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About 2019 Film Selections 2019 "Shorts" Competition 2019 Special Guests LPFF 2019 Events LPFF 2019 Underwriters, Partners, Sponsors Schedule Volunteer
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Home The Show About 2019 Film Selections 2019 "Shorts" Competition 2019 Special Guests LPFF 2019 Events LPFF 2019 Underwriters, Partners, Sponsors Schedule Volunteer News Press Releases Announcements Media Program 2018 Archives Newsletters AFSContactTickets
Welcome to the Show!
The Line-up
2018 Film Selections Video
The Lake Placid Film Festival 2018 film selections. Join us for the 17th edition on October 26-28 in Lake Placid, NY.
On Her Shoulders - Official Trailer - Oscilloscope Laboratories HD
SCIENCE FAIR 2018 - Official Movie Trailer
ASAKO I & II Clip | TIFF 2018
School of Life / L'École buissonnière (2017) - Trailer (English Subs)
3100: RUN AND BECOME. Official Trailer
FELIZ AÑO TIJUANA - Official Trailer
THE MISEDUCATION OF CAMERON POST Official Trailer (2018) Chloë Grace Moretz Drama Movie HD
BURNING (2018) Official US Trailer | Steven Yeun Movie
Diamantino | Trailer | NYFF56
The 20th Annual Animation Show of Shows Trailer
'Vaya' Official Trailer HD
Free Solo - Official Trailer (2018)
WHAT IS DEMOCRACY? Trailer | TIFF 2018
THE BIG BAD FOX AND OTHER TALES Trailer (2018)
'' searching for ingmar bergman '' - official trailer - 2018.
Maria By Callas | Official US Trailer HD (2018)
https://sonyclassics.com/mariabycallas/#
Bisbee '17 (2018) Official Trailer [HD]
In the Aisles - Trailer - SFF 18
HAVE YOU SEEN MY MOVIE? Official Trailer
Moving Stories - Trailer
AFRO ANDALUSIAN MEMORIES, GURUMBÉ - TRAILER
http://www.africanfilm.com/Gurumbe.html
Calgary Film 2017: ROOM FOR RENT (Trailer)
The Children Act | Official Trailer | A24
1985 Official Trailer
Time for Ilhan (Trailer) - AIFF 2018
Ramen Shop | JAPAN CUTS 2018
Birds of Passage - Trailer
https://www.imdb.com/title/tt6386748/?ref_=ttvi_tt
PROSPECT Official Trailer (2018) Movie Trailer HD
http://shepfilms.com/prospect
Making Montgomery Clift
Behind the Curve - Official Teaser Trailer
BECOMING ASTRID
https://www.imdb.com/title/tt6433456/?ref_=ttpl_pl_tt
THE LAST SUIT - Trailer with english subtitles
http://www.latidofilms.com/the-last-suit-2/
Rodents Of Unusual Size Trailer #1 2018 Official HD Movie Trailers
The Lion In Winter (1968) - Trailer
Ingmar Bergman - Wild Strawberries
Adirondack Holiday, 1960
Documentary 27.55 minutes
The Heiress (1949) trailer
Mapplethorpe: Look At The Pictures - Official trailer
"Halloween" 1978 Original Movie Trailer (HD)
The Song Of Sway Lake (2018) | Official Trailer
The Last Suit
Abraham Bursztein, an 88 year-old Jewish tailor, runs away from Buenos Aires to Poland, where he proposes to find a friend who saved him from certain death at the end of World War II. After seven decades without any contact with him, Abraham will try to find his old friend and keep his promise to return one day.
(Drama: 1hr & 31min)
Biopic of Swedish writer Astrid Lindgren, the author of numerous children's books and creator of Pippi Longstocking.
(Biography, Drama: 2hrs & 3min)
Film sponsor - Berkshire Farm
306 Hollywood
When two siblings undertake an archaeological excavation of their late grandmother's house, they embark on a magical-realist journey in search of what life remains in the objects we leave behind.
(Documentary: 1hr & 22min)
Film sponsor - Bob Miller, Real Estate Associate Broker
During the marijuana bonanza, a violent decade that saw the origins of drug trafficking in Colombia, Rapayet and his indigenous family get involved in a war to control the business that ends up destroying their lives and their culture.
(Drama: 2hrs & 5min)
Big Bad Fox and Other Tales
Whoever thinks that the countryside is calm and peaceful is mistaken. In it we find especially agitated animals, a Fox that thinks it's a chicken, a Rabbit that acts like a stork, and a Duck who wants to replace Father Christmas. If you want to take a vacation, keep driving past this place.
(Animation, Adventure, Comedy: 1hr & 23min)
Film Sponsor - High Peaks Optimal Health
A tour of the Adirondack region in 1960.
(Documentary: 27.55 Minutes)
Classic film star and queer icon Montgomery Clift's legacy has long been a story of tragedy and self-destruction. But when his nephew dives into the family archives, a much more complicated picture emerges.
A teenage girl and her father travel to a remote moon on the hunt for elusive riches. But there are others roving the moon's toxic forest and the job quickly devolves into a desperate fight to escape.
(Sci-Fi: 1hr & 38min)
Film sponsor - Local ADK Magazine
Gurumbe Afro-Andalusian Memories
With the commercial exploitation of the American colonies, thousands of Africans are brought to Seville to be sold as slaves. Some are exported to the colonies and others stay in the city.
(Documentary, History, Music: 1hr & 12min)
Film sponsor - AddytheInfluencer, Adison Barton
Rodents of Unusual Size
A story about giant swamp rats invading coastal Louisiana and the defiant people on the edge of the world, who are defending their communities, culture, and livelihoods from the onslaught of this curious and unexpected invasive species.
Film sponsor - Adirondack Premium Pest Services
A young man who is curious about his deceased parents' past takes a food journey to Singapore where he uncovers more than just delicious meals.
(Drama: 1hr 29min)
Film sponsor - Eat ADK Restaurant Week
A closeted young man goes home for the holidays and struggles to reveal his dire circumstances to his conservative family.
Maria by Callas
An intimate look at the life and work of Greek-American opera singer, Maria Callas, as told in her own words.
(Documentary: 1hr 53 min)
Film sponsor - Terry Robards Wine & Spirits
Moving Stories
Six dancers from the acclaimed Battery Dance company travel the world, working with young people who've experienced war, poverty, prejudice, sexual exploitation, and severe trauma as refugees.
(Documentary: 1hr 24min)
When a broke thirty-two year old ex-lottery winner convinces his parents to rent their spare room to save from downsizing, a creepy stranger with a hidden agenda moves in.
(Comedy, Mystery: 1hr & 29min)
Time for Ilhan
On November 8, 2016, a young, hijab-wearing mother-of-three named Ilhan Omar made history, becoming the first Somali Muslim woman to be elected to state office in America. A fresh take on the old story of the American Dream, TIME FOR ILHAN offers an inspiring, stereotype-busting portrait of a rising political star as she begins a bold and powerful political career.
Behind the Curve
BEHIND THE CURVE delves into the outlandish world of Flat-Earthers — people who honestly believe that the world is flat, and that a worldwide conspiracy is keeping us from the truth.
Searching for Ingmar Bergman
He is considered the most important filmmaker of all time. In 2018 Ingmar Bergman would have turned 100 years old. On this occasion, the internationally known and well-respected German director Margarethe von Trotta approaches the work and the person of Ingmar Bergman, under whose film heritage talks to a new generation of filmmakers.
The Children Act
Smart, elegant, and deeply moving, The Children Act stars two-time Academy Award-winner Emma Thompson in a riveting performance as Fiona Maye, a British High Court judge who, in the midst of a marital crisis, must rule on a life-changing legal case concerning the survival of a teenage boy. At issue whether to order a blood transfusion on the boy (Dunkirk's Fionn Whitehead), a Jehovah's Witness who, just months short of his eighteenth birthday, is refusing on religious grounds the procedure that would save his life.
Film Sponsor - The Breakfast Club
Monrovia, Indiana
Explores a small town in rural, mid-America and illustrates how values like community service, duty, spiritual life, generosity and authenticity are formed, experienced and lived along with conflicting stereotypes. The film gives a complex and nuanced view of daily life in Monrovia and provides some understanding of a way of life whose influence and force have not always been recognized or understood in the big cities on the east and west coasts of America and in other countries.
(Documentary: 2hrs & 23min)
Directed by legendary filmmaker, Fred Wiseman
An old mining town on the Arizona-Mexico border finally reckons with its darkest day: the deportation of 1200 immigrant miners exactly 100 years ago. Locals collaborate to stage recreations of their controversial past.
Film sponsor - Mis Amigos
Christian begins to work as a shelf stacker at a supermarket and finds himself in a new, unknown world: the long aisles, the bustle at the checkouts, the forklifts. In the Aisles is a 2018 German drama film directed by Thomas Stuber.
1183 A.D.: King Henry II's three sons all want to inherit the throne, but he won't commit to a choice. They and his wife variously plot to force him.
Film introduced by Jeremy Arnold, TCM Contributor
Film Sponsor - Nelson E. Page, Ft. Lee Film Commission
Follow Alex Honnold as he becomes the first person to ever free solo climb Yosemite's 3,000ft high El Capitan Wall. With no ropes or safety gear, he completed arguably the greatest feat in rock climbing history.
Film sponsor - High Peaks Cyclery
Three people board the train bound for Johannesburg. Strangers, each on their own mission, with a simple task to complete and in search of family to help them. But when they are betrayed by the very people whose protection they sought, they find themselves trapped in the city - invisible and alone.
Miseducation of
Cameron Post
In 1993, a teenage girl is forced into a gay conversion therapy center by her conservative guardians.
(Drama/Romance: 1hr & 31 min)
BURNING is the searing examination of an alienated young man, Jongsu, a frustrated introvert whose already difficult life is complicated by the appearance of two people into his orbit: first, Haemi, a spirited woman who offers romantic possibility, and then, Ben, a wealthy and sophisticated young man she returns from a trip with.
(Drama: 2hrs & 28min)
What is Democracy
This reflection on democracy spans millennia and continents, from ancient Athens' groundbreaking experiment in self-government to capitalism's roots in medieval Italy, and from modern-day Greece grappling the with its financial collapse and mounting refugee crisis to the United States reckoning with its past and the growing gap between rich and poor.
When he misses the big goal on the world's largest stage, chiseled fútbol star Diamantino (Carloto Cotta) flees the public eye; no longer able to conjure the giant fluffy puppies that guided him to superstardom, he is rendered a vessel without a purpose. And thus begins an unexpected journey toward love and enlightenment that involves cloning, the CIA, a Syrian refugee, and Diamantino's nefarious twin sisters. A perversely pleasurable sendup of Brexit, genetic science, and the ongoing refugee crises.
(Drama/Comedy: 1 hr & 32min)
3100: Run and Become
What if running could lead to enlightenment? 3100: Run and Become follows an unassuming Finnish paperboy in the Self-Transcendence 3100 Miler - the world's longest race. His story takes the viewer around the world to the Kalahari Desert, the mountain temples of Japan and the Navajo Reservation.
Nine high school students from disparate corners of the globe navigate rivalries, setbacks, and hormones on their quest to win the international science fair. Only one can be named "Best in Fair."
FELIZ AÑO TIJUANA
(Happy New Year Tijuana)
A chance encounter with a former student in Tijuana on New Year's Eve leads to an emotionally turbulent night for a professor who's at a crossroads in his life.
(Drama, Comedy: 1 hr & 15min)
A look at the life of photographer Robert Mapplethorpe from his rise to fame in the 1970s to his untimely death in 1989.
(Biography, Drama: 1hr & 42min)
Film Sponsor - Kathie Smith
Catherine (Olivia de Havilland), a young woman who stands to inherit her father's large fortune, falls in love when she meets Morris (Montgomery Clift), who gives her the love and affection her father doesn't, and which she desperately needs. Film directed by William Wyler.
Wild Strawberries
With the exception of his elderly housekeeper Miss Agda who he treats almost like a surrogate platonic wife, widowed seventy-eight year old Dr. Isak Borg, a former medical doctor and professor, has retreated from any human contact, partly his own want but partly the decision of others who do not want to spend time with him because of his cold demeanor. Film directed by Ingmar Bergman.
Asako I & II
Asako lives in Osaka. She falls in love with Baku, a free-spirit. One day, Baku suddenly disappears. Two years later, Asako now lives in Tokyo and meets Ryohei. He looks just like Baku, but has a completely different personality.
(Drama, Romance: 1hr & 59min)
Nadia Murad, a 23-year-old Yazidi, survived genocide and sexual slavery committed by ISIS. Repeating her story to the world, this ordinary girl finds herself thrust onto the international stage as the voice of her people.
(Documentary, Bio: 1hr & 35min)
Showtimes: Friday 10/26 Palace
Film Sponsor - Charlene Trotter, Trotter Consulting
Nadia Murad awarded Nobel Peace Prize 10/5/18 - read more...
In 1920s France an orphan is adopted by a rustic couple who work for a rural landowner. Left to himself, he soon comes under the spell of the local poacher.
(Comedy, Family Drama: 1 hr & 56min)
Showtime: Sunday 10/29 - Palace Theatre #3 at 7PM
Fifteen years after murdering his sister on Halloween night 1963, Michael Myers escapes from a mental hospital and returns to the small town of Haddonfield to kill again.
(Horror, Thriller: 1hr & 31min)
1978 Horror Classic
Showtime Friday 10/26 - Palace Theatre #1 - 11:59pm
20th Annual Animation
Returning to theaters across North America this fall, the ANIMATION SHOW OF SHOWS will present 15 thought-provoking, poignant, and very funny animated shorts from around the world. In a year when the best and worst of human nature has been on constant display, the works in this year's show remind us of both the universality of shared ideals, as well as the diverse challenges we face.
(Shorts, Animation)
Showtimes: Friday 10/27 - High Peaks Resort - 9PM & Saturday - 8PM
Have You Seen My Movie?
A massive montage of movie characters going to the movies. Clips from 100+ films are cut together to create a new cinema-going experience. Romance, musical, action, horror, noir, comedy - and countless characters watch in the dark with you.
(Adventure, Comedy, Romance - 2hr & 16min)
Showtime: Friday 10/26 - Palace Theatre #4 - 3PM & Sunday 10/28 - 4:30PM
Dorothy Gale is swept away from a farm in Kansas to a magical land of Oz in a tornado and embarks on a quest with her new friends to see the Wizard who can help her return home to Kansas and help her friends as well.
(Adventure, Family, Family: 1hr & 42min)
Showtime: Sunday 10/29 - Palace Theatre at 1:00pm
Note: this film is replacing SNOW WHITE in the LPFF2018 Program
Sustaining Partners
Meet our Underwriters, Partners, Sponsors
Lake Placid Film Festival / Adirondack Film Society
Lake Placid, NY,
518-523-3456 charlene@lakeplacidfilmfestival.org
An Adirondack Film Society event.
A 501 (c)(3) Organization


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Home » MAA Publications » Periodicals » Convergence » Mathematical Treasures of Japan in the Edo Period: Determinants
Mathematical Treasures of Japan in the Edo Period: Determinants
‹ Mathematical Treasures of Japan in the Edo Period: Arithmetic and Algebra up Mathematical Treasures of Japan in the Edo Period: Circles and Spheres ›
Frank J. Swetz (Pennsylvania State University)
Seki Takakazu (c.1642-1708), the leading mathematician of the Edo Period (1603-1867) in Japan, is credited with developing a theory of mathematical determinants for solving systems of linear equations. Kaifuku dai no ho is a page of an existing manuscript illustrating Takakazu's methods of setting up and working with determinants.
These images are presented through the kind cooperation of the National Diet Library, Japan, and are used with permission. They were obtained from the library's digital gallery exhibit, Japanese Mathematics in the Edo Period, where a complete examination and viewing of the item presented above can be found.
Frank J. Swetz (Pennsylvania State University), "Mathematical Treasures of Japan in the Edo Period: Determinants," Convergence (July 2018)
Non-Western Cultures
Mathematical Treasures of Japan in the Edo Period
Mathematical Treasures of Japan in the Edo Period: Arithmetic on the Japanese Abacus
Mathematical Treasures of Japan in the Edo Period: Arithmetic
Mathematical Treasures of Japan in the Edo Period: Arithmetic and Algebra
Mathematical Treasures of Japan in the Edo Period: Circles and Spheres
Mathematical Treasures of Japan in the Edo Period: Surveying
Mathematical Treasures of Japan in the Edo Period: Napier's Rods for Japanese Samurai
Mathematical Treasures of Japan in the Edo Period: The Chinese Nine Chapters in Japan
Mathematical Treasures of Japan in the Edo Period: Geometry
Mathematical Treasures of Japan in the Edo Period: Practical Mathematics
Mathematical Treasures of Japan in the Edo Period: Circle Packing

redpajama_set_name: RedPajamaCommonCrawl


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Q: Purely "algebraic" proof of Young's Inequality Young's inequality states that if $a, b \geq 0$, $p, q > 0$, and $\frac{1}{p} + \frac{1}{q} = 1$, then $$ab\leq \frac{a^p}{p} + \frac{b^q}{q}$$ (with equality only when $a^p = b^q$).  Back when I was in my first course in real analysis, I was assigned this as homework, but I couldn't figure it out.  I kept trying to manipulate the expressions algebraically, and I couldn't get anywhere.  But every proof that I've seen since uses calculus in some way to prove this.  For example, a common proof is based on this proof without words and integration.  The proof on Wikipedia uses the fact that $\log$ is concave, which I believe requires the analytic definition of the logarithm to prove (correct me if I'm wrong).
Can this be proven using just algebraic manipulations?  I know that that is a somewhat vague question, because "algebraic" is not well-defined, but I'm not sure how to make it more rigorous. But for example, the proof when $p = q = 2$ is something I would consider to be "purely algebraic":
$$0 \leq (a - b)^2 = a^2 + b^2 - 2ab,$$ so $$ab \leq \frac{a^2}{2} + \frac{b^2}{2}.$$

A: It might be essentially easier to write $x=a^p,y=b^q$ and $t=\frac 1 p$. Then you want to prove the inequality:
$$x^{t}y^{1-t}\leq tx + (1-t)y$$
for $0<t<1$ and with equality only when $x=y$.
First, we prove the general AM-GM for any $2^k$ variables. The case $k=1$ is the obvious case:
$$(x+y)^2-4xy = (x-y)^2\geq 0$$
With equality only when $x=y$.
Now assume we have proven AM-GM for $n$ terms, we will prove it for $2n$ terms.
If $x_1,...,x_{2n}$ are real, assume they are in linear order. Then:
$$\begin{align}\sqrt[2n]{x_1...x_{2n}} &= \sqrt{\sqrt[n]{x_1...x_n}\sqrt[n]{x_{n+1}...x_{2n}}}\\
&\leq \frac{1}{2}\sqrt[n]{x_1...x_n}+\frac{1}{2}\sqrt[n]{x_{n+1}...x_{2n}} \\
&\leq \frac{1}{2n}(x_1+...+x_n)+\frac{1}{2n}(x_{n+1}+...+x_{2n})
\end{align}$$
Since we linearly ordered them, the equality holds only if all the $x_i$ are equal. (Check yourself here.)
So, by induction, the AM/GM applies to any set of $2^k$ variables. If $t=r/2^k$, we can choose $x_1=x_2=..=x_r=x$ and $x_{r+1}=...=x_s=y$.  Then $$\sqrt[2^k]{x^ry^{2^k-r}}\leq \frac{r}{2^k} x + \frac{2^k-r}{2^k} y$$
Which is just $$x^ty^{1-t}\leq tx + (1-t)y$$
(That was just Ben's argument above, but restricted to the $2^k$ case.)
Since the set of $t$ of the form $r/2^k$, $r,k\in\mathbb Z$ is dense in $(0,1)$, you have this inequality everywhere (although density does not obviously let you conclude that equality only occurs when $x=y$ for the arbitrary real $t$.)

A: This proof is from "Mathematical Toolchest" published by the Australian Mathematics Trust (image).

Example. If $p$ and $q$ are positive rationals such that $\frac1p + \frac1q = 1$, then for positive $x$ and $y$ $$\frac{x^p}p + \frac{y^q}q \ge xy.$$
Since $\frac1p + \frac1q = 1$, we can write $p = \frac{m+n}m$, $q = \frac{m+n}n$ where $m$ and $n$ are positive integers. Write $x = a^{1/p}$, $y = b^{1/q}$. Then $$\frac{x^p}p + \frac{y^q}q = \frac a{\frac{m+n}m} + \frac b{\frac{m+n}n} = \frac{ma + nb}{m + n}.$$
However, by the AM–GM inequality, $$\frac{ma + nb}{m + n} \ge (a^m \cdot b^n)^{\frac1{m+n}} = a^{\frac1p} b^{\frac1q} = xy,$$ and thus $$\frac{x^p}p + \frac{y^q}q \ge xy.$$

A: Yes, at least for rational $p, q$. There is a general statement here, which can be summarized as follows:

Every polynomial inequality is a consequence of the trivial inequality $x^2 \ge 0$.

In more detail, to prove Young's inequality for general $p, q$, it suffices by a continuity argument to prove it for $p, q$ rational. By making an appropriate substitution of the form $a = x^n, b = y^m$ where $n, m$ are even integers, Young's inequality for a fixed choice of rational $p, q$ becomes equivalent to the statement that a certain polynomial with real coefficients always takes on non-negative real values when fed real inputs.
By Artin's solution to Hilbert's 17th problem, a polynomial with this property is a sum of squares of rational functions. An expression of this polynomial as a sum of squares of rational functions constitutes a proof of the corresponding case of Young's inequality from repeated application of the trivial inequality.
I don't see how you could avoid analysis for irrational $p, q$, since you can't even define the relevant functions without analysis.

A: With $\dfrac1p+\dfrac1q=1$, $u=x^p$, $v=y^q$, and $1+pt=u/v$, the following are equivalent:
$$
\begin{align}
xy&\le\frac{x^p}{p}+\frac{y^q}{q}\\
u^{1/p}v^{1/q}&\le\frac{u}{p}+\frac{v}{q}\\
(u/v)^{1/p}&\le\frac{u/v}{p}+\frac{1}{q}\\
(1+pt)^{1/p}&\le\frac{1+pt}{p}+\frac{1}{q}\\
1+pt&\le(1+t)^p\tag{1}
\end{align}
$$
Where $(1)$ is the rational version of the Bernoulli inequality, proven below.

Bernoulli's Inequality for Rational Exponents
Using the integral version of the Bernoulli Inequality, proven at the end of this answer, we get that for $x\gt-n$,
$$
\begin{align}
\frac{\left(1+\frac{x}{n+1}\right)^{n+1}}{\left(1+\frac{x}{n}\right)^n}
&=\left(\frac{(n+x+1)n}{(n+1)(n+x)}\right)^{n+1}\frac{n+x}{n}\\
&=\left(1-\frac{x}{(n+1)(n+x)}\right)^{n+1}\frac1{1-\frac{x}{n+x}}\\
&\ge\left(1-\frac{x}{n+x}\right)\frac1{1-\frac{x}{n+x}}\\[8pt]
&=1\\[8pt]
\left(1+\frac{x}{n+1}\right)^{n+1}
&\ge\left(1+\frac{x}{n}\right)^n\tag{2}
\end{align}
$$
where the inequality is strict if $x\ne0$ and $n\ge1$.
Applying induction with $(2)$, we get that for $x\gt-m$ and integers $n\ge m$,
$$
\left(1+\frac{x}{n}\right)^n\ge\left(1+\frac{x}{m}\right)^m\tag{3}
$$
Letting $t=\frac{x}{n}\gt-\frac{m}{n}$ and taking $m^\text{th}$ roots gives
$$
\left(1+t\right)^{n/m}\ge1+\frac{n}{m}t\tag{4}
$$
Note that $(4)$ is trivially true for $-1\le t\le-\frac{m}{n}$. Thus, for all $t\ge-1$ and rational $p\ge1$,
$$
\left(1+t\right)^p\ge1+pt\tag{5}
$$
where the inequality is strict if $t\ne0$ and $p\gt1$.

Negative Exponents
As shown in $(2)$, both $\left(1+\frac xn\right)^n$ and $\left(1-\frac xn\right)^n$ are increasing in $n$, as long as $|x|\le n$. Thus, for $m=\max(k,n)$,
$$
\begin{align}
\left(1+\frac xk\right)^k\left(1-\frac xn\right)^n
&\le\left(1+\frac xm\right)^m\left(1-\frac xm\right)^m\\
&=\left(1-\frac{x^2}{m^2}\right)^m\\[3pt]
&\le1\tag6
\end{align}
$$
Thus, substituting $x\mapsto kx$, and taking $n^\text{th}$ roots, we get
$$
(1+x)^{k/n}\left(1-\tfrac knx\right)\le1\tag7
$$
Finally, setting $p=\tfrac kn$ yields
$$
1-px\le(1+x)^{-p}\tag8
$$
where the inequality is strict when $x\ne0$ and $p\gt0$.

redpajama_set_name: RedPajamaStackExchange


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Carla Parslow, PhD, CAHP
Dr. Carla Parslow has over 20 years of experience in the cultural heritage resource management (CHRM) industry in Canada. As the President of PHC Inc., Carla is responsible for the for the management of CHRM projects, as well as the technical review and quality assurance of all archaeological and cultural heritage projects. Throughout her career, Carla has managed both large (50+) and small (4+) teams of CHRM and Environmental professionals. Dr. Parslow has also written, contributed to, or reviewed over 400 archaeological reports in the province of Ontario and has experience in leading teams on small scale projects (<$20,000) as well as large complex projects (>$5,000,000).
Carla has worked extensively in the municipal and provincial sector and has a comprehensive understanding of heritage legislation at the municipal, regional, and provincial level of government for both cultural heritage and archaeology. Carla is a licensed Ontario professional archaeologist through the Ontario Ministry of Heritage, Sport, Tourism and Cultural Industries (MHSTCI) and is a member of the Canadian Association of Heritage Professionals (CAHP) and also a member in good standing with the Register of Professional Archaeology.
Christopher Lemon, BSc, Dip Heritage, CAHP
Mr. Lemon is a Cultural Heritage Specialist (CAHP member in good standing) and Licensed Archaeologist with 15 years' experience. He received an Honours B.Sc. in Anthropology from the University of Toronto and has completed course work towards an M.A. from the University of Western Ontario. Mr. Lemon has a Diploma in Heritage Carpentry and Joinery and a Certificate in Heritage Planning from Algonquin College. During his career Mr. Lemon has participated in cultural heritage assessments across Ontario as both a Senior Field Director in archaeology and as a Built Heritage Practitioner. He has managed field teams and projects ranging in value from <$5,000.00 to in excess of $1,000,000.00. Mr. Lemon is a member of the Ontario Archaeological Society and the Council for Northeast Historical Archaeology. Chris's previous experience includes representation on Joint Health and Safety Committees; he is dedicated to maintaining a safety-first focus on all job sites.
Adam Long, MSc
Mr. Long is a Senior Field Director at PHC. Graduating with an Hons. BSc in anthropological science, and an MSc in evolutionary anthropology from the University of Toronto, Adam has worked on archaeological projects in Jordan, taken part in palaeontological expeditions to find remains of the earliest primates in Wyoming and Montana, and for the last 6 years has undertaken many archaeological consulting projects across Ontario. He holds a Professional license from the MHSTCI and has directed crews ranging in size from 4 people, to 55+ people on a variety of project types, from cemeteries to lithic scatters. Adam also assists in Cultural Heritage projects, having aided in both large and small scale built heritage assessments across the province, including updating the City of Brantford's Heritage Register. Adam is a member of the Ontario Archaeological Society, as well as the Canadian Association of Physical Anthropologists.
Jamie Lemon, MA
Ms. Jamie Lemon is a Senior Archaeologist and Project Manager with Parslow Heritage Consultancy Inc. and is responsible for managing projects and work crews across Ontario. She is the primary author of numerous archaeological licence reports for archaeological assessments ranging from Stage 1 to Stage 4 investigations, and is proficient at artifact and archaeobotanical analysis. In addition, she is a former field technician and field director with experience in both pre-contact Indigenous and Euro-Canadian historic sites. She has worked on archaeological projects for such sectors as mining, land development, transportation, aggregates, and energy. Jamie received a B.A. in Anthropology from the University of Waterloo in 2007, an M.A. from Trent University in 2014 and has been active in Cultural Resource Management in Ontario for 15 years. Jamie currently holds a valid professional licence with the Ontario Ministry of Heritage, Sport, Tourism and Culture Industries. Jamie regularly assists clients with navigating the life cycle of archaeological assessments as it relates to their Project, included interpretation of MHSTCI Standards and Guidelines, scheduling of archaeological assessments to best suit the needs of the client, and engaging with Indigenous communities.


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\section{Introduction:}
Suppose that $ X $ and $ Y $ are real Banach spaces and $ U $ is an open subset of $ X. $\ A subset $ B \subset U $ is $ U $-bounded, if it is bounded and the distance
between $ B$ and the boundary $ $ of $ U$ is strictly positive \cite{ce3}.\
Let $ C^{1u}(U, Y )$ be the space of all differentiable mappings
$ f : U \rightarrow Y $ whose derivative $ f^{\prime} : U \rightarrow L(X, Y ) $ is uniformly continuous on
$ U$-bounded subsets of $ U. $\ In recent years, several authors have studied properties of $ C^{1u} $ mappings between Banach spaces.\  For more information in this area, we refer the reader to \cite{dh, DM,h} and references therein.\ Recall that, a mapping $ f : U \rightarrow Y $ is compact if it takes $ U$-bounded subsets of $ U $ into relatively compact subsets of $ Y. $\
Aron {\rm (\cite[Theorem 1.7]{A})}, proved that a holomorphic linear function $ f : X \rightarrow \mathbb{C} $
is compact on bounded subsets if and only if its derivative
$ f^{\prime}:X\rightarrow X^{\ast} $ is a compact mapping.\ Bombal et al. \cite{ce},
for a holomorphic function $  f$ of bounded type on a complex Banach space $ X, $  proverd
that its derivative $ f^{\prime} :X\rightarrow X^{\ast}$ takes bounded sets into certain families of sets if and only
if $ f $ may be factored in the form $ f = g \circ S, $ where $  S$ is in some associated operator ideal,
and $ g $ is a holomorphic function of bounded type.\ Following this, Cilia et al. {\rm (\cite[Theorem 3.1]{ce4})}, proved that if $ f^{\prime} $ is uniformly continuous on bounded sets and with values in the space $ K(X, Y )$ of compact operators from $ X$ into $ Y, $ then $ f^{\prime} $ is compact if and only if $ f$ is weakly uniformly
continuous on bounded sets.\
It is well known {\rm (\cite[Proposition 3.2]{gg})}, that a bounded linear operator $ T:X\rightarrow Y $ between Banach spaces is completely
continuous if and only if its adjoint $ T^{\ast}$ takes bounded subsets of $ Y^{\ast} $ into
uniformly completely continuous subsets, often called $ (L) $-subsets, of $ X^{\ast} .$\ Let us recall from \cite{spd}, that
a subset $ K \subseteq L(X, Y ) $ is called uniformly completely
continuous, if for every weakly null sequence $ (x_{n})_{n} $ in $ X, $ it follows:
$$\lim_{n\rightarrow \infty}\sup_{T \in K}\parallel T(x_{n}) \parallel =0. $$
Motivated  by this work, Cilia and Guti\'errez {\rm (\cite[Theorem 2.1]{ce2})}  gave a similar
result for differentiable mappings.\ In fact, they showed that if $ f \in C^{1u}(U, Y ) ,$ then $ f$ takes weakly Cauchy  $ U$-bounded
sequences into convergent sequences if and only if $ f^{\prime} $ takes $ U$-bounded Rosenthal subsets
of $ U$ into uniformly completely continuous subsets of $ X^{\ast} .$\\
Recently, Li et al.\cite{ccl1} generalized the concepts $ (L) $ sets and $ (V) $ sets to
the $ p $-$ (V ) $ sets for $ 1\leq p \leq \infty. $\ It is well known {\rm (\cite[Theorem 14]{g12})} that, a bounded linear operator $T:X\rightarrow Y $ between Banach spaces is $ p$-convergent
if and only if its adjoint $ T^{\ast} : Y^{\ast}\rightarrow X^{\ast}$ takes bounded subsets of $ Y^{\ast} $ into $p $-$ (V) $ subsets of $ X^{\ast} .$\\
Inspired by the above works, we introduce the notions uniformly $ p $-convergent sets and weakly $ p$-sequentially continuous mappings.\ In the sequel, we obtain a sufficient condition for those Banach spaces which either contains no copy of $ \ell_{1} $ or have the $ p $-Schur property.\
Finally,
we show that
if $ U $ is an open convex subset of $ X $ and $ f \in C^{1u}(U, Y ) ,$ then $ f $ takes $ U$-bounded and
weakly $ p $-Cauchy
sequences into norm convergent sequences if and only if $ f^{\prime} $ takes $ U$-bounded and weakly $ p $-precompact subsets of $ U$ into uniformly $ p $-convergent
subsets of $ L(X, Y ). $\
\section{Notions and Definitions:}
Throughout this paper $ 1\leq p < \infty $ and $ 1\leq p < q\leq \infty,$ except for the cases where we consider other assumptions.\ Also, we suppose
$ X $ and $ Y$ will denote real Banach spaces, $ U \subseteq X $ will be an open convex subset,
$p^{\ast}$ is the H$\ddot{\mathrm{o}}$lder conjugate of $p.$\ The word `operator' will always mean
bounded linear operator. For any Banach space X, the dual space of bounded
linear functionals on X will be denoted by $ X^{\ast} .$\ Also, we denote the closed unit ball of $ X$ by $ B_{X}. $\ For a bounded linear operator $ T : X \rightarrow Y, $ the adjoint of the operator $ T $
is denoted by $ T^{\ast}. $\ The space of all bounded linear operators and weakly compact operators from $ X$ to $ Y$ will be denoted by $ L(X,Y ) $ and
$ W(X,Y ), $ respectively.\ If $ X_{1},\cdot\cdot\cdot, X_{k} $ are Banach spaces, the space of all $ k$-linear (continuous) mappings
from $ X_{1}\times\cdot\cdot\cdot\times X_{k} $ into $ Y$ is denoted by $ L^{k}(X_{1},\cdot\cdot\cdot,X_{k}, Y) .$\ A mapping $ P:X\rightarrow Y $ is a $ k$-homogeneous (continuous) polynomial if there is a $ k$-linear mapping
$ A : X\times\cdot\cdot\cdot\times X \rightarrow Y $ such that $ P(x) = A(x, . . . , x) $ for all $ x \in X. $\
The space of all $ k$-homogeneous continuous polynomials from $ X $ into $ Y $ is denoted by $ P(^{k}X,Y).$\
Note that correspondent each $ P\in P(^{k}X , Y), $ we can associate a unique symmetric $ k $-linear mapping $ \hat{P}: X\times\cdot\cdot\cdot\times X\rightarrow Y $ so that $ P(x)=\hat{P}(x,\cdot\cdot\cdot,x). $\
A mapping $ f:X\rightarrow Y $ is holomorphic if, for each $ x\in X $ there are $ r>0 $ and a sequence $ (P_{k}) $ of polynomials, with
$P_{k}\in P(^{k}X,Y)$ such that $ f$ may be given by its Taylor series expansion around $ x: $
$$ f(y)=\sum_{k=0} ^{\infty}P_{k}(y-x),$$
uniformly for $ \parallel y-x\parallel < r. $\ We use the notation $ \mathcal{H} (X,Y)$ for the space of all holomorphic mappings from $ X$ into $ Y. $\ A mapping $ f \in \mathcal{H} (X,Y)$ is called bounded type, if $ f $ is bounded on bounded sets.\ The space of all bounded type mappings from $ X$ into $ Y $ is denoted by $ \mathcal{H}_{b} (X,Y).$
If the range space is omitted in the above notations, it is understood to be the real field $ \mathbb{R} $ for instance, $ \mathcal{H}(X):= \mathcal{H} (X,\mathbb{R}) ,$
$ P(^{k}X):=P(^{k}X, \mathbb{R}) $ and  $ \mathcal{H}_{b} (X):= \mathcal{H}_{b} (X,\mathbb{R}). $\
Given $ x, y \in X, $ we write $ I(x, y) $ for the
segment with bounds x and y, that is,
$$ I(x, y)=\lbrace x+\lambda (y-x): 0\leq \lambda \leq 1 \rbrace .$$\
An operator is completely
continuous, if it takes weakly convergent sequences into norm convergent sequences.\ The subspace of all such operators
is denoted by $ CC(X, Y ).$\
Let us recall from \cite{djt}, that a sequence $ (x_{n})_{n} $ in $ X $ is called weakly $ p $-summable, if $ (x^{\ast}(x_{n}))_{n} \in \ell_{p}$ for each $ x^{\ast}\in X^{\ast} $.\ A sequence $(x_{n})_{n}$ in $ X $ is called weakly $ p $-convergent to $ x\in X,$ if $ (x_{n} - x)_{n}$ is weakly $ p$-summable.\ A sequence $(x_{n})_{n}$ in $ X $ is called weakly
$ p $-Cauchy, if $ (x_{m_{k}}-x_{n_{k}})_{k}$ is weakly $ p $-summable for any increasing sequences $ (m_{k})_{k} $
and $ (n_{k})_{k} $ of positive integers \cite{ccl}.\ Note that, every weakly $ p $-convergent sequence is
weakly $ p$-Cauchy, and the weakly $ \infty $-Cauchy sequences are precisely the weakly
Cauchy sequences.\
 An operator $ T : X \rightarrow Y $ is called $ p$-convergent, if $ T $ maps weakly $ p $-summable
sequences into norm null sequences \cite{cs}.\ The class of all $ p$-convergent operators from $ X$
into $ Y $ is denoted by $ C_{p}(X,Y) .$\ A  Banach space $ X $ has the $ p$-Schur property, if the
identity operator on $ X$ is $ p $-convergent.\ A bounded subset $ K$ of
$ X^{\ast} $ is a $ p $-$ (V ) $ set, if for every weakly $ p $-summable sequence
$ (x_{n})_{n} $ in $ X, $ it follows:
$$ \lim _{n} \sup_{x^{\ast}\in K} \Vert x^{\ast}(x_{n})\Vert =0.$$
A subset $ K$ of $ X $ is called weakly $ p$-precompact,
if every sequence from $ K $ has a weakly $ p$-Cauchy subsequence \cite{ccl}.\ Note that the
weakly $ \infty $-precompact sets are precisely the weakly precompact sets or Rosenthal sets.\
We refer the reader for undefined terminologies to the
classical references \cite{AlbKal, djt}.\
\section{Main results:}
In this section, we obtain a characterization for
the weakly p-sequentially continuous mappings.\ Namely,
we show
that $ f:U\rightarrow Y $ is weakly $ p $-sequentially continuous if and only if $ f^{\prime} $ takes $ U$-bounded and weakly $ p $-precompact subsets of $ U$ into uniformly $ p $-convergent
subsets of $ L(X, Y ). $\

\begin{defn}\label{d1}
Let $ K \subset L(X, Y ). $\ We say that $ K $ is a uniformly $ p $-convergent set, if for every weakly $ p $-summable sequence
$ (x_{n})_{n} $ in $ X, $ it follows:
$$ \lim _{n} \sup_{T \in K} \Vert T(x_{n})\Vert =0.$$
\end{defn}
As an immediate consequence of the Definition \ref{d1}, one can conclude
that the following elementary results.
\begin{prop}\label{p1}
$ \rm{(i)} $ Every subset of an uniformly $ p $-convergent set in $ L(X,Y) $ is uniformly $ p $-convergent.\\
$ \rm{(ii)} $ Absolutely closed convex hull of an uniformly $ p $-convergent set in $ L(X,Y) $ is uniformly $ p $-convergent.\\
$ \rm{(iii)} $ If $ K_{1},\cdot \cdot\cdot, K_{n} $ are uniformly $ p $-convergent sets in $ L(X,Y), $ then $ \displaystyle\bigcup_{i=1}^{n} K_{i}$ and $ \displaystyle \sum_{i=1}^{n} K_{i} $ are uniformly $ p $-convergent sets in $ L(X,Y). $\
\end{prop}
\begin{rem}
$ \rm{(i)} $ If $ K\subset X^{\ast} ,$ then the definition of uniformly $ p $-convergent sets coincide
with the definition of $ p$-$ (V) $ sets.\
Also, every
uniformly $ q $-convergnt subset of $L(X,Y) $ is
uniformly $ p $-convergnt, whenever $1\leq p < q \leq \infty. $\ Also, it would be interesting to obtain conditions under which every uniformly $ p $-convergent set in $L(X,Y) $ is
uniformly $ q $-convergnt.\ In my opinion, this is a very interesting, but it is
a difficult question?\ In particular, we
answer this question.\ Indeed, we obtain a characterization for those Banach
spaces in which uniformly $ p $-convergent sets in $ X^{\ast} $ are uniformly $ q $-convergent (see Definition $ \rm{2.1} $ and Theorem
$ \rm{2.4} $ in \cite{afz}).\\
$ \rm{(ii)} $ Suppose that $ P\in P(^{k}X) .$\ It is easy to verify that the equivalence $ (a) \Leftrightarrow (e) $ in {\rm (\cite[Corollary 9 ]{ce})}, shows that the operator
$ \overline{P}:X\rightarrow P(^{k}X) $ given by $ \overline{P}(x)(y) =\hat{P}(x,\cdot\cdot\cdot,x ,y)~~~(x,y \in X)$ belongs to $ C_{p} $
if and only if the derivative $ P^{\prime} \in P(^{k}X, X^{\ast}) $ defined by $ P^{\prime}(x)(y)=k \hat{P} (x,\cdot\cdot\cdot,x ,y)$ takes bounded sets of $ X $ into uniformly $ p $-convergent sets in $ X^{\ast} .$\\
$ \rm{(iii)} $ It is well known {\rm (\cite[Theorem 11]{ce})}, that for a holomorphic function $ f $ of bounded type on a complex Banach space $ X, $
its derivative $ f^{\prime} :X\rightarrow X^{\ast}$
takes bounded sets into uniformly $ p $-convergent sets in $ X^{\ast} $ if and only
if $ f $ may be factored in the form $ f=g \circ S $ where $ S $ is $ p $-convergent
and $ g\in \mathcal{H}_{b} (X).$
\end{rem}

The following example show that, there exists a uniformly $ p $-convergnt subset of $ L(\ell_{2},Y) $ so that
it is not uniformly $ q $-convergnt.\
\begin{ex} Let $ X=\ell_{2} $ and $ Y$ be an arbitrary Banach space.\
Since $ \ell_{2} $ does not have $ 2 $-Schur property, $ B_{\ell_{2}} $ is not a $ 2$-$ (V ) $ set in $ \ell_{2} $.\ Therefore $B_{\ell_{2}} $
is not uniformly $ 2 $-convergnt subsets of $ \ell_{2} .$\
On the other hand, $ \ell_{2} $ contains no copy of $ c_{0} .$\ Therefore, $ \ell_{2} $ has the $ 1 $-Schur property (see \cite{dm}).\ Hence,
$ B_{\ell_{2}} $ is a $ 1 $-$ (V ) $ set and so, $ B_{\ell_{2}} $ is a uniformly $ 1 $-convergnt subsets of $ \ell_{2} .$\ Now, let $ 0\neq y_{0}\in B_{Y} $ and
$ S : \mathbb{R}\rightarrow Y $ be the operator
given by $ S(\lambda) := \lambda y_{0}~(\lambda \in \mathbb{R}). $\ Define an operator $ T : \ell_{2}\rightarrow L(\ell_{2}, Y ) $ by
$T (\phi)(h) := \phi(h) y_{0}, $ for $ \phi \in \ell_{2}^{\ast}=\ell_{2} $ and $ h \in \ell_{2}. $\ Then
$$ \parallel T(\phi) \parallel=\sup_{h\in B_{\ell_{2}}}\parallel T(\phi) (h) \parallel=\sup_{h\in B_{\ell_{2}}}\parallel \phi(h) y_{0} \parallel=\parallel \phi \parallel .$$
Since, uniformly $ p $-convergent sets are stable under isometry,
there exists a uniformly $ 1 $-convergnt subset of $ L(\ell_{2},Y) $ so that
it is not uniformly $ 2 $-convergnt.\
\end{ex}
Recall that a sequence $ (x_{n}) \subset U $ is $ U $-bounded, if the set $ \lbrace x_{n}: n \in \mathbb{N}\rbrace $ is $ U $-bounded.\ A
mapping $ f : U \rightarrow Y $ is weakly sequentially continuous, if it takes $ U $-bounded and weakly Cauchy sequences of $ U $ into norm convergent sequences in $ Y. $\ The space of all such mappings is denoted by $ C_{wsc}(U, Y )$ \cite{ce2}.
\begin{defn} \label{d2} Let $ U$ be an open convex subset of $ X$ and $ 1 \leq p \leq \infty. $\
We say that $ f: U\rightarrow Y $ is a weakly $ p $-sequentially continuous map, if it takes weakly $ p $-Cauchy and $ U $-bounded sequences of $ U $ into norm convergent
sequences in $ Y. $\ The space of all such mappings is denoted by $ C_{wsc}^{p}(U, Y ). $
\end{defn}
\begin{rem}
It is easy to show that the weakly $ \infty $-sequentially continuous maps are precisely the weakly sequentially continuous.\
Also, it is clear that
for all $ X, Y , $ and for every open subset $ U \subseteq X, $ we have $ C^{q}_{wsc} (U,Y)\subseteq C^{p}_{wsc} (U,Y), $ whenever $ 1\leq p<q \leq \infty. $\ But, we do not have any example of a mapping $ f \in C^{1u}(U, Y ) \cap C^{p}_{wsc}(U, Y ) $ which does not belong to $ C^{q}_{wsc}(U, Y ). $\
Also, it would be interesting to obtain conditions under which every mapping in the space $ C^{1u}(U, Y ) \cap C^{p}_{wsc}(U, Y ) $ takes $ U $-bounded and weakly
$ q $-Cauchy sequences into norm convergent sequences.\ In my opinion, this is a very interesting, but it is a difficult question?\

\end{rem}
\begin{prop}\label{p2}
Suppose that $ U$ is an open subset of $ X. $\ If $ f $ is compact and takes $ U $-bounded weakly $ p $-Cauchy sequences into weakly Cauchy sequences, then $ f \in C_{wsc}^{p}(U, Y ). $
\end{prop}
\begin{proof}
Let $ (x_{n})_{n} $ be a weakly $ p $-Cauchy and $ U$-bounded sequence.\ Then $ ( f (x_{n}))_{n} $ is weakly Cauchy so that, $ \lbrace f(x_{n}) :n\in\mathbb{N} \rbrace $ is a
relatively compact set.\ It is easy to show that this implies the norm convergence of $ ( f (x_{n}))_{n} .$\ Hence, $ f \in C_{wsc}^{p}(U, Y ). $
\end{proof}

\begin{prop}\label{p3}
Let $ U $ be an open convex subset of $ X$ and let $ f \in C^{1u}(U, Y ). $\ If $ f^{\prime} \in C^{p}_{wsc} (U, C_{p}(X,Y)),$ then $ f\in C_{wsc}^{p} (U,Y).$
\end{prop}
\begin{proof}
Let $ (x_{n})_{n} $ be a $ U $-bounded weakly $ p $-Cauchy sequence.\ By the Mean Value Theorem {\rm (\cite[Theorem 6.4]{ch})}, we have
$$ \parallel f(x_{n})-f(x_{m}) \parallel ~\leq ~\parallel f^{\prime}(c_{n,m}) (x_{n}-x_{m})\parallel$$
for some $ c_{n,m} \in I(x_{n}, x_{m}). $\ Since the sequence $ (c_{n,m}) $ is $ U$-bounded and weakly $ p $-Cauchy, by the hypothesis the sequence $ (f^{\prime}(c_{n,m})) $ norm
converges
to some $ T \in C_{p}(X, Y ). $\ Therefore we have:\\ $$ \displaystyle\lim_{n,m\rightarrow \infty} \parallel f^{\prime}(c_{n,m}) (x_{n}-x_{m})-T(x_{n}-x_{m})\parallel+T(x_{n}-x_{m}) \parallel $$\\ $$ \leq \lim_{n,m\rightarrow \infty} \parallel f^{\prime}(c_{n,m}) (x_{n}-x_{m})-T(x_{n}-x_{m})\parallel+\lim_{n,m\rightarrow\infty}\parallel T(x_{n}-x_{m}) \parallel=0.$$
Hence,
$ \displaystyle\lim_{n,m\rightarrow \infty}\parallel f^{\prime}(c_{n,m}) (x_{n}-x_{m})\parallel=0.$
\end{proof}
\begin{lem}\label{l1}
If $ X $ does not have the $ p $-Schur property, then there is a non $ p $-convergent operator $ T:X\rightarrow L_{\infty}[0,1].$
\end{lem}
\begin{proof}
If X is separable, then by {\rm (\cite[Theorem 2.5.7]{AlbKal})} $ X $ embeds isometrically into $ \ell_{\infty}.$\
Hence,
there is an into isometry $ T:X\rightarrow \ell_{\infty} $ which is obviously not $ p $-convergent.
If $ X $ is not separable, it is easy to show that it has a separable subspace $ Z $ without the $ p $-Schur property.\ Hence, there is
an into isometry $ T_{1} \in L(Z, \ell_{\infty}) $ and thus using the fact that $ \ell_{\infty} $ is injective we can
find a bounded linear operator $ T:X\rightarrow \ell_{\infty} $ which extends the operator $ T_{1} .$\ It is clear that $ T $ is not a $ p $-convergent operator.\ Since $ \ell_{\infty} $ is isomorphic to $ L_{\infty}[0, 1] $ (see {\rm (\cite[Theorem 4.3.10]{AlbKal})} ), we obtain a non $p $-convergent operator $ T :X\rightarrow L_{\infty}[0, 1]. $\
\end{proof}
The proof of following lemma with some minor modifications is similar to the
proof of {\rm (\cite[Theorem 2.3]{AHV})}.\ Hence, we omit its proof.
\begin{lem}\label{l2}
A polynomial is weakly $ p $-sequentially continuous if and only if it is $ p$-convergent.
\end{lem}
A Banach space $ X$ is
said to have the Dunford-Pettis-property of order $ p $ (or briefly, $ X$ has the $ (DPP_{P}) $),
if the inclusion $ W(X, Y ) \subseteq C_{p}(X, Y ) $ holds for all Banach spaces $ Y  $ \cite{cs}.
\begin{thm}\label{t4}
Let $ U $ be an open convex subset of $ X. $\ If for all $ k \in \mathbb{N} ~(k\geq2),$ every Banach space $ Y, $ and every weakly $ p $-sequentially continuous polynomial $ P \in P(^{k}X, Y ), $ the derivative
$ P^{\prime} \in P( ^{k-1}X,L(X, Y )) $ is weakly $ p $-sequentially continuous, then either $ X $ has the $ p $-Schur property or it
contains no copy of $ \ell_{1}. $
\end{thm}
\begin{proof}
Assume on the contrary that $ X $ contains a copy of $ \ell_{1}$ and does not have the $ p $-Schur property.\ Therefore, by Corollary 4.16 and Theorem 2.17 of \cite{djt}, there is a $ p $-convergent operator from $ X $ onto $ \ell_{2} .$\ Since $ \ell_{2} $ is isometrically
isomorphic to $ L_{2}[0, 1] $, we obtain a surjective operator $ S \in C_{p}(X, L_{2}[0, 1]) .$\ On the other hand, by Lemma \ref{l1}, there is a non $ p $-convergent operator $ T:X\rightarrow L_{\infty}[0,1].$\ Now, let $ k\geq 2 $ be the integer.\ Define a $ k $-linear mapping $ L:X^{k} \rightarrow L_{2}[0,1]$ by\\

$ L(x_{1},\cdot\cdot\cdot,x_{k}) =\frac{1}{k}[S(x_{1})T(x_{2})\cdot\cdot\cdot T(x_{k}) +\cdot\cdot\cdot +T(x_{1})T(x_{2})\cdot\cdot\cdot T(x_{k-1})S(x_{k})]$ for $ x_{1},\cdot\cdot\cdot, x_{k} \in X.$\
Obviously, $ L$ is well defined, symmetric, and continuous.\ For each $ x\in X, $  consider the associated polynomial
$ P(x)=S(x) T(x)^{k-1}.$\ We claim that $ P $ is weakly $ p $-sequentially continuous.\ For this purpose,
suppose that $ (x_{n}-x)_{n} $ is a
weakly $p $-summable sequence in $ B_{X}. $\ Hence, we have:
\begin{eqnarray*}
 \parallel P(x_{n}) -P(x)\parallel= \parallel S(x_{n}) T(x_{n})^{k-1} - S(x) T(x)^{k-1} \parallel &\leq&\\ \parallel S(x_{n}) T(x_{n})^{k-1} - S(x) T(x_{n})^{k-1} \parallel +\parallel S(x) T(x_{n})^{k-1} - S(x) T(x)^{k-1} \parallel &= &\\ ( \int_{0}^{1} \vert S(x_{n})(t) -S(x)(t) \vert^{2} \vert T(x_{n}) (t)\vert^{2k-2} dt)^{\frac{1}{2}} &+ &\\ ( \int_{0}^{1} \vert S(x)(t) \vert^{2} \vert T(x_{n}) (t)^{k-1} -T(x)(t)^{k-1}\vert^{2} dt )^{\frac{1}{2}} &\leq &\\ \parallel T \parallel^{k-1} ( \int _{0}^{1} \vert S(x_{n}-x)(t)\vert^{2} dt)^{\frac{1}{2}}+ \langle S(x)^{2}, [T(x_{n}) (t)^{k-1} -T(x)(t)^{k-1}]^{2} \rangle^{\frac{1}{2}} &= &\\ \parallel T \parallel^{k-1} \Vert S(x_{n}-x)\Vert_{L_{2}}+\langle S(x)^{2}, [T(x_{n}) (t)^{k-1} -T(x)(t)^{k-1}]^{2} \rangle^{\frac{1}{2}}.
\end{eqnarray*}
Since $ S \in C_{p}(X, L_{2}[0, 1]) ,$ we have
$\lim_{n\rightarrow \infty}\parallel S(x_{n}-x) \parallel_{L_{2}}=0. $\
Now, for $ m\in \mathbb{N} ~(m\geq 2), $ we consider the polynomial $ \varphi:L_{\infty} [0,1]\rightarrow L_{\infty} [0,1]$ defined by $ \varphi(g):=g^{m}. $\ Since $ L_{\infty} [0,1] $ has the $ (DPP_{p}) ,$
this polynomial takes weakly $ p $-convergent sequences into norm convergent sequences and so, the sequence $ ([T (x_{n})^{k-1}-T (x)^{k-1}]^{2})_{n} $ is weakly null in $ L_{\infty} [0,1] . $\ On the other hand, $ S(x)^{2}\in L_{1}[0,1] .$\ Hence,
$$ \lim_{n\rightarrow \infty} \langle S(x)^{2}, [T(x_{n}) (t)^{k-1} -T(x)(t)^{k-1}]^{2} \rangle^{\frac{1}{2}} =0.$$
Therefore, $ \displaystyle \lim_{n\rightarrow \infty} \parallel P(x_{n}) -P(x)\parallel=0 $ and so,
Lemma \ref{l2} implies that the polynomial
$ P $ is weakly $ p $-sequentially continuous.\ By using the same
argument as in the proof of
{\rm (\cite[Theorem 2.9]{ce2})}, $ P^{\prime} $ is not weakly $ p $-sequentially continuous, which is a contradiction.
\end{proof}

By using the same
argument as in the proof of {\rm (\cite[Theorem 2.1]{ce2})}, we obtain the following similar
result.
\begin{thm}\label{t1}
Let $ U\subseteq X $ be an open convex subset and let $ f \in C^{1u}(U, Y ). $\ Then the following assertions are equivalent:\\
$ \rm{(i)} $ $ f\in C_{wsc}^{p} (U,Y);$\\
$ \rm{(ii)} $ For every $ U $-bounded and weakly $ p $-Cauchy sequence $ (x_{n}) $ and every weakly $ p $-Cauchy sequence $ (h_{n}) \subset X, $ the sequence $ (f^{\prime}(x_{n})(h_{n}))_{n} $ norm converges
in $ Y; $\\
$ \rm{(iii)} $ For every $ U $-bounded weakly $ p $-Cauchy sequence $ (x_{n})_{n} $ and every weakly $ p $-summable sequence $ (h_{n})_{n} \subset X, $ we have
$$\lim_{n}\sup_{m}\parallel f^{\prime}(x_{m}) (h_{n}) \parallel =0;$$\
$ \rm{(iv)} $ For every $ U$-bounded weakly $ p $-Cauchy sequence $ (x_{n})_{n} $ and every weakly $ p $-summable sequence $ (h_{n})_{n} \subset X, $ we have
$$\lim_{n} f^{\prime}(x_{n}) (h_{n}) =0;$$
$ \rm{(v)} $ $ f^{\prime} $ takes $ U$-bounded and weakly $ p $-precompact subsets of $ U$ into uniformly $ p $-convergent subsets of $ L(X, Y ). $
\end{thm}
\begin{proof}
(i) $ \Rightarrow $ (ii) Suppose that $ (x_{n})_{n} $ is a $ U $-bounded and weakly $ p $-Cauchy sequence.\ Let $ (h_{n})_{n} $ be a weakly $ p $-Cauchy sequence in $ X. $\ Without loss
of generality, we assume that $ (h_{n})_{n}$ is bounded.\ Consider $ B := \lbrace x_{n}: n \in \mathbb{N} \rbrace $ and let $ d := min\lbrace 1, dist(B, \partial U)\rbrace. $\ It is easy to show that the set
$$ B^{\prime}:=B+\frac{d}{2}B_{X}\subset U$$
is also $ U $-bounded.\ Since $ f \in C^{1u}(U, Y ),$ $ f^{\prime} $ is uniformly continuous on $ B^{\prime}.$\ Hence, for given $ \varepsilon >0, $ there exists $ 0 <\delta <\frac{d}{4} $ such that if $t_{1} ,t_{2}\in B^{\prime}$
satisfy $ \parallel t_{1} -t_{2}\parallel <2\delta,$ then
\begin{equation}\label{eq}
\parallel f^{\prime}(t_{1})-f^{\prime}(t_{2}) \parallel <\frac{\varepsilon}{4}.
\end{equation}
If $ c\in I(x_{n},x_{n}+\delta h_{n}) $ for some $ n\in \mathbb{N}, $ then
$$ \parallel c-x_{n} \parallel \leq \delta \parallel h_{n} \parallel <\delta <2\delta <\frac{d}{2},$$
and so,
$$c=x_{n} +(c-x_{n})\in B^{\prime}=B+\frac{d}{2}B_{X} $$
As an immediate consequence of the Mean Value Theorem {\rm (\cite[Theorem 6.4]{ch})}, and formula (\ref{eq}), we obtain
\begin{flushleft}
$ \parallel f^{\prime}(x_{n}) ( \delta h_{n})-f(x_{n}+
\delta h_{n})+f(x_{n})\parallel $
\end{flushleft}
\begin{center}
$ \leq \displaystyle\sup_{c\in I(x_{n},x_{n}+\delta h_{n})} \parallel f^{\prime} (c) - f^{\prime} (x_{n}) \parallel \parallel\delta h_{n}\parallel
\leq\frac{\varepsilon \delta}{4} .$
\end{center}
Similary,
\begin{flushleft}
$ \parallel f(x_{m}+\delta h_{m})-f(x_{m})- f^{\prime}(x_{m}) ( h_{m})\parallel $
\end{flushleft}
\begin{center}
$
\leq \displaystyle\sup_{c\in I(x_{m},x_{m}+\delta h_{m})} \parallel f^{\prime} (c) - f^{\prime} (x_{m}) \parallel \parallel\delta h_{m}\parallel
\leq\frac{\varepsilon \delta}{4}.\
$
\end{center}
In the other word, the sequences $ (x_{n}+\delta h_{n})_{n} $ and $ (x_{n})_{n} $ are $ U$-bounded and weakly $ p $-Cauchy in $ U. $\ Hence, by the hypothesis the
sequences $ ( f (x_{n} +\delta h_{n}))_{n} $ and $ ( f (x_{n}))_{n} $ are norm convergent in $ Y. $\ Hence, we can find $ n_{0}\in \mathbb{N} $ so that for $ n,m > n_{0} :$
\begin{flushleft}
$ \parallel f(x_{n}+\delta h_{n})-f(x_{m}+\delta h_{m})\parallel <\frac{\varepsilon \delta}{4},~~~~~~~~~~~~~ \parallel f(x_{n})-f(x_{m})\parallel <\frac{\varepsilon \delta}{4} $
\end{flushleft}
So, for $ n,m > n_{0} ,$ we have\
$$\parallel f^{\prime}(x_{n}) (h_{n}) - f^{\prime}(x_{m}) (h_{m})\parallel< \varepsilon.$$\
(ii) $ \Rightarrow $ (iii) Let $ (x_{n})_{n} $ be a $ U $-bounded weakly $ p $-Cauchy sequence and let $ (h_{n})_{n} $ be a weakly $ p $-summable sequence in $ X. $\ By the part $ \rm{(ii)} $, for every $ h \in X, $ the set $ \lbrace f^{\prime} (x_{n})(h) :n\in \mathbb{N}\rbrace$ is bounded in $ Y. $\ On the other hand, there exists a subsequence $ (x_{m_{k}}) _{k}$ of $ (x_{m})_{m} $ in $ U $ such that
$$ \parallel f^{\prime} (x_{m_{k}})(h_{k}) \parallel \geq \sup_{m}\parallel f^{\prime} (x_{m})(h_{k}) \parallel-\frac{1}{k} ~~~~(k\in \mathbb{N}).$$
Since the sequences $ (x_{m_{k}}) _{k}$ in $ U $ and $ (h_{1},0,h_{2},0,h_{3},0,\cdot\cdot\cdot) $ in $ X $
are weakly $ p $-Cauchy, the sequence
$$ (f^{\prime}(x_{m_{1}})(h_{1}),0,f^{\prime}(x_{m_{2}})(h_{2}),0, f^{\prime}(x_{m_{3}})(h_{3}),0,\cdot\cdot\cdot) $$
converges in $ Y. $\ Therefore, $ \displaystyle\lim_{k} f^{\prime}(x_{m_{k}})(h_{k})=0.$\ Hence, $ \rm{(ii)} $ implies that
$$ \lim_{k} \sup_{m}\parallel f^{\prime}(x_{m}) (h_{k}) \parallel =0.$$
(iii) $ \Rightarrow $ (iv) is obvious.\\
(iv) $ \Rightarrow $ (v) Let $ K$ be a weakly $ p $-precompact $ U $-bounded set.\ It is clear that, for every $ h \in X, $ the set $ f^{\prime}(K)(h) $
is bounded
in $ Y. $\ Let $ (h_{n}) _{n}$ is a weakly $ p $-summable sequence in $ X. $\
If $ (h_{n_{k}})_{k} $ is a subsequence of $ (h_{n}) _{n},$ then for every $ k\in \mathbb{N}, $ there exists $ a_{k}\in K $ such that
$$ \sup_{a \in K}\parallel f^{\prime}(a) (h_{n_{k}}) \parallel < \parallel f^{\prime}(a_{k}) (h_{n_{k}}) \parallel+\frac{1}{k}. $$
Since $ K $ is a weakly $ p $-precompact set, the sequence $ (a_{k})_{k} $ admits a weakly $ p $-Cauchy subsequence $ (a_{k_{r}}) _{r}.$\ Hence, by the hypothesis,
$$ \displaystyle\lim_{r} \parallel f^{\prime}(a_{k_{r}}) (h_{n_{k_{r}}}) \parallel=0. $$
Therefore we have,
$ \displaystyle\lim_{r}\sup_{a\in K} \parallel f^{\prime}(a) (h_{n_{k_{r}}}) \parallel=0. $\ Hence, every subsequence of
$ ( \displaystyle \sup_{a \in K} \parallel f^{\prime}(a) (h_{n}) \parallel) _{n}$
has a subsequence converging to $ 0. $\ Therefore, the sequence itself converges to $ 0, $ that is, $ \displaystyle \lim_{n}\sup_{a \in K} \parallel f^{\prime}(a) (h_{n}) \parallel =0.$\\
(v) $ \Rightarrow $ (i) Let $ (x_{n})_{n} $ be a $ U $-bounded and weakly $ p $-Cauchy sequence.\ Since $ U$ is convex, the segment $ I(x_{n}, x_{m}) $ is contained in $ U$
for all $ n,m \in \mathbb{N}. $\ By the Mean Value Theorem {\rm (\cite[Theorem 6.4]{ch})},
there exists $ c_{nm} \in I(x_{n}, x_{m}) $ such that
$$ \parallel f(x_{n}) -f(x_{m}) \parallel \leq \parallel f^{\prime}(c_{n,m}) (x_{n}-x_{m}) \parallel \leq \sup_{i,j \in \mathbb{N}}\parallel f^{\prime}(c_{i,j}) (x_{n}-x_{m}) \parallel .$$
Since $ (c_{i,j})_{i,j} $ is a weakly $ p $-Cauchy and $ U $-bounded sequence, by $ \rm{(v)} $ we have
$$ \lim_{n,m}\sup_{i,j \in \mathbb{N}}\parallel f^{\prime}(c_{i,j}) (x_{n}-x_{m}) \parallel=0. $$
Therefore, $\displaystyle \lim_{n,m\rightarrow\infty}\parallel f(x_{n}) -f(x_{m}) \parallel =0.$
\end{proof}
\begin{rem}\label{r2}
If $ U \subseteq X $ is an open subset, let $ f \in C^{1u}(U, Y ) \cap C^{p}_{wsc}(U, Y ). $ \ Then, by $ \rm{(ii)} $ of Theorem $ \rm{\ref{t1}} $, $ f^{\prime}(U) \subseteq C_{p}(X, Y ). $\
\end{rem}
\begin{thm}\label{t2}
Let $ B_{X} $ be weakly $ p $-precompact and let $ U $ be an open subset of $ X$ and let $ f \in C^{1u}(U, \mathbb{R} )\cap C^{p}_{wsc}(U, \mathbb{R} ). $\ If every uniformly $ p $-convergent set in $ K(X, \mathbb{R} ) $ is uniformly completely continuous, then $ f^{\prime} $ is compact with values in $ C_{p}(X, \mathbb{R} ) .$
\end{thm}
\begin{proof}
By the Remark \ref{r2}, the range of $ f^{\prime} $ is contained in $ C_{p}(X, \mathbb{R} ) = K(X, \mathbb{R} ) $ (see Theorem 2.6 in \cite{ccl}), where we have used
the fact that $ B_{X} $ is weakly $ p $-precompact. Let $ B$ be a $ U $-bounded set.\ Given $ h \in X, $ let $ (x_{n})_{n} \subset B $ be a sequence.\ Since $ B_{X} $ is weakly $ p $-precompact, we can assume that $ (x_{n})_{n} $ is weakly $ p $-Cauchy.\ Hence Theorem \ref{t1}$ \rm{(ii)} $, implies that the sequence $ ( f^{\prime} (x_{n})(h))_{n} $ is converges
in $ \mathbb{R} $ and so, $ f^{\prime} (B)(h) $ is relatively compact in $ \mathbb{R}.$\ Moreover, by the  Theorem \ref{t1}$ \rm{(v)} $, $ f^{\prime} (B) $ is a uniformly $ p $-convergent set in $ K(X, \mathbb{R} ) .$\ Hence by the hypothesis $ f^{\prime} (B) $is
uniformly completely continuous
in $ K(X, \mathbb{R} ) .$\ On the other hand by using again the fact that $ B_{X} $ is weakly $ p $-precompact, we observation that
$ X $ contains no copy of $ \ell_{1} .$\ Therefore, {\rm (\cite[Theorem 1]{m})} implies that
$ f^{\prime} (B) $ is relatively
compact in $ C_{p}(X, \mathbb{R} ) .$
\end{proof}

\begin{defn}\label{d3}
A mapping $ f:U \rightarrow Y $ is $ p $-convergent, if for every $ U $-bounded and weakly $ p $-converging sequence $ (x_{n}) _{n}$ to $ x\in U $, the sequence
$ ( f (x_{n}))_{n} $ norm converges to $ f (x) .$\ We denote the space of $ p $-convergent mappings by $ C_{C_{p}}(U, Y ) .$\
It is clear that for all $ X, Y , $ and for every open subset $ U \subseteq X, $ we have $ C_{wsc}^{p} (U,Y)\subseteq C_{C_{p}}(U, Y ) .$\\
We do not have any example of a mapping $ f\in C^{1u}(U, Y ) \cap C_{C_{p}}(U, Y ) $ which does not belong to $ C_{wsc}^{p} (U,Y). $
\end{defn}
\begin{thm}\label{t3}
Let $ U\subseteq X $ be an open convex subset and let $ f \in C^{1u}(U, Y ). $\ If $ f^{\prime} $ takes $ U$-bounded weakly $ p $-compact subsets of $ U$ into relatively compact subsets of $ K(X, Y), $ then the following assertions are hold:\\
$ \rm{(i)} $ $ f \in C_{C_{p}}(U, Y ); $\\
$ \rm{(ii)} $ $ f^{\prime} \in C_{C_{p}}(U,K(X, Y )). $
\end{thm}
\begin{proof}
$ \rm{(i)}$ Let $ (x_{n})_{n} $ be a $ U$-bounded sequence and weakly $ p $-convergent to $ x \in U. $\ Since the set $ K:=\lbrace x_{n} :n\in \mathbb{N} \rbrace \cup\lbrace x\rbrace $ is weakly $ p $-compact subset of $ U,$ by the Mean Value Theorem {\rm (\cite[Theorem 6.4]{ch})},
for each $ n \in \mathbb{N} , $ there is $ c_{n} \in I(x_{n}, x) $ such that
$$ \parallel f(x_{n}) -f(x) \parallel \leq \parallel f^{\prime}(c_{n}) (x_{n}-x) \parallel \leq \sup_{k}\parallel f^{\prime}(c_{k}) (x_{n}-x)\parallel ~~~~~~(n\in \mathbb{N}).$$
But, $ (c_{n})_{n} $ is a weakly $ p $-convergent sequence to $ x$ and $ U $-bounded.\ Therefore, by the hypothesis, the set $ \lbrace f^{\prime}(c_{n}) :n\in \mathbb{N} \rbrace $ is relatively compact in $ K(X, Y ) $
and so, uniformly $ p $-convergent.\ Since $ (x_{n}- x)_{n} $ is weakly $ p $-summable, we have:
$$ \displaystyle\lim_{n} \parallel f(x_{n})-f(x) \parallel\leq \lim_{n} \sup_{k}\parallel f^{\prime}(c_{k}) (x_{n}-x)\parallel =0.$$
$\rm{(ii)} $ Suppose that $ (x_{n})_{n} $ is a $ U $-bounded and weakly $ p $-convergent sequence.\ Consider $ B := \lbrace x_{n}: n \in \mathbb{N} \rbrace\cup\lbrace x\rbrace $ and let $ d := min\lbrace 1, dist(B, \partial U)\rbrace. $\ The set
$$ B^{\prime}:=B+\frac{d}{2}B_{X}\subset U$$
is also $ U $-bounded.\ Since $ f \in C^{1u}(U, Y ),$ $ f^{\prime} $ is uniformly continuous on $ B^{\prime}.$\ Hence, for given $ \varepsilon >0, $ there exists $ 0 <\delta <\frac{d}{4} $ such that if $t_{1} ,t_{2}\in B^{\prime}$
satisfy $ \parallel t_{1} -t_{2}\parallel <2\delta,$ then
\begin{equation}\label{eq1}
\parallel f^{\prime}(t_{1})-f^{\prime}(t_{2}) \parallel <\frac{\varepsilon}{4}.
\end{equation}
Fix $ n\in\mathbb{N} $ and $ h\in B_{X}. $\
If $ c\in I(x_{n},x_{n}+ x_{n}h) ,$ then as in the proof of Theorem \ref{t1} we have
$$ \parallel c-x_{n} \parallel \leq <2\delta <\frac{d}{2},$$
and so,
$c=x_{n} +(c-x_{n})\in B^{\prime}=B+\frac{d}{2}B_{X}. $\ Therefore, $ I(x_{n}, x_{n} +\delta h)\subset B^{\prime}. $\ Similarly, $ I(x, x+\delta h) \subset B^{\prime}.$\
As an immediate consequence of the Mean Value Theorem {\rm (\cite[Theorem 6.4]{ch})},
and formula (\ref{eq1}), we obtain
\begin{flushleft}
$ \parallel f^{\prime}(x_{n}) ( \delta h)-f(x_{n}+
\delta h)+f(x_{n})\parallel ~ ~~~`$
\end{flushleft}
$$ ~~~~~~~\leq \displaystyle\sup_{c\in I(x_{n},x_{n}+\delta h)} \parallel f^{\prime} (c) - f^{\prime} (x_{n}) \parallel \parallel\delta h\parallel\leq\frac{\varepsilon \delta}{4} . $$
Similary,
\begin{flushleft}
$ \parallel f(x+
\delta h)-f(x)- f^{\prime}(x) ( \delta h)\parallel ~ $
\end{flushleft}
$$ \leq \displaystyle\sup_{c\in I(x,x+\delta h)} \parallel f^{\prime} (c) - f^{\prime} (x) \parallel \parallel\delta h\parallel\leq\frac{\varepsilon \delta}{4} . $$
In the other word, the sequences $ (x_{n}+\delta h)_{n} $ and $ (x_{n})_{n} $ are $ U$-bounded and weakly $ p $-convergent in $ U $ to $ x + \delta h $ and $ x, $ respectively.\
 So, there exists $ n_{0}\in \mathbb{N} $ so that for $ n> n_{0},$\
$ \parallel f(x_{n}+\delta h)-f(x+\delta h)\parallel <\frac{\varepsilon \delta}{4},~~~$  and $~~~~ \parallel f(x_{n})-f(x)\parallel <\frac{\varepsilon \delta}{4}. $

Therefore, for $ n> n_{0} ,$
$\parallel f^{\prime}(x_{n}) (h) - f^{\prime}(x) (h)\parallel< \varepsilon.$\
Hence, for every $ h \in X, $ we have $ \displaystyle \lim_{n}f^{\prime}(x_{n})(h)=f^{\prime}(x)(h).$\ Since $ f^{\prime}(B) $ is relatively compact in $ K(X, Y ), $  Lemma 4.2 of \cite{va}, implies that
$ \displaystyle \lim_{n}f^{\prime}(x_{n})=f^{\prime}(x).$\
\end{proof}

redpajama_set_name: RedPajamaArXiv


text:
New Bulletin Edition: You are viewing the 2022-2023 edition of the Undergraduate Bulletin. Undergraduate students who entered the university prior to Summer 2022 should follow the requirements published in the Bulletin edition from their entry year. Past editions of the Bulletin are available in the archive.
Baccalaureate Degree Programs
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Penn State Abington, The Abington College/
American Studies, B.A. (Abington)
Program Code: AMSAB_BA
Abington College
How to Get In
Suggested Academic Plan
Accounting, B.S. (Abington)
Art, B.A. (Abington)
Biology, B.S. (Abington)
Business Administration, A.S. (Abington)
Business, B.S. (Abington)
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English, B.A. (Abington)
Finance, B.S. (Abington)
Health Humanities, B.A.
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Integrative Arts, B.A. (Abington)
Multidisciplinary Studies, A.A. (Abington)
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Project and Supply Chain Management, B.S. (Abington)
Psychological and Social Sciences, B.A.
Psychological and Social Sciences, B.S.
Public History, Minor
Race and Ethnic Studies, B.A.
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Science, B.S. (Abington)
At which campus can I study this program?
Begin Campus
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Degree Information At Additional Campuses
Choose a Campus...BrandywineHarrisburg
This interdisciplinary major is designed to provide students with an integrated and critical knowledge of American culture, drawing on courses in American Studies and in the traditional disciplines and culminating in two senior seminars. A number of interests may be pursued within the major, including popular culture, art, technology, business, law, archives, museology, and conservation. The major helps prepare students for careers in business, teaching, government, and a number of other areas, and for enrollment in law and other professional programs.
What is American Studies?
American Studies examines the country's history in a way that emphasizes culture – literature, art & architecture, film, folklore, music, and media. While discovering America's past, students learn to think critically – to analyze and evaluate information; to write and speak clearly and expressively; and to conduct research.
You Might Like This Program If...
You enjoy pop culture and wonder what social and historical forces helped shape it.
You like making connections between history, society, economics, literature, film, and art.
You want to understand the American experience beyond just what is relayed in a history text.
You want to explore the experiences of women, minorities, and different ethnic and religious groups.
You want to pursue a career in education, law, government, museums, cultural agencies, archives, public policy, or communications.
Entrance to Major
For entrance into the major, the following must be met:
At the end of the sophomore year, any student in good standing may gain entrance into the major without having completed specific courses.
Any student seeking entrance during the fifth semester will be granted entrance at the discretion of the American Studies Committee and/or Director following evaluation of the student's record.
Any student seeking entrance during or after the sixth semester will be expected to have completed at least 12 credits, which may be counted toward the major in American Studies.
For the Bachelor of Arts degree in American Studies, a minimum of 123 credits is required:
General Education 45
Electives 21
Bachelor of Arts Degree Requirements 24
Requirements for the Major 33
3 of the 24 credits for Bachelor of Arts Degree Requirements are included in the Requirements for the Major, General Education, or Electives and 0-12 credits are included in Electives if foreign language proficiency is demonstrated by examination.
Requirements for the Major
A grade of C or better is required for all courses in the major. To graduate, a student enrolled in the major must earn at least a C grade in each course designated by the major as a C-required course, as specified by Senate Policy 82-44.
Prescribed Courses
Prescribed Courses: Require a grade of C or better
AMST 491W American Studies Perspectives 6
Additional Courses: Require a grade of C or better
AMST 100 Introduction to American Studies 3
or AMST 100Y Introduction to American Studies
Supporting Courses and Related Areas
Supporting Courses and Related Areas: Require a grade of C or better
Select 9 credits in each of two of the following areas and 6 credits in one other of the areas (include 12 credits at the 400 level distributed in at least two of the areas): 24
American art, philosophy, and religion (humanities)
American social sciences
Connecting career and curiosity, the General Education curriculum provides the opportunity for students to acquire transferable skills necessary to be successful in the future and to thrive while living in interconnected contexts. General Education aids students in developing intellectual curiosity, a strengthened ability to think, and a deeper sense of aesthetic appreciation. These are requirements for all baccalaureate students and are often partially incorporated into the requirements of a program. For additional information, see the General Education Requirements section of the Bulletin and consult your academic adviser.
The keystone symbol appears next to the title of any course that is designated as a General Education course. Program requirements may also satisfy General Education requirements and vary for each program.
Foundations (grade of C or better is required.)
Quantification (GQ): 6 credits
Writing and Speaking (GWS): 9 credits
Knowledge Domains
Arts (GA): 6 credits
Health and Wellness (GHW): 3 credits
Humanities (GH): 6 credits
Social and Behavioral Sciences (GS): 6 credits
Natural Sciences (GN): 9 credits
Integrative Studies (may also complete a Knowledge Domain requirement)
Inter-Domain or Approved Linked Courses: 6 credits
University Degree Requirements
First Year Engagement
All students enrolled in a college or the Division of Undergraduate Studies at University Park, and the World Campus are required to take 1 to 3 credits of the First-Year Seminar, as specified by their college First-Year Engagement Plan.
Other Penn State colleges and campuses may require the First-Year Seminar; colleges and campuses that do not require a First-Year Seminar provide students with a first-year engagement experience.
First-year baccalaureate students entering Penn State should consult their academic adviser for these requirements.
Cultures Requirement
6 credits are required and may satisfy other requirements
United States Cultures: 3 credits
International Cultures: 3 credits
3 credits required from the college of graduation and likely prescribed as part of major requirements.
Total Minimum Credits
A minimum of 120 degree credits must be earned for a baccalaureate degree. The requirements for some programs may exceed 120 credits. Students should consult with their college or department adviser for information on specific credit requirements.
Candidates must complete the degree requirements for their major and earn at least a 2.00 grade-point average for all courses completed within their degree program.
Limitations on Source and Time for Credit Acquisition
The college dean or campus chancellor and program faculty may require up to 24 credits of course work in the major to be taken at the location or in the college or program where the degree is earned. Credit used toward degree programs may need to be earned from a particular source or within time constraints (see Senate Policy 83-80). For more information, check the Suggested Academic Plan for your intended program.
B.A. Degree Requirements
Foreign Language (0-12 credits): Student must attain 12th credit level of proficiency in one foreign language. See the Placement Policy for Penn State Foreign Language Courses.
B.A. Fields (9 credits): Humanities, Social and Behavioral Sciences, Arts, Foreign Languages, Natural Sciences, Quantification (may not be taken in the area of the student's primary major; foreign language credits in this category must be in a second foreign language or beyond the 12th credit level of proficiency in the first language)
Other Cultures (0-3 credits): Select 3 credits from approved list. Students may count courses in this category in order to meet other major, minor, elective, or General Education requirements, except for the General Education US/IL requirement.
Program Learning Objectives
Identify major themes and issues prompted by the question "What does it mean to be an American".
Recognize the multiple ways Americans have expressed, institutionalized, celebrated, and contested identity in visual and material culture, literature, history, politics, and popular culture.
Appreciate the cultural diversity of the American experience, especially in terms of class, ethnicity, gender, sexual orientation, and race.
Analyze in depth an aspect of American culture using interdisciplinary source materials, research methodologies, and intellectual approaches.
Develop conclusions based on that analysis and communicate them effectively.
The objectives of the university's academic advising program are to help advisees identify and achieve their academic goals, to promote their intellectual discovery, and to encourage students to take advantage of both in-and out-of class educational opportunities in order that they become self-directed learners and decision makers.
Both advisers and advisees share responsibility for making the advising relationship succeed. By encouraging their advisees to become engaged in their education, to meet their educational goals, and to develop the habit of learning, advisers assume a significant educational role. The advisee's unit of enrollment will provide each advisee with a primary academic adviser, the information needed to plan the chosen program of study, and referrals to other specialized resources.
READ SENATE POLICY 32-00: ADVISING POLICY
David Ruth
Program Chair, American Studies
1600 Woodland Road
dxr35@psu.edu
Anthony Buccitelli, Ph.D.
Olmsted Building, W356
Middletown, PA 17057
abb20@psu.edu
David Macauley, Ph.D.
Associate Professor, Philosophy, Associate Professor, Environmental Studies
Main Building, 212 C
25 Yearsley Mill Road
dmm53@psu.edu
The suggested academic plan(s) listed on this page are the plan(s) that are in effect during the 2022-23 academic year. To access previous years' suggested academic plans, please visit the archive to view the appropriate Undergraduate Bulletin edition (Note: the archive only contains suggested academic plans beginning with the 2018-19 edition of the Undergraduate Bulletin).
American Studies, B.A. at Abington Campus
The course series listed below provides only one of the many possible ways to move through this curriculum. The University may make changes in policies, procedures, educational offerings, and requirements at any time. This plan should be used in conjunction with your degree audit (accessible in LionPATH as either an Academic Requirements or What If report). Please consult with a Penn State academic adviser on a regular basis to develop and refine an academic plan that is appropriate for you.
ENGL 15 or 30H 3 World Language level 2 4
General Education Course 3 General Education Course 3
General Education Course (GHW) 1.5 General Education Course 3
World Language level 1 4 General Education Course 3
World Language level 3 4 AMST 100 or 100Y (GH;US)* 3
General Education Course 3 ENGL 202B3 3
CAS 100A or 100B 3 General Education Course 3
General Education 3 General Education Course 3
Elective (US;IL) 3 Bachelor of Arts Requirement 3
General Education Course (GHW) 1.5
AMST Supporting Course1 * 3 AMST Supporting Course1 * 3
400 Level AMST Supporting Course2 * 3 AMST Supporting Course1 * 3
General Education Course 3 400 Level AMST Supporting Course2 * 3
Elective (OC) 3 Bahelor of Arts Requirement 3
Bachelor of Arts Requirement 3 Elective (US;IL) 3
AMST 491W (Course is to be taken as two separate offerings)* 3 AMST 491W (Course is to be taken as two separate offerings)* 3
400 Level AMST Supporting Course2 * 3 400 Level AMST Supporting Course2 * 3
AMST Supporting Course1 * 3 Elective 3
Elective (US;IL) 3 Elective 3
Elective 3 Elective 3
Total Credits 123
Course requires a grade of C or better for the major
Course requires a grade of C or better for General Education
Course is an Entrance to Major requirement
Course satisfies General Education and degree requirement
University Requirements and General Education Notes:
US and IL are abbreviations used to designate courses that satisfy University Requirements (United States and International Cultures).
W, M, X, and Y are the suffixes at the end of a course number used to designate courses that satisfy University Writing Across the Curriculum requirement.
GWS, GQ, GHW, GN, GA, GH, and GS are abbreviations used to identify General Education program courses. General Education includes Foundations (GWS and GQ) and Knowledge Domains (GHW, GN, GA, GH, GS, and Integrative Studies). Foundations courses (GWS and GQ) require a grade of 'C' or better.
Integrative Studies courses are required for the General Education program. N is the suffix at the end of a course number used to designate an Inter-Domain course and Z is the suffix at the end of a course number used to designate a Linked course.
Bachelor of Arts Requirements:
Bachelor of Arts students must take 9 credits in Bachelor of Arts (B.A.) Fields (Humanities; Social and Behavioral Sciences; Arts; World Languages [2nd language or beyond the 12th credit level of proficiency in the 1st]; Natural Sciences; Quantification). The B.A. Fields courses may not be taken in the area of the student's primary major. See your adviser and the Degree Requirements section of this Bulletin.
Bachelor of Arts students must take 3 credits in Other Cultures.
See your adviser and the full list of courses approved as Other Cultures courses.
AMST supporting courses are distributed among arts, history, humanities, literature, and social sciences courses containing at least 50% American content. Students take three courses each from two areas and two courses from a third.
At least 12 of these credits are at the 400 level.
ENGL 202B is recommended for American Studies majors.
The American Studies program benefits from Penn State Harrisburg's location in a capital region in close proximity to internationally known heritage sites such as the Gettysburg Battlefield, National Civil War Museum, and U.S. Army Heritage and Education Center. Harrisburg is also home to the Pennsylvania Historical and Museum Commission, the State Archives, and the State Museum.
American Studies majors at Penn State Harrisburg have opportunities to gain a core set of skills in writing, presentation, exhibition, website development, digital documentation, fieldwork and ethnography, and records and cultural resource management in addition to contextual knowledge of American culture, society, arts, and history that can be applied to a number of occupations, particularly in heritage, communications, education, and government sectors. At Penn State Harrisburg, certificates (heritage and museum practice, folklore and ethnography), internships, assistantships, professional workshops, career services, alumni interaction, social media, and online job postings serve to enhance the marketability of majors at various levels.
MORE INFORMATION ABOUT POTENTIAL CAREER OPTIONS FOR GRADUATES OF THE AMERICAN STUDIES PROGRAM
Opportunities for Graduate Studies
The American Studies major at Penn State Harrisburg prepares students for a variety of professions and to participate in the world as critical thinkers, clear communicators, and global citizens, including Penn State's Master of Arts in American Studies and the Doctor of Philosophy in American Studies programs.
MORE INFORMATION ABOUT OPPORTUNITIES FOR GRADUATE STUDIES
Popular Culture Association/American Culture Association
American Folklore Society
Eastern American Studies Association
Pennsylvania Historical Association
Pennsylvania German Society
Pennsylvania Heritage Society
Pennsylvania Federation of Museums and Historical Organizations
DIVISION OF ARTS AND HUMANITIES
https://www.abington.psu.edu/academics/american-studies
dzs640@psu.edu
https://harrisburg.psu.edu/humanities/american-studies/bachelor-arts-american-studies
https://www.brandywine.psu.edu/academics/bachelors-degrees/american-studies
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We Should Keep an Eye on Dash Radio
November 25, 2015 November 25, 2015 Alan Cross	0 Comments	Dash, DJ Skee, Radio
I'd heard of Dash Radio–vaguely–but now I'm going to have to find a way to properly check it out. From The Daily Dot.
If you think streaming services like Spotify and Apple Music have grown to prominence because people want their music on demand—something traditional radio can't provide—you're only half right. Traditional radio can't provide what people want, but what people want is good radio.
No one knows that better than Scott Keeney, better known as DJ Skee. He's been a staple on the radio airwaves since taking his first gig at age 16, hosting flagship shows on Sirius XM and KIIS-FM in Los Angeles. Skee is responsible for giving early spins to Kendrick Lamar, Lorde and Lady Gaga.
"My whole life has revolved around radio," he told the Daily Dot. "It's the reason I'm in the position I am."
A digital radio platform offering 24/7 streaming programming, Dash is what radio would look like if a Silicon Valley startup built it: the stations aren't regional or restricted by signal strength, everything is accessible, and you can see what's currently playing on every station at all times.
The main draw is the litany of big name hosts. The lineup of personalities on Dash looks like one you'd expect to see at a music festival. There's universally known talent like Snoop Dogg, acts with cult followings like Tech N9ne, and forgotten favorites like T-Boz of TLC.
Tuning in to Snoop's station on Dash isn't like tapping "Snoop Dogg Radio" on Pandora. Snoop is more inclined to share stuff he's been listening to and music that has influenced him rather than just the artists he shares a genre tag with.
By putting experts at the helm, Dash is attempting restore the human element to music curation. Regardless of where you fall in the human versus algorithm debate, it seems obvious that radio should at least provide a viable alternative to computer-driven services. In most cases, there isn't one. Skee got confirmation of that when he was still a part of the beast.
← More Music From The Inbox 25 Nov 2015 White Reaper, Younghusband, Christine & the Queens and More!
A Nice Surprise for Ottawa Grocery Shoppers from a Kenyan Boys Choir →
Another Legendary DJ Has Passed On
February 15, 2015 Alan Cross	1
Is Radio Caught in a Streaming Music Service Pinch?
January 31, 2014 Alan Cross	0
Radio: Not Dead Yet, Especially in the Car
March 3, 2015 Alan Cross	1


The synthetic peptide sequence used to generate the antibody AP8471d was selected from the Y584 region of human SHP2. A 10 to 100 fold molar excess to antibody is recommended. Precise conditions should be optimized for a particular assay.
Acts downstream of various receptor and cytoplasmic protein tyrosine kinases to participate in the signal transduction from the cell surface to the nucleus. Positively regulates MAPK signal transduction pathway (PubMed:28074573). Dephosphorylates GAB1, ARHGAP35 and EGFR (PubMed:28074573). Dephosphorylates ROCK2 at 'Tyr-722' resulting in stimulatation of its RhoA binding activity. Dephosphorylates CDC73 (PubMed:26742426).
Widely expressed, with highest levels in heart, brain, and skeletal muscle.
SHP2, also known as PTPN11, is a member of the protein tyrosine phosphatase (PTP) family. PTPs are known to be signaling molecules that regulate a variety of cellular processes including cell growth, differentiation, mitotic cycle, and oncogenic transformation. This PTP contains two tandem Src homology-2 domains, which function as phospho-tyrosine binding domains and mediate the interaction of this PTP with its substrates. This PTP is widely expressed in most tissues and plays a regulatory role in various cell signaling events that are important for a diversity of cell functions, such as mitogenic activation, metabolic control, transcription regulation, and cell migration. Mutations in the gene are a cause of Noonan syndrome as well as acute myeloid leukemia.
Chan, R.J., et al., Blood 105(9):3737-3742 (2005).Sturla, L.M., et al., J. Biol. Chem. 280(15):14597-14604 (2005).Loh, M.L., et al., Leuk. Res. 29(4):459-462 (2005).Wang, Q., et al., J. Biol. Chem. 280(9):8397-8406 (2005).Niihori, T., et al., J. Hum. Genet. 50(4):192-202 (2005).


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Q: Data Scraping With ImportHTML in Apps Script & Google Sheets Goal: I am trying to pull data from a website and use it to create a big table.  I can tell that I'm very close to getting this to work, but I've reached a roadblock.
Background:
I have a google sheet with three pages.  (1) Titled "tickers" is a list of every ticker in the S&P 500, in rows A1-A500.  (2) Titled actionField is just a blank page used during the script. (3) Titled resultField will hold the results.  The website I am pulling from is (http://www.reuters.com/finance/stocks/companyOfficers?symbol=V)  Though, I want the script to work (with minor modification) for any data accessible through importHtml.
Script:
The script I currently have is as follows:
function populateData() {
var googleSheet = SpreadsheetApp.getActive();

// Reading Section

var sheet = googleSheet.getSheetByName('tickers');

var tickerArray = sheet.getDataRange().getValues();
var arrayLength = tickerArray.length;
var blankSyntaxA = 'ImportHtml("http://www.reuters.com/finance/stocks/companyOfficers?symbol=';
var blankSyntaxB = '", "table", 1)';

// Writing Section

for (var i = 0; i < arrayLength; i++)
  {
     var sheet = googleSheet.getSheetByName('actionField');
     var liveSyntax = blankSyntaxA+tickerArray[i][0]+blankSyntaxB;
     sheet.getRange('A1').setFormula(liveSyntax);
     Utilities.sleep(5000);
     var importedData = sheet.getDataRange().getValues();
     var sheet = googleSheet.getSheetByName('resultField');
     sheet.appendRow(importedData)
  }
}

This successfully grabs the ticker from the tickers page.  Calls importHtml. Copies the data. And appends SOMETHING to the right page.  It loops through and does this for each item in the ticker list.
However, the data being appended is as follows:
[Ljava.lang.Object;@42782e7c
[Ljava.lang.Object;@2de9f184
[Ljava.lang.Object;@4b86a4d0

That displays across many columns, for as many rows as there are iterations in the loop.
How do I successfully append the data?
(And any advice on improving this script?)

A: The appendRow method is not suitable here. As it only appends one row, its argument is expected to be a 1D array of values.
What you get from getValues is normally a 2D array of values, like [[a,b], [c,d]]. Even if it's just one row, getValues will return [[a,b]]. The only exception is a single-cell range, for which you get just the value in that cell. It's never a 1D array.
If just one row is needed, use, e.g., appendRow(importedData[0]).
Otherwise, insert the required number of rows and assign the 2D array of values to them.
 var sheet = googleSheet.getSheetByName('resultField');
 var lastRow = sheet.getLastRow();
 sheet.insertRowsAfter(lastRow, importedData.length);
 sheet.getRange(lastRow + 1, 1, importedData.length, importedData[0].length)
      .setValues(importedData);


text:
US weapons and advisors used in Saudi Arabia-Yemeni conflict
In 2017, the U.S. military sold the Kingdom a $750 million program focused on how to carry out airstrikes.
NSFW YEMEN — Germany, Finland, and Denmark have stopped arms sales to Saudi Arabia due to the assassination of Washington Post columnist Jamal Khashoggi and the ongoing humanitarian crisis in Yemen. The US, however, has not.
According to a report by the Stockholm International Peace Research Institute, Saudi Arabia is America's number one weapons buyer. The country accounts for 18 percent of total U.S. arms sales, which is equivalent to roughly $9 billion.
According to CNN, the US signed a $29.4 billion deal in 2011 for 84 new F-15SA fighter jets, and the modernization of 70 current F-15s, including munitions, spare parts, training, maintenance, and logistics.
In 2017, the U.S. military sold the Kingdom a $750 million program focused on how to carry out airstrikes. They also authorized the sale of over $510 million in precision-guided munitions, according to The New York Times.
In the same year, the U.S. brokered a $110 billion arms deal that should be fulfilled over the next ten years.
According to an official statement released by the U.S. State Department, Saudi Arabia is expected to purchase tanks, fighter jets, combat ships, and Air and Missile Defense systems.
Currently, there are around 100 American military personnel providing intelligence support for the coalition. However, fewer than 35 are reportedly based in Saudi Arabia.
According to the Council on Foreign Relations, the US has had an alliance with Saudi Arabia since 1933, when the Standard Oil Company of California — now known as Chevron — won a sixty-year concession to explore eastern Saudi Arabia for oil.
Chinese version of AirBnb planning facial recognition locks


High-Tech industries demand precision and quality above all else. At GTI Precision Components, that's our passion. From the time of our founding, making intriguing parts for discriminating customers has been our focus.
From CNC machining services to CAD/CAM engineering, we cover the gamut of custom manufacturing services. Our 8,000 square foot facility, located in Powder Springs, GA, features state-of-the-art, wire EDM, CMM metrology equipment, and multi-axis, CNC, turning machine tools made by the leading German and Swiss manufacturers. We work with all non-ferrous metals. And we're ISO 9001:2008 certified.
We welcome the opportunity to develop long term relationships with companies who demand the very highest levels of quality and precision. Why not take a moment now to contact us with your questions or to request a quote?


but if I copy paste the single letter to any other page or file it appears correctly as "è", "ù". If I save the page in pdf I get the и and щ.
In other webpages the rendering is as supposed to be.
I don't know how to better constrain the issue to be more specific.
Is there a page where this is happening that you can share the link of? And make a screenshot of how it looks for you and share that as well.
Both pages, news1 and news2, display here correctly, i.e. with special Italian characters, not with Cyrillic characters.
Could it be that inside the Firefox preferences => Fonts you switched from "Latin" script to "Cyrillic" script by mistake?
Also scroll down and check / correct the setting for "Text Encoding for Legacy Content"
xenopeek wrote: Does it display correctly here?
karlchen wrote: Could it be that inside the Firefox preferences => Fonts you switched from "Latin" script to "Cyrillic" script by mistake?
I checked and the settings are for "Latin"
karlchen wrote: the setting for "Text Encoding for Legacy Content"
Here I have "Predefined for current language". In the language settings I have it, en, en-us.
PS: I post the thread in the wrong section, I'm actually using LMDE and not the main edition. I would like to move it in the right place. Is it possible?
Last edited by xenopeek on Fri Jan 19, 2018 5:08 am, edited 1 time in total.
If I open the pdf file I also see those и characters and if I copy them to somewhere else they turn into è like you said. I'm stumped as what could cause this.
Only thing that comes to mind is do you perhaps have enabled something to block web fonts? In that case your web browser tries to find a font on your computer that best matches what the website uses. Possibly it picks a completely wrong font.
I'm using uBlock Origin 1.14.24 (and HTTPS everywhere) addon for Firefox but I already tried in switching it off and re-loading the page. No changes.
What is strange to me is that it is not happening in all webpages... I don't know if it is random or if there is a link with some specific settings. In any case, it's just bothering, I can still read things (most important).


text:
Gram-positive bakterier er en klasse af bakterier, som er kendetegnet ved, at de, i modsætning til gram-negative bakterier,  farves blå ved en gramfarvning. Forskellen skyldes forskelle i opbygningen af cellevæggene. Gram-positive celler er kendetegnet ved at have et tykt lag peptidoglycan, samt ved at indeholde teikoidsyrer, der bidrager til strukturen og den negative ladning. Modsat gram-negative bakterier, kan nogle arter danne sporer.

Gram-positive bakteriers vækst hæmmes af normalt af penicillin men mange bakterier udvikler antibiotikaresistens også mod penicillin.

Kendetegn

Man finder almindeligvis følgende kendetegn hos de Gram-positive bakterier:

 En meget tyk cellevæg, bestående af peptido-glycan
 Hvis bakterien har en flagel, har denne to støttende ringe
 Der findes teikoidsyrer, der virker som chelater og i visse tilfælde som klæbestof
 Der er ingen lipoproteiner

Eksempler på Gram-positive bakterier
Typiske gram-positive bakterier er:
 Aerobe sporedannende bacilli
 Bacillus anthracis (Miltbrand)
 Anaerobe sporedannende bacilli
 Clostridium botulinum (Pølseforgiftning)
 Clostridium tetani (Stivkrampe)
 Clostridium perfringens (Gasgangræn)
 Clostridium novyi (Gasgangræn)
 Clostridium septicum (Gasgangræn)
 Clostridium difficile (Antibiotika associeret tyktarmsbetændelse)
 Corynebakterier
 Corynebacterium diphteriae (Difteri)
 Corynebacterium vaginale
 Staphylococcus aureus (Betændelse, Tamponsyge)
 Bacillus subtilis
 Lactobacillus acidophilus (normal tarmflora)
 Lactococcus lactis (Surmælksprodukter)
 Bacillus thuringiensis (Biologisk bekæmpelse)
 Bacillus subtilis

Se også
 Gram-negative bakterier

Henvisninger

Mikrobiologi
Bakterier

redpajama_set_name: RedPajamaWikipedia


Bah, humbug! Several months ago we learned that the Internet's most famous cat was getting her own movie, and the first trailer for Lifetime's Grumpy Cat's Worst Christmas Ever is finally here. Featuring Aubrey Plaza as the voice of the stone-faced feline, the storyline focuses on a 12-year-old girl who asks for a friend for Christmas and is gifted with the perpetually unhappy Grumpy Cat.
Filled with witty quips and punchy one-liners from the star kitty, Grumpy Cat even pokes fun at the flick itself. "Don't get sappy on me," she says in the clip. "Wait, I forgot—it's a Lifetime movie." Packed full of holiday hijinks and more, the movie is sure to be hilarious.
Watch the trailer above, and tune in to Grumpy Cat's Worst Christmas Ever when it premieres Nov. 29 at 8 p.m. ET on Lifetime.


text:
Historic multiple kidney swap ops featured on 'Dr. Oz Show'
Robert A. Montgomery, director of the Johns Hopkins Comprehensive Transplant Center, and 11 Johns Hopkins patients who were part of the first eight-way, multihospital, domino kidney transplant this summer, were featured last week on the new Dr. Oz Show.
The segment, which aired Sept. 24, was recorded in New York earlier in the month.
"I think this was an excellent venue to increase awareness for kidney paired donation and the alarming fact that we are in a midst of a crisis in organ transplantation in this country," Montgomery said. "I hope the segment will answer viewers' questions about kidney donation and possibly encourage them to help those in need by being donors."
Filed under In Brief


Find great deals for Dead Island Riptide Zombie Bait Edition -. Shop with confidence on eBay! Apr 23, - "We deeply apologise for any offence caused by the Dead Island Riptide Zombie Bait Edition, the collector's edition announced for Europe and.


Courtesy Fox News video screenshot from Daily Caller YouTube page.
For those of you who caught Thursday's Montana Talks statewide radio show, we played audio of Tucker Carlson apologizing to former Vice President Joe Biden on Fox News.
What? Tucker Carlson apologizing to Joe Biden?


Sep. 14, 2017—Carol Etherington, MSN, R.N., associate professor of Nursing, emerita, was recently elected chair of the Metropolitan Board of Health of Nashville and Davidson County, and Alex Jahangir, M.D., MMHC, medical director of the Vanderbilt Center for Trauma, Burn and Emergency Surgery, joined the board as a member.
Mar. 3, 2015—Research soon to be published in the Journal of the American College of Surgeons (JACS) shows that airlifted trauma victims who receive blood transfusions in the helicopter before arriving at a trauma center have a higher chance of survival.
Oct. 31, 2013—Knowing who your doctor is — and a couple of facts about that person — may go a long way toward improving patient satisfaction, according to a Vanderbilt study in the Journal of Orthopaedic Trauma.
Jan. 17, 2013—This past fall, 150 sixth graders at Cameron College Prep middle school completed a violence prevention program that was the end result of an idea formed years before in a Vanderbilt University Medical Center operating room.
Feb. 9, 2012—A Vanderbilt study suggests unnecessary costs associated with the practice of defensive medicine play a substantial role in the nation's rising cost of health care.


text:
"If I gain more than two or three pounds, like I have right now, I'm going to eat vegetables tonight. I don't ever cut out vodka and tonics. My t
Britt Aboutaleb
"If I gain more than two or three pounds, like I have right now, I'm going to eat vegetables tonight. I don't ever cut out vodka and tonics. My trick is that if I eat vegetables at night three or four days in a row, I quickly snap back to my ideal weight." --Tom Ford to Prestige magazine
Krupp Group Is Seeking A Spring '22 PR Intern In New York, NY
LOLA Production Is Seeking A Production Intern In Los Angeles & Accounting Intern In New York (Paid Internships)
OMA THE LABEL Is Hiring An Operations Assistant In New York, NY
PrestigeQuote of the Day
Kim Noorda's Food Diary, in Vogue
"I gained 1.6 pounds in three days...Not a single person has told me that I have gained weight since the start of the shows. Not during the castings,
By Britt Aboutaleb
"Oh. My. God. We just got the new GQ. And Scott Speedman wears Rag & Bone. And Joshua Jackson wears Tom Ford. And I feel fifteen, but better." -- B
Quotes of the Day: Tom Ford's Five Most Ridiculous Quotes from his Interview Interview
Oh, Tom Ford. You are a ridiculously amazing human who never fails to say and do ridiculous things. Take for example, Ford's recent interview with John Currin in Interview. He says so many awesomely over-the-top things we couldn't pick just one. Here are his top five quotes: 1. I lust after beautiful women. First of all, I love women. But I lust after beautiful women in the way that I lust after a beautiful piece of sculpture—this will probably get me in trouble—or a beautiful car. I believe everyone's on a sliding scale of sexuality. There are moments where I am sexually attracted to women. But it doesn't overpower my first impulse; my lust for them is the same as my lust for beauty in all things. It's not like I ever think, "Oh, my god, I've got to spread her legs and fuck her." 2. I'm an equal-opportunity objectifier...I'm sorry, I don't understand why our culture both worships and objectifies beauty, and then slams those of us who participate in it. Because I make that detachment, I'm capable of objectifying a beautiful woman, but that doesn't demean her in any way. She's beautiful because she's a creature who exists physically, in the physical world, who happens to be in a moment of prime.
By Leah Chernikoff
Quote of the Day: Tom Ford Kisses and Tells
"Terry and I decided to do a kissing shot, so we kissed and kissed and kissed. And Terry is such a soft, sweet kisser. That's what I think is sexy now


The short clip promotes the potentials of Vira Verna Advertising Agency in applying innovative ideas, unique and appealing styles in various graphical projects.
The animation developed by using 3Ds Max in modeling animal characters; After Effects in shaping space, stars and other elements; Photoshop in designing some nebulas layers, and Premier in editing. The music score and sound effects were done by Veera Vision's own composer. Extraterrestrial sounds induce a sense of suspension in galactic space. This music can be categorized in New Age genre.