Penetration Testing Why conduct a penetration test?
Why do you need to conduct penetration tests?
Security executives need to align their investments with business goals and justify their activities with a favorable return on investment—be it risk reduction, business enablement, and/or financial savings.
Penetration tests are important in the process of identifying, measuring, and communicating your cyber risks so that smart risk mitigation can be implemented. With the results of a successful pen test, you can show that the investments you are making have actual benefits that will support your organization's overall business objectives.
Frequent and comprehensive penetration testing means that your organization can more effectively anticipate and assess emerging security risks and thus prevent unauthorized access to critical systems and valuable data.
Penetration testing should be performed on a regular basis to identify vulnerabilities and reveal how they may be exploited to gain unauthorized access to your system.
Pen testing helps safeguard your organization against failure by helping you to put in place effective controls that: prevent financial losses through fraud (hackers, extortionists, and disgruntled employees) or lost revenue due to unreliable business systems and processes.
Proving due diligence and compliance to your industry regulators, customers, and stockholders is vital in today's competitive business environment. Non-compliance can result in your organization losing business, receiving heavy fines, gathering bad PR, or ultimately failing.
Penetration testing evaluates your organization's ability to protect its networks, applications, endpoints, and users from external or internal attempts to circumvent its security controls to gain unauthorized or privileged access to protected assets. Test results validate the risk posed by specific security vulnerabilities or flawed processes, enabling IT management and security professionals to prioritize remediation.
Today's "web apps" typically use TCP Port 80. Traditional firewalls are unable to identify or effectively control any Internet applications on this port without slowing down business traffic that relies on the http protocol.
Regular Vulnerability Assessments and Penetration Tests are the only sensible defense. We offer penetration testing either as a one-off service or a regular annual package. It only takes us a few minutes to discuss your situation and quote you a price.
Please contact us for further information about our penetration testing services, or to speak to an expert.


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Andrews University Berrien Springs, MI
3.881, Four 3.9 Average Rating
Colleges › By State › Michigan › Andrews University › Discussions
What are others saying about Andrews University?
Bang for the buck
Most Helpful Review for Andrews University
Category: Am learning a lot
Review by: Danika from Hamburg, PA
The opportunity to learn is definitely obvious at Andrews University. The options are numerous. Classes are challenging and, for the most part, engaging.
To find more tips for prospective students, what to do for fun and whether this school is great for a particular type of student read the 32 reviews for Andrews University
Create an account to write a review
Curious about something that isn't answered here? Feel free to ask Andrews University a question
Student Responses to Review Topic: in 3 Sentences
Kerry from Granger, IN
What a great place for an education. The teachers really do care about the students success in life. The University as a whole does all it can to ensure student success.
Wynique from Getzville, NY
There are lots of opportunities to work on your spiritual life at Andrews University. There are many undergrad degrees available with skilled faculty and staff. The school represents many countries from around the world.
Joelle from New York City, NY
Andrews University has helped me grow mentally, physically, and spiritually through its variety of programs. I have made connections and friendships and memories that will stay with me forever, and I
Cady from Berrien Springs, MI
Andrews University is a place where I feel safe and comfortable. I feel like I am getting the most I can out of my education here. I am happy that I am able to attend a Seventh-day Adventist school where my faith can be incorporated into my education.
Karacan from Berrien Springs, MI
Andrews University is a school that is diverse in culture, race, and ethnic backgrounds. At this school students are taught that school is important and that God is the center of everything. Students at Andrews University learn the meaning of life and what in their educational and spiritual lives.
Alexandria from Kailua, HI
The teachers are devoted and caring experts. The academic and social programs are excellent and fulfilling. The food is decent.
A. from Berrien Springs, MI
An amazing place to meet international students, have professors that truly love their profession and God, and a place where a student can really build up their relationship with God.
Katrina from Hurricane, WV
Andrews has been great for me academically. It is the only Adventist university in the top 200 and it was also given a most underrated college award. It's a good school and the faculty is always willing to help you understand a subject better.
Sarah from Eldersburg, MD
Andrews University has a huge variety of people and is very diverse. It has strong academic values. Overall it is a good school to attend.
Karla from Saint Joseph, MI
Andrews University is incredibly supportive to its campus family. The faculty and staff do everything they can to encourage their students. The campus atmosphere is unparalleled.
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Movie Review: Spider-Man: Into the Spider-Verse (2018)
Floyd Smith III
When Sony announced its plans for a theatrical release of an animated Spider-Man film, even hardcore fans of the web swinger may have considered it to be just another unwarranted adaptation. "Haven't we seen enough portrayals of Spider-Man?," those with comic-book movie fatigue asked, and yet in his seventh major solo theatrical release since 2002,…
Movie Review: Fantastic Beasts: The Crimes of Grindelwald (2018)
Zoë Kravitz's ("Rough Night") character in Fantastic Beasts: The Crimes of Grindelwald, Leta Lestrange, tells the franchise's bashful hero, Newt Scamander (Eddie Redmayne, "The Danish Girl"), "You never met a monster you couldn't love." The line is actually quite interchangeable with the film itself. While the narrative is somewhat of a slog, there is just…
Movie Review: Rough Night (2017)
Oh no, ladies, what are youse doing? Not asking this is not an option when every action to clear bride-to-be Jess (Scarlett Johansson, "Hail, Caesar!") and her friends' involuntary-manslaughtering ways in Rough Night is just reducing Lt. Horatio Caine and team's investigation time. The bachelorette's activist friend Frankie (Ilana Glazer, "The Night Before") said it…
Movie Review: The LEGO Batman Movie (2017)
Greg Eichelberger
"Sir . . . I've seen you go through similar phases in 2016 and 2012 and 2008 and 2005 and 1997 and 1995 and 1992 and 1989 and that weird one in 1966." — Alfred Pennyworth (voice of Ralph Fiennes) to Batman Like its 2014 predecessor, "The LEGO Movie," The LEGO Batman Movie, a sequel…
Movie Review: Fantastic Beasts and Where to Find Them (2016)
Half the fun of watching Fantastic Beasts and Where to Find Them, a prequel of sorts to the "Harry Potter" franchise, is trying to figure out just who will be a vital link to that amazingly popular film series. J.K. Rowling (the author of the original "Potter" books, as well as this screenplay) seeks, like,…
Movie Review: The Divergent Series – Allegiant (2016)
LisaPas
Every now and then, Hollywood suffers from fatigue — the hot new thing that catches everyone's attention and is insanely popular gets reproduced over and over and over until it's everywhere, and everyone loves it even more . . . until they don't. Then, there are the last few gasps of a trend until it…
Movie Trailer: Allegiant (2016)
You know you've wondered what's beyond the great wall surrounding the remains of Chicago since it was introduced in 2014's "Divergent" and further explored in 2015's sequel "Insurgent." Well wonder no more as the first real glimpse into the wasteland has been delivered in Summit Entertainment's Allegiant. It's red. And barren. Kind of lackluster really….
Movie Review: Summer Children (1965)
Movie Review: B.T.K. (2008)


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Autocar names top 100 women in the British car industry
Jones said: "It's an honour to join the impressive list of winners at the Great Women in the British Car Industry awards. The initiative is a fantastic way to showcase the breadth of talent across the industry. I strongly believe, as do my colleagues at Groupe PSA, that a diverse and inclusive workplace, in all aspects, is a successful workplace. We work together to constantly drive improvements in this area, which is great for our colleagues, and our business results."
Chair of the judging panel and managing director of Autocar and Haymarket Automotive, Rachael Prasher, added: "The phenomenal success of all our Top 100 Great Women demonstrates the scope of career opportunities in the automotive world and the achievements possible. Each year, the talent pool gets bigger, making our job as judges harder, but it's a fantastic sign of the breadth of talented women working in the industry."
Run in partnership with the SMMT, Autocar's Great British Women in the Car Industry initiative is supported by sponsors Bentley, Nissan, Toyota and the Institute of the Motor Industry.
SMMT chief executive Mike Hawes commented: "We are pleased and honoured to continue our association with Autocar and its Great Women in the British Car Industry initiative. Looking across the Top 100 list, we can see women leading and excelling in all aspects of the industry, from vehicle engineering to production, sales, marketing and beyond."
Hawes added: "There's much more we need to do to improve all aspects of the sector's diversity, but it is role models such as those recognised here who can help ensure our sector is an exciting and inspiring place in which to work, attracting the best and brightest for the future."
This year's virtual event features a panel debate with some of the industry's biggest names chaired by Prasher, alongside appearances from PSA's Linda Jackson, Bentley board member Astrid Fontaine and former England Women's cricket captain Clare Connor.
You can view the Top 100 by visiting www.autocar.co.uk/greatwomen/2020. The social media hashtag for the initiative is #AutocarGreatWomen
The full list of category winners is as follows:
Design – Lisa Reeves, head of interior design, Volvo Cars
Executive – Alison Jones, group managing director and senior vice-president, PSA Group UK
Government affairs – Helen Foord, head of government relations and public policy, PSA Group UK
Manufacturing – Josephine Payne, Craiova vehicle operations assistant plant manager, Ford
Marketing – Michelle Roberts, marketing director, BMW UK
Mobility and digital – Paula Cooper, director, Consumer One, Toyota GB
Operations – Sue Slaughter, director, global material cost and supply base sustainability, Ford
People development – Alison Clarke, chief human resource officer, Inchcape PLC
PR and communications – Nikki Rooke, vice-president, communications, Volvo Cars
Sales, manufacturers – Paula Stevenson, director of sales operations, Aston Martin
Sales, retail – Angela Shepherd, CEO, Mercedes-Benz Retail Group
Vehicle development – Danella Bagnall, vehicle programme quality director, JLR
See the full list of Top 100 Great Women in the British Car Industry
The woman leading PSA UK's reinvention: 2020's Great Women in the British Car Industry winner
Great British Women: Judy Murray on her success
Autocar Great British Women 2019: Aston Martin's Laura Schwab on how to succeed in the car industry
Tags: Autocar, British, Car, Industry, names, Top, women
Nissan Z Proto sports car revealed with retro style
Automotive Industry Veteran Joe Sbuttoni Joins Scali Rasmussen


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Forget Braun, new film reminds us we have Al Rosen to go with Koufax and Greenberg
By	Hillel Kuttler	 August 26, 2013 4:31 pm
JTA PREMIUM PHOTOS: Forget Braun, new film reminds us we have Al Rosen to go with Koufax and Greenberg Al Rosen, a four-time All-Star with the Cleveland Indians, was the unanimous pick for American League MVP in 1953. (Cleveland Press Archives at Cleveland State University)
Al Rosen, a four-time All-Star with the Cleveland Indians, was the unanimous pick for American League MVP in 1953. (Cleveland Press Archives at Cleveland State University)
BALTIMORE (JTA) — When Ryan Braun was named the National League's Most Valuable Player in 2011, Jewish sports nuts talked about whether the Milwaukee Brewers' slugger would end up in the pantheon with Hank Greenberg and Sandy Koufax.
Following Major League Baseball's recent suspension of Braun for using performance-enhancing drugs, the answer seems to be a clear no.
Forgotten in the discussion of Jewish diamond greats is Al Rosen, a power-hitting third baseman who was a member of the tribe in more ways than one, playing his entire career for the Cleveland Indians.
But now comes a new documentary, "Beating the Odds: The Al Rosen Story," celebrating Rosen's contributions to baseball as a player and executive, as well as being a role model for American Jews.
Rosen's MVP season of 1953 followed on the heels of Greenberg's two MVPs (1935 and 1940) and preceded Koufax's one MVP (1963) and three Cy Young Awards (1963, 1965 and 1966).
Like the Detroit Tigers' Greenberg — his idol — Rosen was nicknamed the Hebrew Hammer. Like the Brooklyn/Los Angeles Dodgers' Koufax, he enjoyed a brilliant career abbreviated by injury.
Rosen was a four-time All-Star who played in the 1948 World Series — the last one won by the Indians — and two seasons later led the American League in home runs with a rookie record 37 (he qualified as a rookie despite appearing in games the previous three seasons with Cleveland). His MVP was the last for an Indian.
He would help lead Cleveland back to the Series in 1954, but the Tribe was swept by the Willie Mays-led New York Giants.
Two years later, at age 32 and after just seven full seasons, Rosen played his last game, done in by a finger injury and back problems. Another factor: He learned Greenberg, by then the Indians' general manager, was planning to cut his salary or trade him.
"I feel like my career was aborted," Rosen, 89, told JTA in a recent interview. "It's been troubling me over the years. I don't dwell on it because it's not worth dwelling on."
The new documentary serves as a reminder that while Rosen might fall short of the Greenberg-Koufax bar, he should never be forgotten in discussions about the greatest Jewish baseball players.
The film was financed in large part by the Indians, who are selling it at Progressive Field souvenir stands and on the team's website.
It chronicles the asthmatic Rosen's rise from his native Spartanburg, S.C., to Miami, where his family moved to improve his health, through his youth exploits as a boxer and on to an accomplished baseball career. Rosen hit for a .285 average, slugged 192 home runs and batted in 100 or more runs five consecutive seasons.
Al Rosen, left, and his childhood idol, Hank Greenberg, were two of the greatest Jewish ballplayers and both became baseball executives. (Cleveland Press Archives at Cleveland State University)
Rosen is "one of the great names" in Indians' history, said Bob DiBiasio, the team's senior vice president for public affairs.
"We really felt it was important to participate in this project because you do need to document the rich history of the game and our franchise," DiBiasio said.
The documentary was completed earlier this month, 60 years since Rosen was named MVP. Due to Major League Baseball's licensing fees for footage, filmmaker Bill Levy opted to tell the story through interviews, narration and still photographs rather than utilize clips of Rosen hitting and fielding.
"He was a hell of a baseball player," said Levy, who produces corporate films but as a journalist covered the team during Rosen's career. "In his era, Al Rosen was a hero, Jewish or not Jewish. He was a hero to me. He carried himself in a dignified way.
"With this Ryan Braun thing, [Rosen's] position as one of the three top Jewish baseball players of all time is still unchallenged."
The 57-minute film's other subtitle, "Making Elmer Yoter Eat His Words," is a slam at the minor league manager who brought the 17-year-old Rosen to tears after a workout by saying he'd never amount to anything as a ballplayer.
"You're wrong, Mr. Yoter, and some day I am going to make you eat your words," Rosen is quoted as responding.
That was hardly the only opposition faced by Rosen. A football coach at his Miami Senior High School implied that Jewish athletes were soft — that they preferred tennis to contact sports.
"That's etched in my memory," Rosen says in the film. "You could never get it out of there because I always wanted to prove this guy wrong."
The film also recalls Rosen approaching the Chicago White Sox dugout to challenge the player who screamed anti-Semitic slurs during a game at Comiskey Park. Rosen never found out the player's identity, and told JTA that he admired Saul Rogovin, a pitcher and also a Jew, for not ratting on his White Sox teammate.
"I could imagine he was in a very difficult spot, and he handled it absolutely correct," said Rosen, who ran into Rogovin years after the incident and asked about the heckler's identity.
Rosen's integrity also comes through in the documentary.
In 1953, Rosen nearly achieved the rare Triple Crown — finishing the season leading the league in home runs, runs batted in and batting average. Miguel Cabrera of the Detroit Tigers won the trifecta last year, only the 13th player in baseball history to accomplish the feat.
Heading into the final game, Rosen was first in homers and RBIs, and was neck and neck with Mickey Vernon of the Washington Senators for the batting title. Vernon had picked up two hits in four at bats against the Philadelphia Athletics; Rosen was 3 for 4 against the Tigers. If Rosen could hit safely in his last at-bat, he could secure the batting title and the Triple Crown.
Rosen topped a slow grounder to third base but was nipped at first trying to leg out the infield hit. He finished at .336, one point short of Vernon. Rosen led the league in homers (43) and RBIs (145), along with runs (115), total bases (367) and slugging percentage (.613).
"I knew I was out," Rosen tells Levy of the deciding play. "I couldn't have accepted being called safe on that play. … I just wouldn't have been able to live with that. I was glad he called it right, and I accepted it. That's just the way it was."
So dominant was Rosen in '53 that he won the MVP unanimously — a first. He wrote thank-you letters to each writer who cast a vote.
The next year, the Indians recorded one of the best regular seasons in baseball history with 111 victories before losing to the Giants in the Series. Rosen was on base when Mays made his legendary catch of Vic Wertz's drive to deep centerfield in Game 1; Rosen said he fully expected Mays to make the play.
Perhaps the documentary's greatest revelation is Rosen's role in helping George Steinbrenner purchase the New York Yankees in 1973. The two had been part of a failed effort to acquire the Indians.
Rosen later worked for Steinbrenner as the Yankees' president and chief executive officer, and was there for the team's 1978 World Series title. Rosen went on to run the Houston Astros and the San Francisco Giants, leading the latter to the 1989 World Series (a loss). He is still the only person to have won an MVP and been named Executive of the Year (in 1987, with the Giants).
Rosen retired from the front office in 1992. Were he heading the Milwaukee Brewers now, Rosen told JTA he's not sure how he would have handled Braun, the son of an Israeli Jewish father and Catholic mother. The film came out before the suspensions of Braun and other players were announced. Rosen recalled that one of his Giants players had a cocaine problem.
The suspensions are "a terrible blow for baseball," Rosen said. "I feel badly that it happened, I feel badly for baseball and I feel badly for the players. There will always be a tarnish on all [their] accomplishments."
He added, "It's not only Ryan Braun but many other fellas. But I know one thing: If I were a player today, I wouldn't take anything without a doctor saying so and without a written note from the doctor."
Rosen, the only living member of the starting lineup of the '54 Indians, occasionally sees some of his contemporaries living nearby, including Hall of Fame slugger Ralph Kiner, an Indians teammate. He follows baseball with great interest, and said he's particularly impressed by the performance of the Tampa Bay Rays and their manager, Joe Maddon.
And he's technologically hip. Rosen follows international affairs closely — he includes three or four Jewish newspapers in his daily online reading — and stays in contact with his widespread family by Skype. All the Rosen households — he and his wife Rita have five children, four grandchildren and a great-granddaughter — have received a DVD of the film.
"That's one of the things that makes me happy," Rosen said of the documentary. "It'll be something the kids will have."
Sue Bird bashes Trump in an essay defending her girlfriend Megan Rapinoe
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Twenty one years ago, Nelson Mandela donned a Springboks shirt and presented Francois Pienaar with the Rugby World Cup. Apartheid had ended four years previously, South Africa had its first black president, and now South African sport was on the world stage, Mandela showing us how sport could lead the way in redressing the balance and striving for equality. A seminal moment – but a seminal moment that was twenty one years ago.
76% of South Africa's population is Black African. Yet, of the 29 batsmen who have scored test centuries since South Africa's test status we reinstated in 1991, just 1 is a black South African – thanks to Bavuma yesterday.
It's taken too long. And there's so much further to go. And so to the perennial question, oft debated by South African sport's (largely white) governing bodies.
The quota systems that have periodically been employed in South African sport have been highly controversial. Recent opinion polls suggested that a marginal majority of South Africans favour quotas, but those who do not argue vociferously for selection on merit, and point to a talent drain caused by the implementation of quotas (Kevin Pietersen's move to England a case in point).
The late Clive Rice, a former South African captain, publically argued against the quota system, going as far to describe it as 'apartheid in reverse'. Yet he also believed it was inevitable that the nation's top cricketers would continue to come from the most privileged backgrounds: from the predominantly white, suburban, private schools (over 35% of South Africa's test players since 1991 went to the same ten private high schools).
On the one hand, he was right: with no action, with no investment in grassroots crickets in the deprived South African townships and rural areas, then of course the best cricketers will continue to come from the most privileged backgrounds. To become a top cricketer takes more than just talent, ambition and drive: it takes facilities, opportunities, nutrition – three things that so many of South Africa's black communities still lack.
On the other hand, we must look for ways to reach the equality that we thought Nelson Mandela's gesture in 1995 heralded. Black cricketers must be developed from the grassroots up, but in fixing a broken sport in a broken nation, this must be driven from top down. Cricket South Africa is taking steps to do this, including offering scholarships to successful cricket schools for talented township residents. But far more importantly, with the recent increase in the quota imposed on South Africa's franchise and semi-professional cricket clubs, Cricket South Africa is providing clubs with a clear incentive for wholesale investment in grassroots cricket in the townships.
Those who argue against a quota system will cite the example of Zimbabwe, whose international cricketing performances have plummeted following a strike by white players in 2001-2 after the imposition of a heavy quota. But by having quotas at a provincial, but not an international, level means that the South African national team can still be the best 11 cricketers in the country (and even include those who have opted to play abroad at club level to avoid quotas), meaning that international performance would not be affected whilst inequalities are addressed from the bottom up.
In a utopian world, race would not be an issue in South African sport, or indeed in South Africa itself. South African Cricket would not require quotas, and certainly the system is not without its flaws. But you cannot bury a history; deny a past. Under apartheid football was the only sport which black people were allowed to play professionally: the legacy which this has left will not disappear of its own accord. The division remains clear for all to see, and change remains slow. Temba Bamuva's achievement is so great precisely because it has come against the odds. He has led the way, but now these odds must change. Managed correctly, domestic level quotas and the consequent investment can have huge positive impact. The direction is the right one – let's not wait another 21 years for that next seminal moment.


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The ocean, CO₂ and climate change – timeline
A look at the history of some aspects of ocean studies, including the interaction of the ocean with climate and atmospheric carbon dioxide.
1859 – Greenhouse effect
John Tyndall identifies water vapour and CO2 as gases in the atmosphere that could trap heat rays.
1896 – Prediction of global warming
Swedish scientists Svante Arrhenius and Arvid Högbom realise oceans take up CO2. First prediction of global warming due to CO2 in the atmosphere from industrial emissions. Many scientists disagree.
1897– Carbon cycle model
Thomas Chamberlin creates model of global carbon cycle. The model includes long-term changes in CO2 in oceans and atmosphere.
1906 – Oceans and climate
Thomas Chamberlin realises that ocean temperature and salinity help control climate. He notes that warm oceans give up CO2, cool ones take it up.
1908 – CO2 and acidification
John Gregory realises that an increase in CO2 will mean an increase in carbonic acid in the oceans.
1938 – CO2 and temperature (again)
Guy Callender argues that CO2 levels are rising and causing an increase in global temperature. This revives earlier interest in the topic, but many scientists disagree.
1942 – Deep ocean currents
Harald Sverdrup describes how cold, dense water could sink and cause deep ocean currents, but there is no way of measuring this at the time.
1948 – Carbon cycle can cope
George Hutchinson states that the carbon cycle regulates itself and can cope with increased carbon from the burning of fossil fuels.
1957 – Oceans and CO2
Roger Revelle and Hans Suess work out that the oceans are not taking up enough CO2 to make up for the increased amounts being pumped into the atmosphere by humans.
1960 – Rising CO2 measured
Dave Keeling accurately measures CO2 in the atmosphere on Mauna Loa in Hawaii and detects an annual rise. In this year, CO2 in the atmosphere is 315ppm (parts per million) and the mean global temperature is 13.9°C.
1967 – A new warning
Syukuro Manabe and Richard Wetherald warn again that increasing CO2 in the atmosphere due to human activities will raise global temperatures due to greenhouse effect.
1969 – First satellite measurements
Nimbus-3 satellite starts to provide global temperature measurements.
1978 – Better remote sensing
Nimbus-7 satellite launched, providing global sea surface temperatures and colour. The colour is related to the amount of phytoplankton growing in the sea.
1981 – Warmest year on record
Strong global warming since the 1970s is reported, with 1981 the warmest year on record.
1985 – Not just CO2
Veerabhadran Ramanathan and others announce that other gases, not just CO2, have a role in the greenhouse effect.
1985 – Villach conference
A conference at Villach, in Austria, marks the start of a rapid acceptance of the idea that humans do play a large part in climate change.
1992 – Drifting ocean floats
Russ Davis and Doug Webb develop pop-up drifter floats to measure ocean currents.
1992 – Sea level satellite
TOPEX/Poseidon satellite starts to very accurately measure global sea levels. Changes in sea level reflect changes in temperature, as water expands when warmed and contracts when cool.
1999 – Global remote sensing
NASA's Terra satellite is launched to collect data monitoring many aspects of Earth's environment and climate systems.
2000 – First Argo floats
First Argo floats launched to measure currents, temperature and salinity. There are over 3,000 floats by 2010, continuously drifting around the oceans and sending back data via satellites.
2009 – CO2 reaches new high
CO2 in atmosphere reaches 385ppm, with a mean global temperature of 14.4°C – the warmest for hundreds, perhaps thousands, of years. Compare these figures to those recorded in 1960.
2010 – Aquarius satellite
In May, the Aquarius satellite is launched to make the first sea surface salinity measurements from space.
2014 – The Deep South – Te Kōmata o Te Tonga
The Deep South National Science Challenge, hosted by NIWA, sets out to understand the role of the Antarctic and the Southern Ocean in determining our climate and our future environment.
2016 – Hottest year on record
Measurements from NASA and the National Oceanic and Atmospheric Administration put the Earth on track to surpass 2015 as the hottest year on record.
2017 onwards – increase in protests
News of disasters, such as tropical cyclones and wildfires, and intensified scientific warnings lead to increasing public concern, especially among younger people. This spurs public demonstrations and civil disobedience, such as school Strikes for climate change.
May 2020 – record temperatures
The mean global temperature is 14.8°C, the warmest in tens of thousands of years. The level of CO2 in the atmosphere is 415 ppm, the highest in millions of years.
October 2020 – NIWA deploys more than 100 Argo floats
A pandemic did not prevent NIWA scientists from deploying more than 100 floats in 2020, but it did prevent them from leaving the RV Kaharoa. NIWA has deployed more than 1100 Argo floats in the Pacific, Indian and Southern Ocean over 22 voyages since 2004.
Our interactive planning pathways and teacher PLD on climate change resources provide excellent support for teachers wanting to use the wicked problem of climate change to promote science learning in their classroom.
Learn more about the impacts of climate change by exploring the climate change topic.
The websites below, provide up-to-date figures and interactives related to climate change:
Global Climate Change – NASA
Climate – NIWA
National Oceanic and Atmosphere Administration (NOAA)
Published 16 June 2010, Updated 1 July 2020 Referencing Hub articles


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You are here: Home / college basketball / ESPNU: Katz Korner Returns for Fourth Season
ESPNU: Katz Korner Returns for Fourth Season
Fourth Season of Weekly College Basketball Show
Head Coaches, Players and Guests Each Week
The fourth season of ESPNU's weekly Katz Korner men's college basketball show will make its season debut Thursday, Jan. 21 and continue through the remainder of the college basketball season. The program — hosted by veteran ESPN basketball reporter Andy Katz — will provide an all-encompassing look at the college basketball landscape and will, typically, air on Thursdays at 1 p.m. and continue throughout the afternoon on ESPNU. Today's season debut will air at 3 p.m. and next week's episode (Jan. 28) will air at 4:30 p.m.
Each week, Katz will be joined by coaches, players and special guests. Highlighting this season's debut episode are interviews with head coaches Mark Turgeon (Maryland), Jay Wright (Villanova) and Andy Enfield (USC). NCAA Selection Committee Chair Joe Castiglione will also join the show.
Other weekly elements:
Journey to the Tourney: Bracketologist Joe Lunardi elaborates on his NCAA Championship projections and provides a report on mid-major programs
Wooden Award: An update on the top players around the nation who are vying for the College Basketball Player of the Year award
About Andy Katz
Katz joined ESPN.com in 1999 as the national college basketball writer. While still contributing regularly for ESPN.com, his role on-air has continued to grow, which now includes hosting Emmy and Murrow-award winning Outside the Lines series when Bob Ley is unavailable. Additionally, he co-hosts two podcasts, ESPNU College Basketball with Seth Greenberg andCapital Games with ABC News' Rick Klein.
Media contact: Derek Volner at 860-384-9986; Derek.Volner@ESPN.com and @DerekVolner
Filed Under: college basketball, ESPN


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December 09 – Heading to the set of "Hawkeye" in New York
Posted on December 10, 2020 December 11, 2020 Written by Victoria
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December 09 – Walks her dog to the makeup hair trailer in New York
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December 08 – On set of "Hawkeye" in New York
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Hailee Steinfeld Talks Adult Acne, Instagram Comparisons And Overcoming Self Esteem Issues | Elle UK
Posted on December 9, 2020 Written by Victoria
Model, actor and singer Hailee Steinfeld bares all about her struggle with adult acne, the debilitating effect it has had on her self esteem and how she's overcome comparison culture to feel her most confident ever, blemishes and all:
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December 07- On set of "Hawkeye" in New York
Posted on December 8, 2020 December 8, 2020 Written by Victoria
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Hailee Steinfeld Confirmed as Kate Bishop as Filming Begins
And now for some casting news that we think is a real bullseye. It is just right on the mark. It is, and we cannot stress this enough, accurate. Hawkeye, the Disney+ series following Jeremy Renner's archer Avenger, began filming in New York this week, and numerous outlets spotted Hailee Steinfeld in costume as Marvel fan-favorite, Kate Bishop.
The inclusion of Kate Bishop in Hawkeye has been the hypest part of this series since it was announced at San Diego Comic-Con 2019. Created by writer Allan Heinberg and artist Jim Cheung, the character is the first woman to adopt the Hawkeye mantle. The daughter of one of New York City's wealthiest families, Kate turns her attention to fighting crime after a life-changing attack in central park, joining the Young Avengers and eventually settling on fellow archer Clint Barton as a mentor. Renner teased Kate's arrival to set on Twitter but there hasn't been an official casting confirmation from Marvel quite yet. So, you know, don't tell them about this.
For as long as people have been talking about Kate Bishop finally making the jump to live-action, they've been discussing Hailee Steinfeld filling the role. The young actress first made a spash at 13 in the Coen Bros' True Grit remake before starring in two Pitch Perfect sequels, leading the Transformers spinoff Bumblebee, and providing the voice for Gwen Stacy in Spider-Man: Into the Spider-Verse.
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No wedding's ever complete without a good wedding photographer. After all, all that remains after your special day is memories and could there be any better way than storing them as photographs and videos?
Wedding photography is nothing new to Indian weddings. Punjabi weddings, Rajasthani weddings, Bengali weddings and Gujarati weddings last for days together and cover several ceremonies. Ceremonies like 'sangeet' can be quite fun filled with people singing and dancing to the tunes of old folk music as well as latest bollywood tracks. All these ceremonies are worth being covered. After all, you'll rarely see your mother in law dance apart from the day of 'Sangeet'.
Even wedding photographers are becoming professional using latest still and video cameras combined with special effects and use of computers to enhance the image quality. You'll probably also come across several wedding photographers who have done specialized courses from reputed universities not just in India but even abroad. However, how will you ever know which wedding photographer is good enough to be chosen as the one who would cover your wedding?
1.Ask Around – Ask your friends, family and neighbors if they know of anyone who has experience in wedding photography. Ask them to recommend some good photographers they have hired or any of their relatives may have hired for a wedding or any other function.
2.Budget – Make sure you know how much money you are willing to spend on wedding photography since the cost can vary not just on the number of days you hire a photographer for but also one photographer to another.
3.Venue – Yes, often this is overlooked and later people repent not having taken this into consideration. Great photographs always depend on the amount of light that is there in the wedding venue. Make sure whichever photographer you have shortlisted has experience in covering indoor as well as outdoor or garden weddings or has sufficient lights to make up for any shortage in the wedding venue.
4.Count Your Ceremonies – Photographers usually charge on a per hour basis, per day basis or for a particular number of photographs and hours of videography. Make sure you know well in advance how many ceremonies you would like to be covered.
5.Short listing – Once you have a list of photographers, it is time you start calling them for a meeting. Make sure they also bring along with them some sample photographs from weddings that they may have covered. Shortlist those you feel have best photographs and the required experience. Also, ensure that your shortlisted photographers are willing to work within your budget.
6.Seeing is Believing – Once you have shortlisted a few photographers, ask them to show you the actual or sample wedding albums so that you can decide what kind of wedding album you would want to get designed. Several options are available these days and wedding albums can be developed in several different ways. This would also give you a firsthand experience of how good and professional the photographer actually is.
7.Final selection – Based on the albums and budget you can easily shortlist a wedding photographer. Invite the photographer to see the wedding venue once so that he or she can arrange for the required logistics like additional lights or camera accessories. Also, make sure you do ask your wedding photographer to give you a small demo by covering any small event in your house at a relative's place.
8.Special inputs – Let your photographer know well in advance if there are some special events that you would like to be covered. If you have bought exclusive and expensive clothes, do make sure you request your photographer to click some solo photographs of each and every family member.


text:
Der Große Preis der Niederlande 1976 fand am 29. August in Zandvoort statt und war das zwölfte Rennen der Automobil-Weltmeisterschaft 1976. Das Rennen hatte auch den FIA-Ehrentitel Großer Preis von Europa.

Berichte

Hintergrund
Zwei Wochen nach dem Großen Preis von Österreich und vier Wochen nach Niki Laudas schweren Unfall beim Großen Preis von Deutschland fand der zwölfte WM-Lauf der Saison in Zandvoort statt. Lauda, der die Weltmeisterschaftswertung weiterhin mit deutlichem Vorsprung anführte, befand sich unterdessen auf dem Weg der Besserung. Er durfte das Krankenhaus verlassen und bereitete sich in seiner Heimat Salzburg bereits langsam auf sein Comeback vor. Die schnelle Genesung seines Fahrers sowie die Tatsache, dass man auch die Konstrukteurs-Weltmeisterschaft anführte, veranlasste Enzo Ferrari dazu, wieder ins Geschehen einzugreifen und einen Wagen für Clay Regazzoni zum Holland-GP anzumelden.

McLaren plante an diesem Wochenende den ersten Einsatz eines neuen Wagens vom Typ M26, den es unter Rennbedingungen zu testen galt. James Hunt entschied sich, zunächst weiterhin mit dem ausgereiften M23 anzutreten und überließ seinem Teamkollegen Jochen Mass die Entwicklungsarbeit. Shadow brachte mit dem DN8 ebenfalls ein Exemplar eines neuen Wagens an die Rennstrecke, welches von Tom Pryce pilotiert wurde, während Jean-Pierre Jarier mit dem herkömmlichen DN5B an den Start ging.

Surtees-Stammfahrer Brett Lunger pausierte an diesem Wochenende und wurde durch den Gaststarter Conny Andersson ersetzt, der somit zu seinem ersten und einzigen Grand-Prix-Einsatz kam. Auf der Suche nach einem neuen Ensign-Stammpiloten wurde man auf den ehemaligen Wolf-Fahrer Jacky Ickx aufmerksam und engagierte ihn für den Rest der Saison. Guy Edwards, der verletzungsbedingt ausfiel, wurde bei Hesketh Racing von Rolf Stommelen vertreten.

Nach einer Pause von vier Rennen nahm das Team HB Bewaking Systems erstmals seit dem Großen Preis von Schweden wieder an einem Grand Prix teil. Als Fahrer des Teams, welches sein Heimrennen bestritt, wurde Larry Perkins beibehalten. Unter dem Namen F&S Properties nahm ein weiteres niederländisches Privatteam an dem Rennwochenende teil. Als Fahrer eines gekauften Penske PC3 wurde der ebenfalls einheimische Debütant Boy Hayje engagiert.

Aufgrund rechtlicher Konflikte mit dem bisherigen Hauptsponsor Tissot verzichtete das Team RAM Racing auf die Teilnahme.

Training
Ronnie Peterson sicherte sich zum ersten Mal seit dem Großen Preis von Argentinien 1974 und zum einzigen Mal in der Saison 1976 die Pole-Position. James Hunt im alten McLaren folgte vor Tom Pryce im neuen Shadow und Österreich-Sieger John Watson. Clay Regazzoni und Mario Andretti bildeten die dritte Startreihe.

Rennen
Peterson übernahm zunächst die Führung, während Watson den vom zweiten Platz gestarteten Hunt vom zweiten Rang verdrängen konnte. Es folgte Andretti vor Pryce. Aufgrund von Handlingproblemen konnte sich Peterson nicht von Watson absetzen. Dieser startete daraufhin mehrere Überholversuche. In der zweiten Runde geriet er dabei neben die Ideallinie, was von Hunt genutzt wurde, um auf den zweiten Platz zu gelangen. In der folgenden Runde fiel Peterson schließlich bis auf den dritten Rang hinter Watson zurück.

In der 18. Runde überholte Regazzoni, der sich zuvor an Andretti und Pryce vorbeigekämpft hatte, den drittplatzierten Peterson. Die Reihenfolge änderte sich daraufhin über mehrere Runden nur unwesentlich, bis Watson im 48. Umlauf aufgrund eines Getriebeschadens ausfiel.

Hunt gewann knapp vor Regazzoni, der zwar deutlich auf aufgeholt hatte, jedoch nicht an ihm vorbeigekommen war. Aufgrund eines Fehlers im Öldrucksystem war Peterson in der 53. Runde ausgeschieden, wodurch der dritte Platz letztendlich an Andretti ging.

Meldeliste

Klassifikationen

Startaufstellung

Rennen

WM-Stände nach dem Rennen
Die ersten sechs des Rennens bekamen 9, 6, 4, 3, 2 bzw. 1 Punkt(e).

Fahrerwertung

Konstrukteurswertung

Einzelnachweise

Weblinks

 Rennergebnis auf der offiziellen Website der Formel 1

Niederlande
1976
1976

redpajama_set_name: RedPajamaWikipedia


Ah! The Royal City of Canada is definitely a sight for sore eyes. The attractive city, which is home to one hundred thousand Canadians, is located approximately seventeen miles east of Waterloo. The city's inviting environment is enough to make you want to become a citizen. In order to do this, you will need to rent apartments in Guelph Ontario. The truth of the matter is that there are many things that you desire out of a home. For instance, you might want to bring your pet along, which means you will need a property that is pet friendly. Meanwhile, smokers will need to put effort into finding a smoker friendly residence. The easiest way to find these properties is to use our site's filtering options!
Our websites offers the easiest, most comprehensive tools for tracking down rental properties, within Guelph. Whether you wish to see the properties on a map or prefer a list, you will be able to pick your poison, with our site. Of course, you will want to sign up for our daily alerts, which can be configured to send customized daily emails to your mailbox, when specific types of properties are added to our database. This will automat the entire process and give you more free time to relax, before the big move! Be sure to use these tools to rent houses in Guelph Ontario.


text:
Q: A_Parity_Error_? Now this is odd:  While copying a tarred directory over my LAN using ssh from a Fedora machine to a FreeBSD machine.  I get:  Uncorrectable parity/CRC error
(All the disks are set with S.M.A.R.T  – disks on both machines are same user, group, and access permissions 770. I already tried changing cables and SATA ports. I also ran a quick test with the bootable WD drive software -- it passed)
As this only appears on one of the four disk on the FreeBSD machine, I was getting ready to toss the disk; now I'm less sure.
By chance, while logged on to the FreeBSD machine as root the error message does not appear. This test was verified several times.
(Also, even while logged in as a regular user and getting the error message the copy completes.  I compared file sizes with ls -l  – so the copies appear to be fine.)

Yes I already ran fsck on it; it's clean
'

redpajama_set_name: RedPajamaStackExchange


Milford Dental Group is a highly experienced practice that you can turn to if you're looking for a dentist in Milford, MA. We feel that everyone in the community should have access to high-quality dental care, which is why we offer free consultations and flexible financing. We want to make it as easy as possible to come in to address a problem that you've been facing or to receive the care that can help you keep issues at bay.
We'll take the time to get to know you and listen carefully as you discuss how you've been feeling. We'll carefully examine your teeth and gums and determine what may be the best action to take to improve or maintain your dental health. If you have any concerns after we've given you an overview of your situation, we can patiently discuss anything in greater detail with you.
Call Milford Dental Group to learn more about the dental care that we provide to those in Milford and the surrounding areas. We look forward to meeting you, and we're ready to welcome you into our office.


Liam Neeson has stepped in to replace Mel Gibson in Warner Bros.' "The Hangover Part II," following a revolt by the cast and crew against Gibson's involvement in the movie.
Neeson says he was invited to take the cameo role via his "A-Team" co-star Bradley Cooper, who stars in "The Hangover Part II" along with Zack Galifianakis.
"I just got a call to do a one day shoot on 'Hangover 2' as a tattooist in Thailand, and that's all I know about it," Neeson told Daily Variety. "I just laughed my leg off when I saw 'The Hangover, I was shooting in Berlin earlier this year and rented it on the hotel TV."
Neeson flew out to the set Thursday from his home in New York.
In a statement released Thursday, director Todd Phillips said, "I thought Mel would have been great in the movie and I had the full backing of Jeff Robinov and his team. But I realize filmmaking is a collaborative effort, and this decision ultimately did not have the full support of my entire cast and crew."
The studio has scheduled "The Hangover 2" for release on May 26.


What Exactly Is a Passive House?
Buried in Snow? Buy a House!
The Polar Vortex has departed, but many are not quick to forget the extreme low temperatures that practically paralyzed cities across the country.
I was recently asked to answer a few questions for an on-line reporter. She wanted tips on how to purchase properties for half their market value.
How do you prepare to write an offer on a home?


text:
\section{#1}}
\renewcommand{\theequation}{\arabic{section}.\arabic{equation}}

\begin{document}

\title{\bf Shearfree Condition and dynamical Instability in $f(R,T)$ gravity}

\author{Ifra Noureen \thanks{ifra.noureen@gmail.com} ${}^{(a)}$,  M. Zubair
\thanks{drmzubair@ciitlahore.edu.pk} ${}^{(b)}$,  A.A. Bhatti
\thanks{drabhatti@umt.edu.pk} ${}^{(a)}$, G. Abbas \thanks{gulamabbas@ciitsahiwal.edu.pk} ${}^{(c)}$\\
${}^{(a)}$ Department of Mathematics, SST,\\University of Management and
Technology, Lahore-54770, Pakistan.\\ ${}^{(b)}$ Department of Mathematics,\\
COMSATS Institute of Information Technology, Lahore-54700, Pakistan.\\
${}^{(c)}$ Department of Mathematics,\\ COMSATS
Institute of Information Technology, Sahiwal-57000, Pakistan}
\date{}
\maketitle

\begin{abstract}
The implications of shearfree condition on instability range of anisotropic
fluid in $f(R,T)$ are studied in this manuscript. A viable $f(R, T)$ model is
chosen to arrive at stability criterion, where $R$ is Ricci scalar and $T$ is
the trace of energy momentum tensor. The evolution of spherical star is
explored by employing perturbation scheme on modified field equations and
contracted Bianchi identities in $f(R, T)$. The effect of imposed shearfree
condition on collapse equation and adiabatic index $\Gamma$ is studied in
Newtonian and post-Newtonian regimes.
\end{abstract}

{\bf Keywords:} Shearfree condition; $f(R,T)$ gravity; Dynamical
equations; Instability range; Adiabatic index.

\section{Introduction}

In a recent work \cite{1}, we have studied the effect of anisotropic fluid on
dynamical instability of spherically symmetric collapsing star in $f(R, T)$
theory. Herein, we plan to explore the instability range of anisotropic
spherically symmetric stars, considering shearfree condition. The role of
shear tensor in evolution of gravitating objects and consequences of
shearfree condition has been studied extensively. Collins and Wainwright
\cite{2} studied the impact of shear on general relativistic cosmological and
stellar models. Herrera et al. \cite{3,4} worked out the homology and
shearfree conditions for dissipative and radiative gravitational evolution.

The features of gravitational evolution and its final outcome is of
great importance in view of General Relativity (GR) as well as in
modified theories of gravity. Shearfree collapse accounting heat
flow is discussed in \cite{5}, it is established that shear plays
critical role in gravitational evolution and may lead to the
formation of naked singularities \cite{6}. It is mentioned in
\cite{6} that occurrence of shearing effects near collapsing stars
detains the apparent horizon leading to formation of naked
singularity. However vanishing shear give rise to the formation of
apparent horizon and so the evolving cloud ends in a black hole
(BH). Thus, relevance of shear tensor in structure formation and its
impressions on dynamical instability range of self gravitating body
is well motivated direction of study.

Stars shine by consuming their nuclear fuel, continuous fuel consumption
cause imbalance between inward acting gravitational pull and outward drawn
pressure giving rise to collapse \cite{7}. The outcome of gravitational
evolution is size dependent as well as other physical aspects \cite{8} such
as isotopy, anisotropy, shear, radiation, dissipation etc. In comparison to
the stars of mass around one solar masses, massive stars tend to lose nuclear
fuel more rapidly and so more unstable. Pressure to density ratio naming
adiabatic index, denoted by $\Gamma$ is utile in estimation of
stability/instability range of stars. Chandrasekhar \cite{9} explored the
instability range of spherical stars in terms of $\Gamma$.

Herrera and his contemporaries \cite{10}-\cite{17} contributed majorally in
addressing the instability problem in general relativity (GR), accompanying
various situations, i.e., isotopy, anisotropy, shearfree condition,
radiation, dissipation, expansionfree condition, shearing expansionfree
fluids. In order to achieve the more precise and generic description of
universe, the dark energy components are incorporated by introducing modified
theories of gravity. Modified theories are significant in advancements
towards accelerated expansion of the universe and to present corrections to
GR on large scales. The modifications are introduced in Einstein Hilbert (EH)
action by inducing minimal or non-minimal coupling of matter and geometry
\cite{17a}.

Dynamical analysis of self gravitating sources in modified theories of
gravity has been discussed extensively in recent years. The null dust
non-static exact solutions in $f(R)$ gravity are studied in \cite{18},
Cembranos et al. \cite{19} studied the evolution of gravitating sources in
the presence of dust fluid. Instability range of spherically and axially
symmetric anisotropic stars has been established in context of $f(R)$ gravity
\cite{20, 21}, concluding that deviations from spherical  symmetry
complicates the subsequent evolution.

Harko et al. \cite{22} presented the $f(R,T)$ theory of gravity as another
alternate to GR and generalization of $f(R)$ theory representing non-minimal
matter to geometry coupling. The action in $f(R,T)$ gravity includes
arbitrary function of Ricci scalar $R$ and trace of energy momentum tensor
$T$ to take into account the exotic matter. After the introduction of
$f(R,T)$ gravity, its cosmological and thermodynamic implications were widely
studied \cite{23}-\cite{26} including the energy conditions. Recently, we
have studied the evolution of anisotropic gravitating source with zero
expansion \cite{27}. Herein, we are interested in exploration of shearfree
condition implications on spherically symmetric gravitating source in
$f(R,T)$ gravity.

The modified action in $f(R,T)$ is as follows \cite{22}
\begin{equation}\label{1}
\int dx^4\sqrt{-g}[\frac{f(R, T)}{16\pi G}+\mathcal{L} _ {(m)}],
\end{equation}
where $\mathcal{L} _ {(m)}$ denote matter Lagrangian, and $g$ represents the
metric tensor. Various choices of $\mathcal{L} _ {(m)}$ can be taken into
account, each of which leads to a specific form of fluid. Many people worked
out this problem in GR and modified theories of gravity, stability of general
relativistic dissipative axially symmetric and spherically symmetric with
shearfree condition has been established in \cite{28, 29}. Dynamical analysis
of shearfree spherically symmetric sources in $f(R)$ gravity is presented in
\cite{30}.

The manuscript arrangement is: Section \textbf{2} comprises of modified
dynamical equations in $f(R,T)$ gravity. Section \textbf{3} includes model
under consideration, perturbation scheme and corresponding collapse equation
alongwith shear-free condition in Newtonian and post Newtonian eras. Section
\textbf{4} contains concluding remarks followed by an appendix.

\section{Dynamical Equations in $f(R,T)$}

In order to study the implications of shearfree condition on evolution of
spherically symmetric anisotropic sources, modified field equations in
$f(R,T)$ gravity are formulated by varying action (\ref{1}) with the metric
$g_{uv}$. Here, we have taken $\mathcal{L} _{(m)}= \rho$ \cite{r5}, for this
choice of $\mathcal{L}_{(m)}$ modified field equations in $f(R,T)$ gravity
takes following form
\begin{eqnarray}\nonumber
G_{uv}&=&\frac{1}{f_R}\left[(f_T+1)T^{(m)}_{uv}-\rho g_{uv}f_T+\frac{f-Rf_R}{2}g_{uv}
\right.\\\label{4}&+&\left.(\nabla_u\nabla_v-g_{uv}\Box)f_R\right].
\end{eqnarray}
Here $T^{(m)}_{uv}$ is energy momentum tensor for usual matter taken to be locally
anisotropic.

The three dimensional spherical boundary surface $\Sigma$ is considered that
constitutes two regions named as interior and exterior spacetimes. The line
element for region inside the boundary $\Sigma$ is
\begin{equation}\label{1'}
ds^2_-=A^2(t,r)dt^{2}-B^2(t,r)dr^{2}-C^2(t,r)(d\theta^{2}+\sin^{2}\theta d\phi^{2}).
\end{equation}
The line
element for region beyond $\Sigma$ is \cite{1}
\begin{equation}\label{25}
ds^2_+=\left(1-\frac{2M}{r}\right)d\nu^2+2drd\nu-r^2(d\theta^2+\sin^{2}\theta
d\phi^{2}),
\end{equation}
where $\nu$ is retarded time and $M$ denote the total mass.

The expression for anisotropic energy momentum tensor $T^{(m)}_{uv}$ is given by
\begin{equation}\label{5}
T^{(m)}_{uv}=(\rho+p_{\bot})V_{u}V_{v}-p_{\bot}g_{uv}+(p_{r}-p_{\bot})\chi_{u}\chi_{v},
\end{equation}
where $\rho$ is energy density, $V_{u}$ describes four-velocity of the fluid,
$\chi_u$ is radial four vector, $p_r$ and $p_{\bot}$ represent the radial and
tangential pressure respectively. These physical quantities are linked as
\begin{equation}\label{3}
V^{u}=A^{-1}\delta^{u}_{0},\quad
V^{u}V_{u}=1,\quad \chi^{u}=B^{-1}\delta^u_1,\quad
\chi^{u}\chi_{u}=-1.
\end{equation}
The shear tensor denoted by $\sigma_{uv}$ is defined as
\begin{equation}\label{d}
\sigma_{uv}=V_{(u;v)}-a_{(u}V_{v)}-\frac{1}{3}\Theta(g_{uv}-V_{u}V_{v}),
\end{equation}
where $a_{u}$ is four acceleration and $\Theta$ is expansion scalar, given by
\begin{equation}\label{dd}
a_{u}=V_{(u;v)}V^{v}, \quad \Theta=V_{;u}^{u}.
\end{equation}
Components of shear tensor are found by variation of Eq. (\ref{d}) and these
are used to find expression for shear scalar in the following form
\begin{equation}\label{ddd}
\sigma=\frac{1}{A}\left(\frac{\dot{B}}{B}-\frac{\dot{C}}{C}\right),
\end{equation}
where dot and prime indicate time and radial derivatives respectively. From shearfree condition we arrive at vanishing shear scalar, i.e., $\sigma=0$,
implying $\frac{\dot{B}}{B}=\frac{\dot{C}}{C}$.

It is worth mentioning here that the expansion scalar and a scalar function described in terms of Weyl tensor and the anisotropy of pressure controls the departure
from shearfree condition. Such function is related to the Tolman mass and appears in a natural way in the orthogonal splitting of the
Reimann tensor \cite{31}. It is obvious that pressure anisotropy and density inhomogeneities have extensive implications on stability of the shear–free condition
but it is not intuitively clear that their specific combination affects stability \cite{29}. Generically shearfree condition remains unstable against the presence of
pressure anisotropy. Alternatively, one can consider such a case that pressure anisotropy and density inhomogeneity are present in a way that the scalar function
appearing in orthogonal splitting of Reimann tensor vanishes, implying non-homogeneous anisotropic stable shear free flow. Since we are dealing with
fluid evolving under shearfree condition, so we shall make use of this
condition while evaluating  the components of field equations and also in
conservation equations.

The components of modified Einstein tensor are
\begin{eqnarray}\label{f1}
G_{00}&=&\frac{1}{f_R}\left[\rho+ \frac{f-Rf_R}{2}+
\frac{f_R''}{B^2}-\frac{3\dot f_R}{A^2}\frac{\dot{B}}{B}
-\frac{f_R'}{B^2}\left(\frac{B'}{B}-\frac{2C'}{C}\right)\right]
,\\\label{f2}
G_{01}&=&\frac{1}{f_R}\left[\dot{f_R}'
-\frac{A'}{A}\dot{f_R}-\frac{\dot{B}}{B}f_R'\right],\\\nonumber
G_{11}&=&\frac{1}{f_R}\left[p_r+\left(\rho+p_r\right)f_T- \frac{f-Rf_R}{2}+
\frac{\ddot{f_R}}{A^2}-\frac{\dot f_R}{A^2}\left(\frac{\dot{A}}{A}-\frac{2\dot{C}}{C}\right)
\right.\\\label{f3}
&&\left.-\frac{f_R'}{B^2}\left(\frac{A'}{A}+\frac{2C'}{C}\right)\right],
\\\nonumber
G_{22}&=&\frac{1}{f_R}\left[p_\perp+\left(\rho + p_\perp\right)f_T-
\frac{f-Rf_R}{2}+
\frac{\ddot{f_R}}{A^2}-\frac{f_R''}{B^2}-\frac{\dot
f_R}{A^2}\left(\frac{\dot{A}}{A} \right.\right.\\\label{f4}
&&\left.\left.-\frac{\dot{2B}}{B}\right)
-\frac{f_R'}{B^2}\left(\frac{A'}{A}-\frac{B'}{B}+\frac{C'}{C}\right)\right].
\end{eqnarray}
The dynamical equations extracted from the conservation laws are vital in the
study of stellar evolution. The conservation of full field equations is
considered to incorporate the non-vanishing divergence terms, Bianchi
identities are
\begin{eqnarray}\label{bb}
&&G^{uv}_{;v}V_{u}=0,\quad
G^{uv}_{;v}\chi_{u}=0,
\end{eqnarray}
on simplification of Eq.(\ref{bb}), we have dynamical equations as follows
\begin{eqnarray}\label{B1} &&\dot{\rho}-\rho\frac{\dot{f_R}}{f_R}+[1+f_T]\left(3\rho+p_r
+2p_\perp\right)\frac{\dot{B}}{B}+ Z_1(r,t)=0,
\\\nonumber &&
(\rho +p_r)f'_T+(1+f_T)\left\{p'_r+\rho \frac{A'}{A}+
p_r\left(\frac{A'}{A}+2\frac{C'}{C}-\frac{f'_R}{f_R}\right)
-2p_\perp\frac{C'}{C}\right\}\\\label{B2}&&+f_T\left(\rho'-\frac{f'_R}{f_R}\right)+Z_2(r,t)=0,
\end{eqnarray}
where $Z_1(r,t)$ and $Z_2(r,t)$ are provided in appendix as Eqs.(\ref{B3})
and (\ref{B4}) respectively. Deviations from equilibrium in conservation
equations with the time transition leads to the stellar evolution,
perturbation approach is devised to the estimate the instability range.

\section{Perturbation Scheme and Shearfree Condition}

We consider a particular $f(R,T)$ model of the form
\begin{eqnarray}\label{m}
&&f(R, T)= R+\alpha R^2+\lambda T,
\end{eqnarray}
where $\alpha$ and $\lambda$ can be any positive constants. Perturbation
approach is utilized to estimate the instability range of spherical star with
shear free condition. This scheme is utile in determination of more generic
analytical constraints on collapse equation, rather to establish dynamical
analysis of special cases numerically. Also, field equations are highly
nonlinear differential equations, in such scenario application of
perturbation lead to beneficial observations.

It is assumed that initially all quantities are independent of time and with
the passage of time perturbed form depends on both time and radial
coordinates. Taking $0<\varepsilon\ll1$, the physical quantities and their
perturbed form can be arranged as
\begin{eqnarray}\label{41} A(t,r)&=&A_0(r)+\varepsilon
D(t)a(r),\\\label{42} B(t,r)&=&B_0(r)+\varepsilon D(t)b(r),\\\label{43}
C(t,r)&=&C_0(r)+\varepsilon D(t)\bar{c}(r),\\\label{44}
\rho(t,r)&=&\rho_0(r)+\varepsilon {\bar{\rho}}(t,r),\\\label{45}
p_r(t,r)&=&p_{r0}(r)+\varepsilon {\bar{p_r}}(t,r),
\\\label{46}
p_\perp(t,r)&=&p_{\perp0}(r)+\varepsilon {\bar{p_\perp}}(t,r), \\\label{47}
m(t,r)&=&m_0(r)+\varepsilon {\bar{m}}(t,r), \\\label{49'}
R(t,r)&=&R_0(r)+\varepsilon D_1(t)e_1(r),\\\label{50'}
T(t,r)&=&T_0(r)+\varepsilon D_2(t)e_2(r),\\\nonumber
f(R, T)&=&[R_0(r)+\alpha R_0^2(r)+\lambda T_0]+\varepsilon(D_1(t)e_1(r)[1\\\label{51'}&+&2\alpha  R_0(r)]+ D_2(t)e_2(r)),\\\label{52'}
f_R&=&1+2\alpha R_0(r)+\varepsilon 2\alpha D_1(t)e_1(r),\\\label{52'}
f_T&=&\lambda.
\end{eqnarray}
Considering Schwarzschild coordinate $C_0=r$ and implementing perturbation
scheme on vanishing shear scalar implies
\begin{equation}\label{dddd}
\frac{b}{B_0}=\frac{\bar{c}}{r}.
\end{equation}
Using Eqs. (\ref{41})-(\ref{52'}) and (\ref{dddd}) in dynamical equations
i.e., Eqs.(\ref{B1}) and (\ref{B2}) leads to following expressions
\begin{eqnarray}\label{B1p}&&
\dot{\bar{\rho}}+\left[\frac{2e\rho_0}{Y}+\lambda_1\frac{\bar{c}}{r}(2\rho_0+p_{r0}+4p_{\perp0})
+YZ_{1p}\right]\dot{D}=0,
\\\nonumber
&&\lambda_1\left\{\bar{p_r}'+\bar{\rho}\frac{A'_0}{A_0}+\bar{p_r}\left(\frac{A'_0}{A_0}+\frac{2}{r}-\frac{2\alpha
R'_0}{Y}\right)-\frac{2\bar{p_\perp}}{r}\right\}+\lambda\bar{\rho'}+2\alpha\ddot{D}\left[\frac{1}{A_0^2}\left(e'
\right.\right.\\\nonumber &&\left.\left.
+2e\frac{B'_0}{B_0}-\frac{\bar{c}}{r}R'_0\right)+B_0^2(Y)\left\{\frac{e}{B_0^2Y}\right\}'\right]
+D\left[\lambda_1[(\frac{a}{A_0})'(\rho_0+p_{r0})\right.\\\nonumber &&\left.-2(p_{r0}+p_{\perp0})(\frac{\bar{c}}{r})']
-\frac{2\alpha}{Y}\left\{\lambda_1\left(p'_{r0}
+\rho_0\frac{A'_0}{A_0}
+p_{r0}\left(\frac{A'_0}{A_0}-\frac{2\alpha R'_0}{Y}+\frac{2}{r}\right)\right)\right\}
\right.\\\label{B2p}&&\left.+\lambda\left(e'+e[\rho'_0-\frac{2\alpha R'_0}{Y}]\right)+YZ_{2p}\right]
=0,
\end{eqnarray}
where $Z_{1p}$ and $Z_{2p}$ are given in appendix, for the sake of simplicity
we put $Y$ in place of $1+2\alpha R_0$ and $\lambda_1=\lambda+1$, assuming
that $D_1=D_2=D$ and $e_1=e_2=e$. Above mentioned perturbed dynamical
equations and perturbed field equations shall be used to arrive at perturbed
physical quantities such as $\bar{\rho}, \bar{p_r}$ and $\bar{p_\perp}$.

The expression for $\bar{\rho}$ can be found from Eq.(\ref{B1p}), as follows.
\begin{equation}\label{B1p'}
\bar{\rho}=-\left[\frac{2e\rho_0}{Y}+\frac{\bar{c}}{r}(3\rho_0+p_{r0}+4p_{\perp0})+YZ_{1p}\right]D.
\end{equation}
The Harrison-Wheeler type
equation of state relate $\bar{\rho}$ and $\bar{p_r}$, given by
\begin{equation}\label{B7}
\bar{p}_r=\Gamma\frac{p_{r0}}{\rho_0+p_{r0}}\bar{\rho}.
\end{equation}
Putting $\bar{\rho}$ from Eq.(\ref{B1p'}) in Eq.(\ref{B7}), we found
\begin{equation}\label{B8}
\bar{p}_r=-\Gamma\frac{p_{r0}}{\rho_0+p_{r0}}\left[\frac{2e\rho_0}{Y}
+\lambda_1\frac{\bar{c}}{r}(3\rho_0+p_{r0}+4p_{\perp0})+YZ_{1p}\right]D.
\end{equation}
Perturbed form of field equation (\ref{f4}) yields expression for $\bar{p}_\perp$, that turns out to be
\begin{eqnarray}\label{B9}
\bar{p}_\perp=\{\frac{Y\bar{c}}{r}-2\alpha e\}\frac{\ddot{D}}{A_0^2}
-\frac{\lambda \bar{\rho}}{\lambda_1}+\left\{\left(p_{\perp0}
-\frac{\lambda}{\lambda_1}\rho_0\right)\frac{2\alpha e}{Y}+\frac{Z_3}{\lambda_1}\right\}D,
\end{eqnarray}
$Z_3$ is effective part of the field equation given in appendix as
Eq.(\ref{Z3}).

Substitution of $\bar{\rho}, \bar{p_r}$ and $\bar{p_\perp}$ from
Eqs.(\ref{B1p'}), (\ref{B8}) and (\ref{B9}) in Eq.(\ref{B2p}) leads to collapse equation as under
\begin{eqnarray}\nonumber
&&\ddot{D}\left[\frac{2\alpha }{A_0^2Y}\left\{e'+2e\frac{B'_0}{B_0}
-\frac{\bar{c}}{r}R'_0\right\}-2\alpha B_0^2\left\{\frac{e}{B_0^2Y}\right\}' +\frac{1}{A_0^2}\{\frac{Y \bar{c}}{r}
-2\alpha e\}\right]\\\nonumber &&+D\left[\frac{1}{Y}\left\{\lambda_1\left((\rho_0+p_{r0})\left(\frac{a}{A_0}\right)'
-2(\rho_0+p_{\perp0})\left(\frac{\bar{c}}{r}\right)'\right)
-\frac{2\alpha }{Y}\left\{\lambda\left(e'-\rho'_0
\right.\right.\right.\right.\\\nonumber &&\left.\left.\left.\left.
-\frac{2\alpha R'_0}{Y}\right)
+\lambda_1\left(e'p_{r0}
+e[p'_{r0}+\rho_0\frac{A'_0}{A_0}+p_{r0}(\frac{A'_0}{A_0}+\frac{2}{r}-\frac{2\alpha R'_0}{Y})]\right)\right\}
-\left(\lambda\right.\right.\right.\\\nonumber &&\left.\left.\left.
+\lambda_1\Gamma\frac{p_{r0}}{\rho_0+p_{r0}}\right)
\left\{
\rho_0\frac{2e}{Y}+\lambda_1\frac{\bar{c}}{r}(3\rho_0+p_{r0}+4p_{\perp0})+Y Z_{1p}\right\}_{,1}+\left\{\frac{A'_0}{A_0}\right.\right.\right.\\\nonumber
&&\left.\left.\left.
+\frac{2}{r}\frac{\lambda}{\lambda_1}+\Gamma\frac{p_{r0}}{\rho_0
+p_{r0}}(\frac{A'_0}{A_0}+\frac{2}{r}-\frac{2\alpha R'_0}{Y})
+\lambda_1\left(\Gamma\frac{p_{r0}}{\rho_0+p_{r0}}\right)'\right\}\left\{\frac{2e\rho_0}{Y}
\right.\right.\right.\\\label{B10} &&\left.\left.\left.
+\lambda_1\frac{\bar{c}}{r}(3\rho_0+p_{r0}+4p_{\perp0})
+(Y)Z_{1p}\right\}+\frac{2}{r}\frac{1}{\lambda_1}Z_3\right\}
+Z_{2p}\right]=0.
\end{eqnarray}

Matching conditions at boundary surface together with perturbed form of Eq.(\ref{f4}) can be
written in the simplified form as follows
\begin{equation}\label{66}
\ddot{D}(t)-Z_4(r) D(t)=0,
\end{equation}
provided that
\begin{equation}\label{67}
Z_4=\frac{rA_0^2}{Y\bar{c}-2\alpha
er}\left[\frac{2\alpha e}{Y}p_{\perp0}+\lambda\frac{\bar{c}}{r}(3\rho_0
+p_{r0}+4p_{\perp0})
+YZ_{1p}+\frac{Z_3}{\lambda_1}\right].
\end{equation}
The valid solution of Eq.(\ref{66}) turns out to be
\begin{equation}\label{68}
D(t)=-e^{\sqrt{Z_4}t}.
\end{equation}
The terms of $Z_4$ must be constrained in a way that all terms maintain
positivity. Impact of shear-free condition on dynamical instability of N and
pN regimes is covered in following subsections.

\subsection{Newtonian Regime}

In order to establish instability range in Newtonian era, we set $\rho_0\gg
p_{r0}$, $\rho_0\gg p_{\perp0}$ and $A_0=1,~B_0=1$. Insertion of these
assumptions and Eq.(\ref{68}) in Eq.(\ref{B10}) leads to the instability
condition, relating usual matter and dark source contribution as under
\begin{equation}\label{N}
\Gamma<\frac{Z_4X_3+X_4+\lambda\rho_0(X_2+YZ_{1p(N)})_{,1}+X_1 X_2-
\frac{2}{r\lambda_1}Z_{3(N)}+YZ_{2p(N)}}{\lambda_1p_{r0}X'_2
+\left\{p_{r0}\left(\frac{2\alpha R'_0}{Y}-\frac{2}{r}\right)\right\}X_2},
\end{equation}
where
\begin{eqnarray}\nonumber&&
X_1=(\lambda\rho'_0+\frac{2\lambda}{r\lambda_1}), \quad X_2 = \frac{2e}{Y}+3\lambda_1b,\quad \quad X_3 = -2\alpha^2b R'_0+Yb,
\\\nonumber && Z_4= \lambda_1\left[\rho_0 a'+2(p_{r0}+p_{\perp0})b'\right]+
\frac{2\alpha}{Y}\left[\lambda\left(\frac{2\alpha R'_0}{Y}-\rho'_0+e'\right)
\right.\\\nonumber &&\left.+\lambda_1\left\{p_{r0}+e[p'_{r0}+p_{r0}\left(\frac{2}{r}-\frac{2\alpha R'_0}{Y}\right)]\right\}\right].
\end{eqnarray}
The quantities $Z_{1p(N)}$ and $Z_{2p(N)}$ are terms of $Z_{1p}$ and $Z_{2p}$ belonging
to Newtonian era.
The gravitating source remains
stable in Newtonian approximation until the inequality for $\Gamma$ satisfies,
for which following constraints must be accomplished.
\begin{equation}\nonumber
 \quad 2\alpha R'_0<Y,
\quad \frac{2\alpha R'_0}{Y}>\rho_0'-e'
\end{equation}
The case when $\alpha\rightarrow0$ and $\lambda\rightarrow0$ leads to GR corrections
and results for $f(R)$ can be retrieved by setting $\lambda\rightarrow0$.

\subsection{Post Newtonian Regime}

We assume $A_0=1-\frac{m_0}{r}$ and $B_0=1+\frac{m_0}{r}$ to evaluate
stability condition in pN regime. On substitution of these assumptions in Eq.
(\ref{B10}), we have following inequality for $\Gamma$ to be fulfilled for
stability range.
\begin{equation}\label{zw}
\Gamma<\frac{Z_4X_5+X_6+\lambda\rho_0(X_7+YZ_{1p(PN)})_{,1}+X_8 X_7-
\frac{2}{r\lambda_1}Z_{3(PN)}+YZ_{2p(PN)}}{\lambda_1p_{r0}X'_7
+\left\{p_{r0}\left(\frac{m_0}{r(r-m_0)}
+\frac{2\alpha R'_0}{Y}+\frac{2}{r}\right)\right\}X_7},
\end{equation}
where
\begin{eqnarray}\nonumber
X_5&=&\frac{2\alpha r^2}{(r-m_0)^2}\left\{e'-\frac{r}{r+m_0}\left(bR'_0+2e\frac{m_0}{r}\right)\right\}+
Y\left[\frac{ r^2}{(r-m_0)^2}\left\{2\alpha e
\right.\right.\\\nonumber&&\left.\left.-Y\frac{\bar{c}}{r}\right\}-\frac{2\alpha(r+m_0)^2}{r^2}
\left\{\frac{er^2}{Y(r+m_0)^2}\right\}'\right],
\\\nonumber
X_6&=&\lambda_1\left\{\rho_0\left(\frac{ar}{r-m_0}\right)'-2(p_{r0}+p_{\perp0})b'\right\}
-\frac{2\alpha}{Y}\left[(\lambda_1 p_{r0}+\lambda)e'\right.\\\nonumber&&\left.
+e\left\{\lambda_1( p'_{r0}+\frac{\rho_0m_0}{r(r-m_0)})+p_{r0}\left(\frac{2}{r}-\frac{2\alpha R'_0}{Y}\right)\right\}
-\lambda\left(\rho'_0-\frac{2\alpha R'_0}{Y}\right)\right],\\\nonumber
X_7&=&\frac{2e}{Y}+\lambda_1b\left(2+\frac{r}{r+m_0}\right), \quad
X_8=\left(\frac{m_0}{r(r-m_0)}
+\frac{2\alpha R'_0}{Y}+\frac{2\lambda}{\lambda_1r}+\lambda\rho'_0\right).
\end{eqnarray}
$Z_{1p(PN)}$ and $Z_{2p(PN)}$ are terms of $Z_{1p}$ and $Z_{2p}$ that lie in
post-Newtonian era. The above inequality (\ref{zw}) holds for positive
definite terms and describe the stability range of subsequent evolution. The
positivity of each term appearing in (\ref{zw}) leads to following
restrictions
\begin{eqnarray}\nonumber&&
\frac{r}{r+m_0}(bR'_0+\frac{2em_0}{r})<e',\quad 2\alpha
e-Yb>\frac{(r^2-m_0^2)^2}{r^4}\left\{\frac{er^2}{Y(r+m_0)^2}\right\}'\\\nonumber &&
\left(\frac{ar}{r-m_0}\right)'>2(p_{r0}+p_{\perp0})b', \quad \rho'_0<\frac{2\alpha R'_0}{Y}.
\end{eqnarray}

\section{Concluding Remarks}

In this manuscript, we carried out a study on implications of shear-free
condition on stability of spherically symmetric anisotropic stars in $f(R,
T)$. Our exploration regarding viability of the $f(R,T)$ model reveals that
the selection of $f(R,T)$ model for dynamical analysis is constrained to the
form $f(R,T)=f(R)+\lambda T$, where $\lambda$ is arbitrary positive constant.
The restriction on $f(R,T)$ form originates from the complexities of
non-linear terms of trace in analytical formulation of field equations. The
model under consideration is of the form $f(R, T)=R+\alpha R^2+\lambda T$,
representing a viable substitute to dark source and the exotic matter
satisfying both viability criterion (positivity of radial derivatives upto
second order).

In $f(R,T)$ gravity, the non-minimal matter geometry coupling include the
terms of trace $T$ in action (\ref{1}) that is beneficent in the description
of quantum effects or so-called exotic matter. The components of modified
field equations together with the implementation of shear-free condition are
developed in section \textbf{2}. Further conservation laws are considered to
arrive at dynamical equations by means of Bianchi identities. These equations
are utilized to estimate the variations in gravitating system with the
passage of time.

The complexities of more generic analytical field equations are dealt by
using linear perturbation of physical quantities. Perturbation scheme induce
significant ease in the description of dynamical system, rather to present
stability analysis by means of numerical simulations. The analytic approach
we have employed here is more general and substantially important in
explorations regarding structure formation. The perturbed shear-free
condition together with the dynamical and field equations lead to the
evolution equation, relating $\Gamma$ with the usual and dark source terms.
It is found that the induction of trace of energy momentum tenor in action
(\ref{1}) contributes positive addition to $\Gamma$, that slows down
subsequent evolution considerably.

The outcome of gravitational evolution is size dependent as well as other
physical aspects such as isotopy, anisotropy, shear, radiation, dissipation
etc. The instability range for N and pN approximations is considered that
impose some restrictions on the physical variables. It is observed that the
terms appearing in $\Gamma$ are less constrained for both the regimes (N and
pN) in comparison to the anisotropic sources \cite{1}. Thus, shear-free
condition benefits in more stable anisotropic configurations. Corrections to
GR and $f(R)$ establishments can be made by setting $\alpha\rightarrow0$,
$\lambda\rightarrow0$ and $\lambda\rightarrow0$ respectively. The local
isotropy of the model can be settled by assuming $p_r=p_\perp=p$. The
extension of this work for shearing expansion free evolution of anisotropic
spherical and cylindrical sources is in process.

\section{Appendix}

\begin{eqnarray}\setcounter{equation}{1}\nonumber
Z_1(r,t)&=&f_R A^2\left[\left\{\frac{1}{f_R A^2}\left(\frac{f-Rf_R}{2}
-\frac{3\dot{f_R}}{A^2}\frac{\dot{B}}{B}-\frac{f'_R}{B^2}\left(\frac{B'}{B}
-\frac{2C'}{C}\right)+\frac{f''_R}{B^2}\right)\right\}_{,0}\right.\\\nonumber &&\left.
+\left\{\frac{1}{f_RA^2B^2}\left(\dot{f'_R}-\frac{A'}{A}\dot{f_R}
-\frac{\dot{B}}{B}f_R'\right)\right\}_{,1}\right]-\frac{\dot{f_R}}{A^2}\left\{
\left(3\frac{\dot{B}}{B}\right)^2+\frac{9\dot{A}}{A}\frac{\dot{B}}{B}
\right\}
\\\nonumber&&
+\frac{3\ddot{f_R}}{A^2}\frac{\dot{B}}{B}+\frac{\dot{A}}{A}(f-Rf_R)
-\frac{2f'_R}{B^2}\left\{\frac{\dot{A}}{A}\left(\frac{B'}{B}
-\frac{C'}{C}\right)+\frac{\dot{B}}{B}\left(\frac{3A'}{A}-\frac{2C'}{C}\right.\right.\\\nonumber
&&\left.\left.
+\frac{B'}{B}\right)\right\}
+\frac{f_R''}{B^2}\left(\frac{2\dot{A}}{A}+\frac{\dot{B}}{B}\right)+\frac{1}{B^2}\left(\dot{f'_R}-\frac{A'}{A}\dot{f_R}
\right)\left(\frac{3A'}{A}
+\frac{B'}{B}+\frac{2C'}{C}\right),\\\label{B3}
&&
\\\nonumber
Z_2(r,t)&=&f_RB^2\left[\left\{\frac{1}{f_RA^2B^2}\left(\dot{f_R}'-\frac{A'}{A}\dot{f_R}
-\frac{\dot{B}}{B}f_R'\right)\right\}_{,0}+\left\{\frac{1}{f_RB^2}\left(\frac{Rf_R-f}{2}
\right.\right.\right.
\\\nonumber &&\left.\left.\left.-\frac{\dot{f_R}}{A^2}\left(\frac{\dot{A}}{A}-\frac{2\dot{C}}{C}\right)-\frac{f'_R}{B^2}\left(\frac{A'}{A}
+\frac{2C'}{C}\right)+\frac{\ddot{f_R}}{A^2}\right)\right\}_{,1}
\right]+(Rf_R-f)\frac{B'}{B}
\\\nonumber
&&-\frac{1}{A^2}\frac{\dot{f_R}}{A^2}\left\{\frac{A'}{A}\left(\frac{\dot{A}}{A}+\frac{\dot{B}}{B}\right)
+\frac{B'}{B}\left(\frac{\dot{A}}{A}-\frac{2\dot{C}}{C}\right)\right\}
+\left(\frac{\dot{A}}{A}+\frac{5\dot{B}}{B}\right)\left(\dot{f_R}'\right.\\\nonumber
&&\left.-\frac{A'}{A}\dot{f_R}
-\frac{\dot{B}}{B}f_R'\right)-\frac{f'_R}{B^2}\left\{\frac{A'}{A}\left(\frac{A'}{A}+\frac{3B'}{B}\right)
+\frac{2C'}{C}\left(\frac{3B'}{B}
+\frac{C'}{C}\right)\right\}
\\\label{B4} &&
+\frac{\ddot{f_R}}{A^2}\left(\frac{A'}{A}+\frac{2B'}{B}\right)
+\frac{f''_R}{B^2}\left(\frac{A'}{A}
+\frac{2C'}{C}\right).
\end{eqnarray}
\begin{eqnarray}\nonumber
Z_{1p}&=& 2\alpha A_0^2\left[\frac{1}{A_0^2B_0^2Y}\left\{e'-e\frac{A'_0}{A_0}-\frac{b}{B_0}R'_0\right\}\right]_{,1}
+\frac{1}{Y}\left[e-[\lambda T_0
\right.\\\nonumber && \left.-\alpha R_0^2]\left(\frac{a}{A_0}+\frac{e}{Y}\right)
+\frac{2\alpha}{B_0^2}\left\{\left(\frac{B'_0}{B_0}-\frac{2}{r}\right)\left(e'-2R'_0\left(\frac{a}{A_0}
+\frac{b}{B_0}\right)\right.\right.\right.\\\nonumber & &\left.\left.\left.
+\frac{2 \alpha e}{Y}R'_0\right)
+ R''_0 \left(\frac{2a}{A_0}+\frac{b}{B_0}\right)-2R'_0\left(\frac{b}{B_0}\left(\frac{2A'_0}{A_0}+
\frac{B'_0}{B_0}+\frac{1}{r}\right)\right.\right.\right.\\\label{Z1p} & &\left.\left.\left.+\frac{\bar{c}}{r}\left(\frac{A'_0}{A_0}-\frac{3}{r}\right)\right)
+\left(e'-e\frac{A'_0}{A_0}\right)\left(\frac{3A'_0}{A_0}+
\frac{B'_0}{B_0}+\frac{2}{r}\right)\right\}\right]
\\\nonumber
Z_{2p}&=&B_0^2Y\left[\frac{1}{B_0^2Y}\left\{e-\frac{2\alpha}{B_0^2}\left\{
\left(\frac{A'_0}{A_0}+\frac{2}{r}\right)\left(e-[\frac{2 \alpha e}{Y}+\frac{4b}{B_0}]R'_0\right)
+R'_0[\left(\frac{a}{A_0}\right)'
\right.\right.\right.\\\nonumber & &\left.\left.\left.
+\left(\frac{\bar{c}}{r}\right)']\right\}-[\lambda T_0
-\alpha R_0^2]\left(\frac{b}{B_0}+\frac{e}{Y}\right)\right\}\right]_{,1}
+bB_0Y\left[\frac{1}{B_0^2Y}\left\{\lambda T_0
-\alpha R_0^2
\right.\right.\\\nonumber &&\left.\left.
-\frac{4\alpha}{B_0^2}\left(\frac{A'_0}{A_0}+\frac{2}{r}\right)R'_0\right\}\right]_{,1}
+\frac{2\alpha}{B_0^2}\left[R''_0\left\{\left(\frac{a}{A_0}\right)'-2\left(\frac{A'_0}{A_0}
+\frac{2}{r}\right)\left(\frac{b}{B_0}+\frac{e}{Y}\right)
\right.\right.\\\nonumber &&\left.\left.+\left(\frac{\bar{c}}{r}\right)'
\right\}-R'_0\left\{\frac{A'_0}{A_0}\left[2\left(\frac{a}{A_0}\right)'+3\left(\frac{b}{B_0}\right)'\right]
+3\frac{B'_0}{B_0}\left[\left(\frac{a}{A_0}\right)'+2\left(\frac{\bar{c}}{r}\right)'\right]
\right.\right.\\\nonumber & &\left.\left.+
\frac{2}{r}\left[\left(3\frac{b}{B_0}\right)'+2\left(\frac{\bar{c}}{r}\right)'\right]\right\}+\left(\frac{2b}{B_0}R'_0
-e\right)
\left\{3\frac{B'_0}{B_0}\left(\frac{A'_0}{A_0}+\frac{2}{r}\right)
+\left(\frac{A'_0}{A_0}\right)^2
\right.\right.\\\label{Z2p} & &\left.\left.+\frac{2}{r^2}\right\}\right]+e\frac{B'_0}{B_0}-[\lambda T_0
-\alpha R_0^2]\left(\frac{b}{B_0}+\frac{2e}{Y}\frac{B'_0}{B_0}\right)
\end{eqnarray}
\begin{eqnarray}\nonumber
Z_{3}&=&\frac{Y}{B_0^2}\left[\frac{a''}{A_0}+\frac{\bar{c}''}{r}-\frac{A''_0}{A_0}
\left(\frac{a}{A_0}+\frac{2b}{B_0}\right)+\frac{A'_0}{A_0}\left\{\frac{2b}{B_0}\left(\frac{B'_0}{B_0}
-\frac{1}{r}\right)+\left(\frac{\bar{c}}{r}\right)'\right.\right.\\\nonumber & &\left.\left.
-\left(\frac{b}{B_0}\right)'\right\}
+\frac{B'_0}{B_0}\left\{\frac{2bB_0'}{rB_0}-\left(\frac{a}{A_0}\right)'-\left(\frac{\bar{c}}{r}\right)'\right\}+
\frac{1}{r}\left\{\left(\frac{a}{A_0}\right)'-\left(\frac{b}{B_0}\right)'\right\}
\right]\\\nonumber & &
-\frac{2\alpha e}{Y}\left\{\frac{\lambda T_0
-\alpha R_0^2}{2}-\frac{2\alpha}{B_0^2}\left(R'_0\left(\frac{A'_0}{A_0}-\frac{B'_0}{B_0}
+\frac{1}{r}\right)-R''_0\right)\right\}-\frac{2\alpha}{B_0^2}\left\{e''\right.\\\label{Z3} & &\left.
+\frac{2b}{B_0}R''_0+\left(\frac{A'_0}{A_0}-\frac{B'_0}{B_0}
+\frac{1}{r}\right)\left(\frac{2b}{B_0}R'_0-e'\right)\right\}
\end{eqnarray}

\vspace{.25cm}

{\bf Acknowledgment}

\vspace{.25cm}

The authors thank the anonymous referee for fruitful comments and
suggestions.

redpajama_set_name: RedPajamaArXiv


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The result? Decreased risk of heart disease, lower blood pressure, weight maintenance and reduced risk of osteoporosis are just some of the benefits of hitting 10,000 daily steps, according to the American Heart Association.
Citing 2013 research in the National Runners' Health Study and National Walkers' Health Study, the AHA argues that moderate-intensity walking is as beneficial as vigorous running, although runners end up exercising twice as much in the same amount of time as walkers. That said, any spurt of activity is beneficial to health, according to the group.
It all begins with that one step. If you're starting from the beginning, nonprofit group Shape Up America offers tips on building up to the magic number. The first tip? Get a pedometer. (Luckily, many smartphones now offer walking apps to track your daily steps, among other things.)
Shape Up says most people walk between 900 and 3,000 steps, but it's easy to build up to 10,000 without strain. Setting daily goals — 2,500 the first week, 3,000 the next — helps scale your walking until you eventually reach 10,000.
And don't think that you have to knock out 10,000 steps all at once. The AHA's Russell Pate, a professor of exercise science in the Arnold School of Public Health at the University of South Carolina in Columbia, suggests breaking up walks into manageable 10- to 15-minute chunks.
'It's not a skill-dependent form of activity,' Pate said. 'It's the most accessible form of physical activity.'
Build in a walk on your lunch break or walk after dinner with a friend or loved one. A few simple changes — even pacing while on the phone — will get you to the magic number in no time.
'You can do it almost anywhere,' Pate said.


Xirrus came out and tried something new this morning for their inaugral session at Wireless Field Day (or any Tech Field Day event for that matter). First they gave a brief solutions overview with lots of stats. Typical deployments see 50%-75% fewer APs resulting in immediate tangible TCO reduction due to less cabling, lower installation, lower maintenance, and less power used. The arrays also feature a modular config allowing customers to add or upgrade radios as needed to stay current with evolving standards and reducing associated labor costs of replacing APs for brand new technology. Xirrus has a belief that one size does not fit all, something I think no one will argue, but they have the portfolio to back it up. With arrays ranging from low usage, low density deployments all the way up to highly dense, maximum capacity conventions center type deployments they've got something for everyone.
On the slightly technical side, they discussed how the arrays provide spectrum optimization via software programmable radios and reduce the amount of units required for deployment by utilizing as many channels as possible. For instance, a typical 5GHz deployment that uses all 21 available channels requires 21 radios and in turn 21 access points. The same deployment using a Xirrus array requires 3 units putting 7 channels on each array. On the controller and management side of the system you're going to see something similar to other distributed architectures (e.g. Aerohive, Juniper, et. al.). Xirrus referred to their AP as a "switch with wifi ports" but intelligence is distributed in order to balance the processing load of the application control, configurations, radio/client management, and everything else that goes on behind the scenes. All of this scales linearly because as a new array is added it simply assimilates to the group and becomes another chunk of the collective brain. The application control is flexible and allows for predicatable performance per application and policy control to limit, prioritize, or block specific traffic/application types. With over 1200 different defined applications, it should be sufficient for most deployments.
Now we get to the "something new" Xirrus did. One of their customers, Optix Media, came onsite and gave us some examples of how Xirrus has been able to do to meet their requirements and solve problems that no other company could do successfully. Shane Moulton, the CTO of Optix, told us a bit about the WISP he is a part of and the some of the locations they've deployed in. Residential higher educational areas, cities, and ski resorts were all talked about and how each is a unique problem. Hotel and dorm wireless is typically a mess, overlapping networks and co-channel interference abound. Shane told us that for his company, Xirrus made sense because of the controllerless architecture, XMS management platform, quality of support, and levels of training provided to him and his staff. It wasn't a technical presentation, but it was a customer reference with some real experience deploying to some difficult locations.
Finally they broke into the architecture and the room got chatty. Oh boy did it get chatty. Xirrus is a bit of a controversial vendor because of their unique arrays and claims about co-channel interference, specifically that their devices don't cause any. To a room full of people who live and breathe real world deployments, "trust us" doesn't fly. The conversation was civil but Xirrus had to cut it off due to time restrictions (look for them at Wireless Field Day 6 possibly, with their antenna team). There was a lot of focus on how specifically any of this is possible, this technology that flies in the face of the wealth of experience sitting in the room and the science that they use.
I think it was a great presentation of a product that I have had no experience with, I learned a lot about what they do and why they do it. Now we need to make sure they come back for Wireless Field Day 6 so we can get a lot more into the "how" of it all. Although I don't think anyone has done a 180° change of heart, I applaud Xirrus for stepping into the fire opening a dialogue. That's what Wireless Field Day is about; exposure to new products, new solutions, new vendors, and new technology in a (fairly) safe environment. It's heart warming.
I'll link through to the video as soon as it becomes available.


New York–native Zoe has an affinity for vintage ROLEX Day-Dates, particularly the reference 1803 in white gold. Zoe explains, "there's just something about them that makes them flawless and the perfect everyday watch." Prior to WatchBox, Zoe worked in the auction industry–at houses including Antiquorum and Auctionata, as well as the online pre-owned watch marketplace Crown & Caliber. Zoe loves the industry and the market behind watches. She began her career with watches during a temporary job at Antiquorum during college, falling in love with the industry then.


Our Christmas Tree configurator is now closed for this year.
However, we do have limited stock and delivery dates still available!
Please email your requirements to christmas.trees@planteriagroup.com and we will check availability for you!
Now covering the whole of the UK, our comprehensive office Christmas tree service is designed to bring festive cheer to any workspace.
With something suitable for any space from smaller commercial Christmas trees, right through to a grand show-stopping centrepiece, both our live and artificial trees are available fully decorated. Choose from a range of colour schemes or go for a bespoke style, even matching your corporate colours. And if you prefer to add your own decorations, we can also supply the corporate Christmas trees undecorated or with lights only.
Additional extras include presents under the tree and artificial garlands and wreaths, created in our standard tree colour choices.
Select your size in either live Nordmann fir, artificial or contemporary cones.
Confirm your delivery and collection dates and let us do the rest. Easy as (mince) pie!
Christmas – exactly when, where and how you want it. Start by browsing through our fantastically festive gallery and Christmas brochure for inspirational ideas, then get in touch to discuss your requirements with our team.
With a professional decoration service on offer, either choose from one of our wide range of designs, or talk to us about a bespoke colour scheme.
Once you've decided, we take care of the rest; delivering and installing your choice of tree, decorations, garlands and wreaths. Delivery and collection is scheduled geographically and will be finalised nearer Christmas, however, we aim to deliver on a week chosen by you.
We are always on the lookout for talented florists and plant technicians with great attitude so get in touch if you think you have something to offer! Email us at enquiries@planteriagroup.com or call us on 0345 505 3333. Alternatively click below to fill in a contact form and request a brochure or call back.


The wall holder set is suitable for scratching posts that don't rest on the floor.
The Z11A is very stable and carries scratching posts with lengths of up to 2000 mm.
The Z1L will keep the post both in its vertical position and from shaking.
If you only wish to attach a single platform (without trunk), please select the single Z11A in the 'options' field.
Please check if your wall is strong enough and supports also heavy parts.


The domestic cat is a typical feline pet without a pedigree. They may also be called house cats and the British use the term moggies. They are all Felis silvestris catus. A lack of papers to show they are purebred no way detracts from them being beautiful, noble, and loving companion animals.
Domestic cats can be large, small, fat, or thin, depending on their lineage, diet, and degree of care. In cat shows that allow them, domestic cats are usually in a class called "Household Pets" or "Domestic Cats."
A mixed breed cat is one that is a cross between cats of two different breeds or a purebred cat and a domestic cat. If your cat resembles a known cat breed you may call him a mix. However, without registration papers from a breeder, you won't be able to enter him in a cat show as a specific breed.
Coat and Color: Domestic cats are often broken out into groups of shorthaired (DSH), longhaired (DLH), and medium length hair (DMH). Colors include black, white, gray, and red (orange). Color patterns include tabby, calico, tortoiseshell, and tuxedo.
Life Expectancy: 14 to 20 years for indoors cats; 3 to 10 years for outdoors cats; 4 to 5 years in the wild.
Domestic cats are rich in history. Cats are believed to have been domesticated in the Middle East at about the time humans developed agriculture. A 9,000-year-old grave on Cyprus revealed a cat buried with a human, presumably due to being a companion animal. Cats served to keep rodents away from stored grain. Cats were believed to be sacred by the Egyptians and cat mummies are well-known. Cats were part of life in the city and the country, always fulfilling the role of rodent hunters.
Domestic cats spread throughout Europe, Asia, Africa, and the Middle East, but were not known in the Americas or Australia until brought there by European explorers. Cats were part of sailing life (again, to control rodents on board) and this is how they were introduced to the New World.
Domestic cats can revert to being feral cats and adapt to a wide variety of environments, from the desert to forests to wetlands to city streets. Some of these alley cats end up in animal shelters and the foster homes of cat rescues.
The number of pet cats exceeds that of dogs, with estimates by the American Veterinary Medical Association of over 74 million pet cats in the U.S., with cat companions in over 30 percent of households nationwide. The feral cat population, by comparison, is somewhere between 25 to 60 million.
Cats are usually self-cleaning and fastidious by nature. Brushing your cat will help reduce matting and may help prevent hairballs. Trim your cat's nails every two to three weeks and provide a scratching post. If your cat will let you, brush your cat's teeth regularly. Cats will usually need dental cleanings by the veterinarian.
Indoor-only cats have the longest lifespans. It is difficult to keep an outdoor cat from roaming as most are good at climbing any fence. When outdoors, cats face the risks of being exposed to infections from other animals, getting into fights, being attacked by predators, or being run over by vehicles. Outdoor cats also have a large impact on birds and other wildlife.
Your indoor cat needs plenty of chances to play and chase toys. You should spend time each day in active play with your cat. Some cats can be trained to walk on a leash. Cats like lots of sleep and cat naps, so provide a comfortable bed and other places around your living area where your cat can lounge and retreat.
Cats have a wide variety of personalities, from standoffish to clingy. Early socialization with a variety of people can help a cat be less timid around newcomers. Cats often do well with other cats and cat-friendly dogs, especially if raised together. However, domestic cats still have predatory instincts for rodents, birds, and fish, whether or not they are pets. It's best to keep those animals safely away from your cat.
Spay or neuter your pet by age 5 months if you don't intend to breed your cat. Be sure to stay up-to-date on veterinary visits and vaccinations to prevent common and serious problems.
Cats are naturally carnivores and require taurine in their diet. A wet food diet is often considered best, but you can leave out dry food for your cat to snack on as well. Discuss your cat's needs with your veterinarian, especially if your cat has diabetes, is obese, or is older. It is good to monitor your cat's weight and take steps to prevent excess weight gain, which can shorten your pet's lifespan. Provide fresh, clean water for your cat at all times.
Before you decide to adopt a domestic cat, be sure to talk to other cat owners, reputable breeders, and rescue organizations. There are many loving domestic cats of every shape, size, coat, and pattern awaiting their forever homes at shelters.
There are many cat breeds out there. With a little research, you can find the right one to bring home.


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