds.) Visit Full of Life Farm's website (link) for more information or just talk to them at the market. Fressen Bakery will start attending the Thursday market next week.
Rick Steffen Farm – asparagus, onions, shallots, scallions, leeks, potatoes, carrots, kohlrabi, spinach, swiss chard, strawberries, raspberries, blackberries, cherries (Chelan, Rainier).
Little Pots and Pans – savory tarts (including gluten free), tartlets including the new Strawberry Basil Goat Cheese Tart.
Fressen Artisan Bakery – Starts next Thursday.
Packer Orchards and Bakery – pear sweetened cookies, fruit hand pies.
Organic greens, fresh local strawberries*, dried crancherries, avocado, glazed walnuts & poppy seed dressing.


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Inside the automotive marketplace you can still find very attractive job options available around the world. Therefore if you are inside the automotive marketplace and would like to produce a change you can still find plenty of options around the world.
In this particular modern world you will find available a massive shortage experienced automotive technicians around the world. Therefore if you are a skilled auto specialist you may decide where you have to work in the world.
Simply by applying on among the numerous automotive recruitment companies webpages, and they're going to search employment chance to suit your needs any world. The simple truth is plenty of emerging automotive markets have opened up in reasoned years, due to the power change in the automotive industry.
This automotive marketplace will end up a good deal bigger afterwards as completely new type of cars will to enter the market. Like every the "EV" cars that are still inside the prototype phase. Every one of these cars might have new technology implemented into them, so new personnel ought to be taught to have fun with them afterwards.
This could bring a paradigm shift into this automotive marketplace, working out techniques as well as the skills that has to certainly learn have to alteration of the forseeable future.
This will make the manufacturers to start running extensive training and develop programs, to own experienced technicians to enable them to establish their brand. You will notice coming new brands and brand to the arena which brands will need to still build their names available on the market place.
To create an item you will need a effective publish sales service you'll be able to assist your customers with. That one factor can produce a completely new automotive marketplace for the auto industry think about a digital or chemical engineer working in the local vehicle dealership.
It could appear farfetched but it is possible since the cars afterwards will probably be driven with power plants like fuel cells, hydrogen emission and electric motors. All of this will showed up in the marketplace devote this contemporary world sooner than many of us do realize. And so the predictions are the big part of the existing automotive workforce leaves.
The device was created to develop several slaves that could be better to condition, into what this slave system needs rather than just what the workers needs. That is probably the main reasons why the older leading hands inside the automotive marketplace can get removed or retrenched. The general modern business conceptions are that seniors are resisters to modern business, because they do not desire to change.
If all this experienced folks are removed afterwards the whole automotive industry may take a hit a massive skills and brain lost that could have forwarded up to the more youthful people. Findings are that lots of the seniors inside the automotive industry shouldn't share their understanding and skills any more, as they do not see themselves as resistors for future increase in the automotive industry.
And so the automotive marketplace may take a hit great losses soon, because of this phenomenon.