This review of Teach Your Child to Read with Movement, Fun & Games - A Games-in-a-Book Reading Programme was written by Chantal Valente BSc. OT Wits and appeared in the 70th Anniversary Special Edition of the South African Journal of Occupational Therapy.
i) The aim of the book is to help to give parents and non-professionals direction and support to help their children learn to read. The book evolved over 20+ years of working with children with learning difficulties and seeing how the movement being used for gross motor and sensory processes was having a positive impact on the children's ability to focus attention and even to make the visual-auditory links between written letters and their phonemes.
ii) The introduction explains and defines concepts/phrases in a concise and user-friendly manner, which is good for parents reading the book. There are explanations of 'bilateral integration','vestibular processing'; 'memory' and 'being alert for reading'.
This is followed by Games and Activities (the bulk of the book which is divided into Playing with the sounds in words; Rhyme and Syllables; Playing to learn the alphabet; Playing with letters of words; Early Reading Games).
The last section consists of Rhymes and Worksheets e.g. Nursery rhymes and Flash word game; sight words).
The activities are presented in a very logical and "developmentally" appropriate way (in terms of reading, and spelling development).
Lovely ideas to build up a child's phonetic awareness and how various letters making up a word, fit together.
Colours are used for grading the activities. Good use of colours in the last section (the templates) in order to make the child aware of different sounds making up the word.
The activities are quite fun and appropriate for Foundation phase, and at the same time, incorporate literacy skills – children will "buy in" to these activities.
It is a relatively easy book to navigate and is quite user-friendly. It is not too simple and teachers and even therapists can get good ideas of games to use to enhance reading skills. The activities could also be presented in groups or in the classroom or in therapy. Each game starts with information about how the game can be used to stimulate for example memory, followed by the headings: "Where to play": "Equipment"; "Layout"; "How to play"; and "Tasks".
The rhymes used are traditional English nursery rhymes, but the games are suitable for all children having to learn to read and spell in English. Although stated that the book was written primarily for Grade R and Grade 1, the activities were tried out on older children, and worked quite successfully and were not too childish for Grade 3 and even Grade 4 children with learning difficulties.
It seems a shame to cut out the worksheets from the back of the book because they make up 100 pages of the book, but the binding of the book when folding the book open as though to scan the pages, seemed to loosen and it looked as though the pages would soon come away from the spine. I felt that the graphics could be better and not quite so immature . . . but perhaps this is the trade off needed to keep the book's price quite low. The fonts used in the worksheets and letter sheets are not all the same and it would perhaps have been better to use a font where the "t" has a curl at the base and doesn't end in a straight line e.g "t" vs "t".
Reviewer: Chantal Valente BSc OT Wits. Occupational therapist in private school practice and at Hamlet school for intellectually impaired.
Apart from running my own occupational therapy private practice, Sensory Kidzone, and various continuing professional development courses for occupational therapists, I organise and manage a monthly study group of occupational therapists who work with children. Sharon has been part of this group for many years, sharing her ideas and experience in helping children with delays in learning to read; particularly children who experience difficulty with sensory- motor skills, and inattention.
I am so grateful that Sharon has put all her valuable time, knowledge and experience into developing these holistic ideas into a cohesive programme that is easy and practical to implement. Teach Your Child To Read With Movement, Fun & Games is user friendly for parents because of it's clear, simple layout, it is easy to see exactly what you need for each game, what teaching the game instils and the use of nursery rhymes and games familiar to most parents. It is also attractive and welcoming to children with its appealing pictures, colourful, bright pages and worksheets.
foundations of reading, Sharon has managed to bridge the gap between the developmental foundations needed for reading and the academic learning which follows.
the importance of movement and play to efficiently develop reading. By integrating the building blocks that are vital for reading such as vestibular processing, bilateral integration and memory, Sharon has managed to combine therapeutic knowledge and strategies into simple games which parents can use to teach reading in a fun and playful way; thus removing the stress and negative feelings many children feel towards learning to read.
as simple games. Teach Your Child To Read With Movement, Fun& Games is a must have book for parents and educators who seek to develop children's reading skills in order to ensure a happy and confident reader. I am proud to know Sharon as a friend and colleague who has a love for children.


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NewSimulationShoes
Gisele Bündchen Says She Split from Leonardo DiCaprio Because She Was "No Longer Numbing" Herself
NewSimulationShoes, September 3, 2019
Gisele Bündchen is opening up about one of her most famous relationships.
The former supermodel says she made the difficult decision to split from ex Leonardo DiCaprio after she realized she needed a change in lifestyle.
"No longer numbing myself with smoking, drinking and too much work, I was becoming more and more aware of things that I'd chosen not to look at," Bündchen recalls in PORTER's Spring issue cover story. "Was I alone in wanting to do some serious soul-searching while he stayed the same? In the end, unfortunately, the answer was yes."
Bündchen, 38, and DiCaprio, 44, dated for 5 years from 2000 to 2005 and were inseparable. She was even his date to the 2005 Oscars where he was nominated for The Aviator — the only time he's brought a girlfriend as his date to the ceremony. She's now married to New England Patriots star quarterback Tom Brady.
The Brazilian model began dating Brady, 41, in late 2006 after her breakup from DiCaprio, and the two married in early 2009. They welcomed son Benjamin, 9, later that year and daughter Vivian Lake, 6, in 2010. They also coparent Brady's 11-year-old son Jack from his previous relationship with Bridget Moynahan.
And while Bündchen is the one known for her glamorous turns on the runway, the former model says it's her husband who values clothes more in their relationship.
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"I'm a jeans and T-shirt kinda girl. If you see me once a year at the Met [Gala] dressed up, it's because I have to wear a dress, otherwise I'd show up like this," she admits. "It's so funny. Tom actually loves clothes more than I do. Sometimes I'm like, 'What is all this clothing that is showing up at my house?' He just loves it. The only time he asks me advice about clothes is when we go to the Met Ball, and he wants to coordinate with what I'm wearing."
To see the full cover story and interviews, buy the latest issue of PORTER, on sale February 8, available in both print and digital editions, or visit PORTER.com.
This article originally appeared on People. For more stories like this, visit people.com.
September 3, 2019 NewSimulationShoes News
Karine Ferri « touchée »: ses premiers mots depuis l'accouchement
Vidéo – Jason Bourne est de retour
Mathieu Valbuena: une nouvelle affaire embarrassante
Meredith Grey va-t-elle retrouver l'amour?
Ronan Farrow: "Woody Allen forçait ma soeur à lui sucer le pouce"
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More TCC scams probed
Chito Lozada @tribunephl_cloz
Anomaly goes back to 1998 — source
The government is expected to unearth more anomalies in the issuance of tax credit certificates (TCC) going back to 1998, a day after the Department of Finance (DoF) said it will file charges against public officials and private individuals involved in issuance of P11 billion worth of certificates from 2008 to 2014.
A Daily Tribune source said investigations now being undertaken on the anomaly will also be based on a Commission on Audit (CoA) report. That also triggered the order of Finance Secretary Carlos Dominguez III for a high-level DoF task force to recover government losses through the TCC issuances by the One-Stop-Shop Inter-Agency and Duty Drawback Center (OSS).
The high-level task force is composed of Finance Undersecretaries Antonette Tionko, who heads the DoF's Revenue Operations Group; Bayani Agabin, who heads the Legal Affairs Group and Gil Beltran, who heads the Policy Development and Management Services Group.
The source said under probe are the same companies which were identified in the CoA report responsible for the erroneous issuance of 3,231 TCC by the OSS from 2008 to 2014.
Some P8.85 billion in tax credits were overstated and supported by spurious documents, and another P2.34 billion in TCCs were granted to claimants whose fiscal incentives had already expired, the CoA audit found.
BoI to hunt TCC users
A copy of the CoA report, Dominguez said, has been turned over to the Board of Investments (BoI) "for appropriate action against the accredited enterprises."
The BoI issued the TCC as an investments break for new companies.
Administrative Order 266 issued on February 7, 1992 created the OSS to speed up the processing of tax credit and duty drawback claims of exporters.
The TCC anomaly was first discovered by the DoF in July 1998 that resulted in a 25 February 1999 order of then Ombudsman Aniano Desierto for a six-month preventive suspension of 17 DoF officials allegedly involved in the tax scam including former Finance Deputy Executive Director Uldarico Andutan, former Acting Deputy Executive Director Raul de Vera and former Undersecretary Antonio Belicena.
All certificates canceled
The source said the DoF Task Force will seek the cancellation of all TCC still in circulation and the coordination with the Bureau of Internal Revenue and the Bureau of Customs in the assessing of taxpayers who used TCC against tax liabilities.
Investigation and administrative sanctions against OSS personnel are also ongoing, the source said.
Scam starts 1998
The DoF found in 1998 that 11 companies of the Chingkoe Group owned and controlled by businessman Faustino Chingkoe and his wife, Gloria, obtained 533 TCC from the OSS worth P2.5 billion.
It was then found that the Chingkoe companies reported sales of only P349.72 million and TCC were issued even during years when the Chingkoe Group companies did not report any sales.
In 2001, the Sandiganbayan's Fourth Division dismissed the 62 cases filed against former DoF officials in connection with the scam after the Ombudsman's failure to submit results of the reinvestigation of the cases.
In 2001, the Ombudsman filed a motion for reconsideration asking the Sandiganbayan to reverse its "untimely and hasty dismissal" of the 62 graft cases.
In 2002, the Sandiganbayan reversed its earlier ruling and revived the 62 cases. On the same year, the Ombudsman filed charges in the Sandiganbayan but downgraded the recommended charges of plunder to violation of the anti-graft law due to insufficiency of evidence.
In 2002, Faustino, one of the principal suspects, was arrested at the Quezon City Hall compound by NBI agents, nine months after he reportedly fled the country.
In July, 2006, however, the Manila RTC dismisses the civil charges filed by the BOC against the Chingkoe couple after the BOC lawyers failed to attend hearings on the pretrial of the case.
Court reversals
In March, 2011. the Sandiganbayan first division dismissed the plunder case filed against former DOF officials in connection with the tax credit scam involving executives of a textile firm, Filstar Textile Industrial Corp., saying that the charge sheet filed by the Ombudsman failed to show that the officials had pocketed ill-gotten wealth.
The Sandiganbayan ruled that there is no probable cause for plunder and dismisses the charges against Belicena, Andutan, Malonzo, the Chingkoe couple, Bautista and Filstar corporate secretary Grace Chingkoe.
The Supreme Court in a ruling in 2013 affirmed the Manila regional trial court's dismissal of civil charges against the Chingkoe couple and faulted the Bureau of Customs and the Office of the Solicitor General for their lawyers' nonappearance at six hearings on the pretrial of the Chingkoe couple.


Besides Iflix, its ambitious video-on-demand play, Patrick Grove's Catcha Group currently is involved in three other online ventures. Back in November 2015, it scored its biggest success with the sale of its real estate group to a News Corp company. A few months later, however, Catcha was unable to escape the curse of the Groupon clones as its chain of listed e-commerce sites collapsed.
Rev Asia: Catcha Group owns 57% of the Bursa Malaysia-listed firm, the result of a $20 million merger of Catcha Media and Says.com in 2013. It runs a social media advertising unit and five online publications, including aggregator Business Insider Malaysia. Ad revenue from magazines published by Catcha Media subsidized online startups for a decade but, as of this year, Rev Asia is out of the print magazine business altogether.
iCar Asia: An operator of online auto classifieds and related content sites, iCar Asia was founded in 2011 and listed on the Australia Stock Exchange (ASX) in 2012. It since acquired sister sites in Indonesia and Thailand. It racked up losses of US$9 million in 2016, but listings grew 18% year on year.
Frontier Digital Ventures: An investor in online classifieds startups in emerging markets of Asia, Africa and Latin America, Frontier Digital Ventures aims for eventual acquisition. So far it has invested in 18 countries including Myanmar, Pakistan and Sri Lanka. Founded in 2014, it listed on ASX in August 2016.
iProperty: A 2007 stake in a Malaysian real estate classifieds website led to an ASX listing the same year and subsequent acquisitions of sites elsewhere in Asia. Australia's REA Group, majority owned by News Corp, acquired a 17% share in 2014, followed by a total buyout for US$414 million in November 2015. IProperty today has active sites in Hong Kong/Macau, Indonesia and Thailand.
iBuy/Ensogo: The final formation as e-commerce chain Ensogo had roots in the heyday of Groupon clones when Catcha co-founded a Malaysia deals site in 2011. After a December 2013 IPO in Australia, iBuy acquired sites in Malaysia, Singapore and Hong Kong. It then bought LivingSocial's final three outlets--Ensogo sites in Thailand, Philippines and Indonesia--for $18.5 million in April 2014. Losses of US$54 million in first half of 2016 led to shutdown on June 30 last year.


Description: 'Gembrook Waratah'PBR is a large shrub, which produces an abundance of large red blooms in Spring.
The flowers of Gembrook Waratah are popular in floral arrangements, due to their straight long stems and uniformity of their flower heads.
Gembrook Waratah is protected by Plant Breeder's Rights.
This waratah should be planted in a well drained soil.
Gembrook Waratah will require frequent watering in the first summer of planting.


Projects operate in a changing and evolving environment. As the future unfolds, be confident you can handle uncertainty and are ready to make decisions quickly. Use Predict! Risk Analyser to test the resilience of your schedule and budget, pinpoint key risk areas impacting project completion and demonstrate the benefit of mitigation actions.
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Predict! Risk Analyser adds extra discipline to performance measurement and project control. It provides reporting that shows you where to focus resources, how to justify expenditure on mitigation actions, and brings managers the confidence that project success – timely and within budget – is in hand.
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On the Caxton Awards Weekend just past, I was introduced as a speaker with this terrific video developed by Ryan Fitzgerald and Annie Egan (Who picked up 3 Caxton Awards on the weekend), a creative team from GPY&R Melbourne.
I reflected on this at the introduction to my speech that while TrinityP3 is almost 11 years old we are known for the things we do that are most relevant to our audience of agencies, clients and the trade publications.
Creative and production people know us as Production Auditors, though we do not do auditing, we do assess production costs on behalf of our clients.
Many marketers know us for our agency remuneration and compensation benchmarking.
The trade media and the agency management know us for running pitches.
And the truth is we do all this and more.


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Home / Artificial intelligence technologies / Connected Cars Bring New Business Models and New Disruption
Connected Cars Bring New Business Models and New Disruption
By Crystal L. Valentine, PhD | October 19, 2017 with 0 Comments
The connected car industry, including self-driving cars, is precipitating an important paradigm shift that will present new opportunities.
In Silicon Valley, it's sometimes easy to miss the forest for the trees. Autonomous driving is shaping up to be the next "killer app," drawing a lot of attention from investors, techies and the media.
I'm frequently asked about the computing technologies and algorithms that go into supporting autonomous driving cars. People want to know about data rates, processing power, the deep learning aspects, neural networks and so forth. In Silicon Valley, it seems people love technology for its own sake. But the push toward autonomous driving cars is not just a story about computation and deep learning.
The connected car industry, including autonomous driving cars, is quietly precipitating important paradigm shifts that will present new opportunities and therefore bear examination. In the end, the data platform providers are poised to become central players in enabling all stakeholders to generate value.
New business models and ecosystem players
The car has evolved over the past two decides with an increasing number of features and services and has also introduced new business models and stakeholders. The connected car era began in earnest in 1996 when GPS was opened to civilian use.
[ Related: Security and Connected Cars: Threat Not Limited to Autonomous Vehicles ]
Soon after, GM announced Onstar which brought new hardware and new players (e.g. Telematics Service Providers) into the equation. Thus, began the massive shifts we are seeing play out in the market today – changing business models, including that of the automotive manufacturers (OEMs) themselves.
Traditionally, OEMs operated as B2B companies. Once the cars passed to the dealerships, the OEM's job was done. Today, the OEMs are seeing themselves as service providers with recurring revenue and insights into the entire customer journey. OEMs can leverage touch points across the entire customer journey to gain insights to help improve retention, a huge opportunity as the car industry suffers from low (less than 50 percent) brand loyalty.
Just as the smartphone was in the 2000s, today the car is becoming the new consumer platform. As features and services are introduced into the car, both OEMs and third-parties are increasing their respective footprints within this new platform and are using the opportunity to engage directly with the customer.
With increased visibility to the end-user, OEMs are now embracing a B2C mentality with an emphasis on the customer experience and with Tesla foregoing the traditional dealership model altogether and selling direct to consumers.
In addition, a remarkable number of new players, including service providers and innovative tier one and tier two suppliers are entering the ecosystem to provide new features to the driver. In the end, the value to OEMs and tier one/two suppliers comes not just from adding more computational systems and features to the car, but from the growing amounts of generated data that they can leverage to gain insights into the end user.
Compute and data out of the cloud and to the edge
For each new connected car feature or use case, the capability to aggregate and analyze car data is the bottleneck. Consider autonomous driving as an extreme example. The averagely driven autonomous car will generate about 4 TB of data per day.
[ Related: Innovation Driving Connected Cars Gears Up at Mcity ]
Even with the advent of 5G mobile networks, the sheer data volume generated by cars will preclude the ability to stream that data to the cloud or any centralized data center. Instead, much of the data will be processed and analyzed onboard the car itself with only relevant summary information being passed on to a centralized fleet management application in a data center for further analysis.
The challenge with then is to process data onboard the vehicle to make timely driving decisions while also streaming some data to a centralized analytics platform that has the advantage of aggregating data across many cars in order to gain a holistic view of how the fleet is performing. In the current phase of connectivity, the data platform providers are key to driving value for all stakeholders.
Connected cars are, therefore, accelerating a major industry trend that we see in the era of IoT – namely, the movement of compute from the data center to the edge. For example, industry estimates from IDC, Gartner and Wikibon put the growth of public cloud computing between 16 percent-19 percent compound annual growth rate (CAGR).
By comparison, the computational power onboard a car today is approximately 10 million times the level of computational power in a typical car in 1990. That's an 82 percent CAGR. The growth of computational power onboard cars, then, is significantly faster than Moore's Law which describes the overall growth in computational power from advancements in digital electronics as attaining about a 41 percent CAGR.
Connected cars are an example of this growth of edge computing, but they are just the tip of the iceberg. Consider, for example, Pratt & Whitney's new Geared Turbofan Engine features an ensemble of 5,000 sensors and generates as much as 36 TB of data per engine-hour.
[Related: Why autonomous motorcycles are destined for the road ]
With an order book of 8,000 of these engines, the aggregate of the Pratt & Whitney engines will process about 2.5 zettabytes of data per year. By comparison, by the end of 2014, Facebook was generating about 219 PB of data per year. The amount of edge computation represented by connected cars and other connected systems, like engines, will soon eclipse the size of the consumer internet.
While the past decade can rightly be termed the "cloud era" with the rise of Amazon Web Services and other public cloud infrastructures figuring prominently into modern enterprise architectures, the next decade will see the growth of computation and data in the data center – both public cloud and private data centers – dwarfed in comparison to the growth of computation and data generated by and processed on edge devices, including cars.
Connected cars become the platform
In summary, as the car becomes the next consumer platform, the automotive industry will continue to grow to encompass more stakeholders and new business models. The truly disruptive applications will require the aggregation and analysis of connected car data at scale.
And as computation and data processing becomes ubiquitous with an increasing proportion taking place on the car itself, the primary challenge will be to manage the massive volume and velocity of data being generated on the car, to facilitate real-time processing of that data, and to connect the car seamlessly with the data center for offline analysis on the collection of data from entire fleets of vehicles.
It's no surprise then that, as with smartphones before, data management platforms are placed squarely at the center of value creation in the connected car ecosystem.
About Crystal L. Valentine, PhD
Crystal Valentine, PhD, is vice president of Technology Strategy at MapR Technologies. She has nearly two decades' experience in big data research and practice. A former professor of computer science at Amherst College, she is the author of several academic publications in the areas of big data, algorithms, and high-performance computing, and she holds a patent for Extreme Virtual Memory. She has consulted extensively with Fortune 500 companies to design and implement high-throughput, mission-critical applications and with equity investors as a technical expert on competing technologies and market trends.
View all posts by Crystal L. Valentine, PhD →
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Ruby logo print transfer sheets add a geometric modern style to your Ruby creations. The high quality PE transfer sheets printed with food-safe design offer an easy way to create a bold visual effect with a high gloss finish on Ruby Chocolate. They are designed to fit on Chocolate World magnet moulds (transfer sheet dimensions: L: 123 X W: 263mm).


The State Gallery of Fine Arts (SGFA) – Hyderabad had organised a five-day 'Art Mela' from June 26th 30th 2011. This event was conducted for the first time by SGFA and has attracted around 100 artists who have submitted their works in various media ranging from figurative, floral, abstracts, native, decorative and a lot more.
Apart from the art mela, there were other events in the gallery space. Whilst the art mela posters promised a host of events un-related to art such as tattoo shacks and chat stalls…. thankfully, there were none. We all were relieved that it was only about art.
The inauguration was a solemn affair. Like always, this ceremony gives everyone a wonderful opportunity to interact with some artists and therefore there is a face to place, whenever we see a nice artwork.
There were around 6000 paintings on display, certainly a lot to look and choose from. For a serious art browser it would take 2-3 days to go through the piles of mounted and unframed artworks on canvas, paper, wood and other media. Each artists was allotted a display table (with a table number) wherein their art works were stacked. The artist name was not displayed. And we wonder why!
The event went smooth. People frequently dropped in to check out the artworks.
Since most of the works were un-framed, on paper, etc., There was a great danger of artworks getting spoilt. The artworks were simply kept on the display tables, ready to be handled by anyone and everyone. Many artists were not satisfied with the display arrangements and tried to display their works against the walls.
But come rain or shine, the show must go on. Beyond this initial hiccups and disappointments, there were some really great works amongst the heaps. Some of the works were stunning.
Understandably, since this was an art mela, many chose to display their old works… as most of their paintings were a clear departure from their style which is now more pronounced.
Some native artworks in brightest of colors.
Some abstracts of mine, unframed.
Some striking floral abstracts which I had dug out from under a heap. Who is this artist?
One day in the life of the SGFA art mela.
This first-of-its-kind show ended well. Some artists sold their artworks. Some artists made new friends. And some artists learnt a bit more about the art of art events.
If you had been to this show as a participant or to see the artworks, do share your experience with me.
A child that no one holds.


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Red Molly 4/26/19
"A blend of serious harmonizing chops and slick pop savvy." -Time Out NY
"[Red Molly has] cut a niche as sunnyside Americana … immaculate vocal harmonies." -The Guardian
Red Molly combines the forces of three songwriters with unique character and style, creating a show that is larger than the sum of its parts. Known for their 3-part harmony, their songs and arrangements lay bare a love of vocal blend. The band weaves together threads of American music—from country & blues to folk & bluegrass. Their innovative instrumentation is suited for roots-rock and heartful ballads alike, and the alchemy of their personalities onstage draws even back row listeners into a sense of intimacy. Red Molly is simply a joy to experience.
Singing spine-tingling high notes, Abbie Gardner is a dobro player and improviser from a musical family. A consummate performer, her songs and performance have the punch of rhythm and blues. Playing guitar and tambourine, Laurie MacAllister draws inspiration from classic folk and singer-songwriters. Her voice stretches octaves, warm and romantic one moment, playful and subversive the next. Molly Venter has a smoky voice that is unforgettable, and a moody approach to song-smithing. Quirky and fashion-forward, she moves in step to the music while playing guitar and tambourine.
Forming in 2004, Red Molly has inspired countless female trios and has since reinvented themselves as a high-octane five-piece band in 2017. They remain a dominant force on the Americana/Folk scene due in part to their laughter and spontaneity onstage. Upright bassist Craig Akin and percussionist and electric guitarist Eben Pariser fill out the sound, giving the show a broad range of musical options—from complex and hard-hitting to sparse and delicate.
About the opener, Marc Douglas Berardo:
Marc Douglas Berardo is the kind of hard working, fast moving, adventure seeking, keen observer who lives for the story and the song. In what amounts to song length works of fiction, Berardo's sharply drawn, award winning song portraits cast a net on unusual and beguiling characters and places. With a painter's eye for detail, and music firmly rooted in the great American sound, Berardo sings about circus retirees, expatriates in Florida rum bars, union iron workers, old poets, aimless New York City debutantes, near death car crashes, hard nosed fishermen and of course, the changes that experience brings to everyone. He does this "simply and well" with what Rambles Cultural Magazine calls: "careful images and great tunes."
"I try to write about people and situations that interest and entertain me. Subjects and places that I feel a connection with and that are unique in a quiet way. Real people and places caught in the moment, almost like a documentary film or a novel. At the same time, I need the music itself to take me somewhere…to make me feel something. The words have to sing and the music has to work. The kind of song that does those things is my idea of a good time."


Agoo-Damortis National Seashore Park is located in La Union, Philippines.
Declared as a National Park, the beach stretching from Sta. Rita, Agoo up to Damortis, Rosario is proposed for development as a tourist destination in La Union.


In 1979, Marion and Barry Roberts moved to Port Hope from Hamilton and started Roberts Electric from their home. Barry had learned his trade of Electrician - Construction and Maintenance 309A from apprenticing with his father, a Master Electrician who had established a successful and reputable electrical contracting business in Hamilton in 1954.
Although not required by local codes at the time, Barry attained Master Electrician status by successfully challenging the difficult examination, attaining a perfect score. Membership in the local Pine Ridge Chapter of the Ontario Electrical League was also obtained. To this day the company continues to be a proud member of this organization as it promotes electrical safety, provides ongoing education to local tradespeople, and supports community charities and events.
As the business grew, the company moved to larger facilities on Theatre Road and then in 2006 to its current location at 8358 Dale Road, just north of Cobourg.
As technology has advanced over the past 33 years, adapting to the changing needs of consumers has always been a priority. To this end we have established two sister companies to better meet these needs. Alliance Security Systems of Northumberland Ltd. was established in 1990, and today is Northumberland's largest full service alarms systems dealer, protecting hundreds of families and businesses with 24 hour monitoring services. And Compton's Telecommunication Services was acquired in 2007, specializing in residential and commercial telephone systems as well as data networking.
All three businesses operate in harmony from our single office and shop facility. By merging three distinct disciplines under one umbrella, we are able to offer our clients a complete range of specialized services.


Enterprise architecture management (EAM) is a concept that focuses on designing and developing IT infrastructure and systems that controls and drives the business objectives. Masters in Enterprise architecture management guides students about design and operation of IT operations and systems that are used for maintaining organization's vision and strategy. Masters in enterprise architecture program will develop ones strategic skills along with learning about business streamline processes, designing and broadening IT architecture solutions. The course focuses on guiding their students with stakeholder management and present modules that helps them stay up-to-date with their field.
MSc enterprise architecture management course is a distance learning program affiliated from Germany's acclaimed university. Subjects are taught through e-learning setup, where students are provided with in-depth information of the topics. The course focuses on preparing students to design and deploy IT infrastructure and guiding them on engagement skills.
Learning about the above mentioned prospects in a period of 18-21 months an individual can get an insight about enterprise architecture management leading to a career in the IT operations and business streamline career.
With MSc Enterprise architecture management students have learnt about business streamlining and stake holder techniques along with deployment of IT operations and infrastructure, individuals can explore various career opportunities in this field, it is a career-forward program which will help students grow, explore and perform in the IT, management and operations field.


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£250 Race
£1k Race
Tag: man united
Transfer news: Manchester United to pay £15million for Thomas Vermaelen
By CB on August 7, 2014in CB News
Manchester United look to beat Barcelona in the chase to sign Arsenal defender Thomas Vermaelen.
The Arsenal leader may come as a fairly cheap replacement for Nemanja Vidic, who recently left to Inter Milan after a eight year stint at Old Trafford. Barcelona looked to have taken pole position in the race to sign the 28-year-old Belgium international on Tuesday when they made a bid of £10million for the player.
However, Sky sources have revealed that United are Vermaelen's preferred destination and the Old Trafford club will have no problem beating Barca's offer.
Vermaelen's future at Arsenal has been the subject of speculation all summer, with the centre-back entering the final year of his contract at the Emirates.
Manager Louis van Gaal is anxious for more signings following the club's return from their pre-season tour in America and wants to close deals for Vermaelen and Ajax wing-back Daley Blind before his Premier League bow against Swansea City on August 16.
Executive vice-chairman Ed Woodward accepts he will have to pay a premium price for Vermaelen however because Arsenal would prefer to see him go to La Liga than play for one of their Premier League rivals.
He is no longer first choice for the Gunners, with boss Arsene Wenger preferring the centre-back pairing of Per Mertesacker and Laurent Koscielny last season.
Wenger also revealed last week he could not be certain Vermaelen would stay, as he could not guarantee the defender first-team football.
Vermaelen started just seven Premier League games last term and it seems the player is keen to move on, with United looking an ideal destination for him as new manager Louis van Gaal seeks to increase his defensive options.
Louis Van Gaal – Inherited a 'Broken Squad' (Sourced from ESPN)
By CB on July 29, 2014in CB News
Manchester United manager Louis van Gaal claims he has inherited an unbalanced and "broken" squad. Apparently he will attempt to repair the squad by removing the likes of Fellaini and Anderson.
Van Gaal denied that succeeding David Moyes would be easier than following Sir Alex Ferguson, who won 13 titles in 26 years at Old Trafford.
In the Dutchman's eyes, Ferguson left Moyes with a team of winners. He says he is inheriting a "broken" squad awash with attacking midfielders.
"No," Van Gaal said when asked whether following Ferguson would have been harder. "I don't agree. I had to follow Bobby Robson at Barcelona the year after he won three titles and there wasn't a problem (Van Gaal won the league that year).
"When there is success you have a very good squad, and now I have to follow and the squad was broken I think.
"When you look at the squad, there is quality. There is [Wayne] Rooney, [Robin] van Persie, [Javier] Hernandez, [Danny] Welbeck, but you also see Juan Mata, Fellaini, and you see [Ander] Herrera. There are a lot of players that can play in the same position.
"It is not in balance. It's more difficult to succeed in a difficult situation than in a fantastic situation."
Van Gaal will look to address the imbalance in his squad by moving Fellaini on with reports suggesting, again, that he has made it clear to senior United figures that the £27.5-million signing by Moyes does not feature in his plans.
Napoli are said to be interested in the Belgium midfielder, who returned to training at United's Carrington training base on Monday, and United are reportedly prepare to take a hit on the price they paid for him, being ready to sell for around £13m. However, Napoli manager Rafael Benitez is thought to prefer a loan deal.
Van Gaal will also address the squad imbalance by trying to sign at least two players over the next three weeks – rumoured to be Thomas Vermaelen and Mats Hummels.
He has been monitoring the recovery of injured Roma midfielder Kevin Strootman, who is valued at £79m, while the club is also thought to be keeping tabs on Real Madrid winger Angel Di Maria.
Van Gaal insists he will not pay over the odds for any transfer targets though after spending more than £50 million on Herrera and Luke Shaw this summer. The manager has been told he can break transfer records
"I don't buy players for buying players – I buy players to improve my selection," Van Gaal said. "First I have to see what we need in all the positions from the system we shall play. At this moment, I don't know for sure if we will play this system [4-3-3].
"When we play 4-3-3 we will use more or less the same players. But I will need more specialists on the wings and more attacking players – then, we have to buy another type of player."
United fans can expect Van Gaal to use that particular system more often as it means he can accommodate Rooney, Van Persie and club-record signing Mata in the same team.
"That is one argument for why I choose this system – then, I can play them all. That's also important but we don't forget all the others. Hernandez can also play in the striker's position, Welbeck can also play in the striker's position and maybe Will Keane can play in that position," Van Gaal said.
"Rooney can play No.10 and No.9 and he said to me he can also play No.11 and No.7. But I like him more at No.9 or No.10."
Rooney impressed in the club's recent friendly victory against Roma and earned special praise from his manager. The England striker is desperate to claim the United captaincy and wants to star under Van Gaal. However, his manager insists he still needs more time to determine who will captain his side in the new season.
"For me the choice of the captain is always very important. He is the captain on the pitch and he can enlarge my influence but he needs to have the same philosophy and way of seeing life. It's not simple to choose so I need time to do that," Van Gaal said.
"It's dependable on personality. The captain doesn't have to be the most senior player. For me, it's more about the personality and mentality and the way he stands in life is very important."
Real Madrid star Di Maria wants to join LVG's Man Utd
According to The Daily Star on Sunday Real Madrid winger Angel Di Maria WANTS to join Manchester United.
Having recently purchasing James Rodriguez Man United know that Di Maria is up for grabs at Real Madrid's £45m asking price BUT Louis Van Gaal is unsure on whether to move for the Argentina star.
Paris St Germain are also on full alert but they are unhappy with Di Maria's supposed interest in moving to Manchester.
United won't quibble over Real's fee as Van Gaal has enough funds at his disposal to negotiate a straight cash deal. On the other hand Louis Van Gaal is currently reviewing his squad on the USA tour. Wilfried Zaha has yet to feature and Nani has not really stood out in the two games he's featured in. Ashley Young played well against L.A Galaxy notching up 2 goals and an assist, while Antonio Valencia looks certain to be in Van Gaal's plans.
Manchester United boss David Moyes in contention for manager of the month
By Chris, Clever Bets on January 9, 2014in CB News
Manchester United manager David Moyes is amongst the nominees for Barclays Premier League manager of the month for December.
It's not a joke. Moyes' men have endured a poor start to 2014 – but they secured four wins and a draw in December which has seen him shortlisted.
Also in contention is Chelsea boss Jose Mourinho, who had a win ratio of 71 per cent after claiming five wins from seven games, losing just once. Manchester City boss Manuel Pellegrini is also up for the honour after going unbeaten in the month, winning six of his seven games. The final name up for the award is Everton's Roberto Martinez, who lost just once in his six games – taking his side to four wins over the festive period. Whoever wins will be taking their first honour of the season, as the previous four winners – Brendan Rodgers, Arsene Wenger, Mauricio Pochettino and Alan Pardew – are not nominated.
Like with the manager award, the player of the month will also be a new contender as none of the previous four winners are up for nomination. Liverpool's Luis Suarez leads the contenders, but Manchester City stars Alvaro Negredo, Vincent Kompany and Yaya Toure are also in contention. England and Everton starlet Ross Barkley is nominated along with Arsenal's Theo Walcott, who has subsequently been ruled out for the season.
Follow Us On Twitter – @CleverBets
© 2013-2018 Clever Bets


text:
WATCH: Ashli Babbitt's Mother Receives Standing Ovation at Trump Rally in Phoenix
The mother of Ashli Babbitt drew a standing ovation at a "Rally to Protect Our Elections" in Phoenix, Arizona on Saturday night. The event was headlined by former President Donald Trump.
Rep. Paul Gosar introduced Babbitt's mother Michelle Witthoeft.
"She came all the way over here to tell you thank you," Gosar said. Watch the crowd's reaction:
The audience not only gave Witthoeft a rousing bout of applause, but they even broke out into a chant, "Ashli! Ashli! Ashli!"
Ashli Babbitt is a central figure in the January 6th riots. Her shooting death, issued by a Capitol Police officer that has not been formally recognized or charged, was the only provable "homicide" at the event.
The decision to shoot Ashli Babbitt has been chalked up as a "split second" decision; but one can see from the video that the man held aloft his gun for at least fifteen seconds before shooting. Police officers who stood behind Babbitt did nothing to prevent her from attempting to climb into the restricted area.
It is undeniable that Babbitt should not have proceeded to go into the area. However, this does not justify the shooting death, nor does it resolve questions about how the incident developed or concluded. The Biden Department of Justice has announced the officer will not be charged for the shooting.
The New York Times and other media outlets have branded Babbitt as a "Q Anon" supporter, as if to dispense with public curiosity or sympathy for the woman's death.
"Ashli wasn't a thug. She wasn't a rioter. Ashli was a peaceful person," said her cousin Justine Babbitt. "She did 14 years in the military. She was not there to destroy the Capitol building. She was there to be heard and be part of a movement. Ashli was a die-hard patriot. Not a Democrat, not a Republican. She was for the people. Ashli carried around the Constitution and the Bill of Rights in her pocketbook."
Ashli Babbitt's attorney Terry Roberts commented on the closed case.
"To date, the officer who shot Ashli has not been identified," Roberts said. "Neither the Capitol Police nor any other governmental authority has given an account of the facts surrounding the shooting. There has been no official explanation or justification for the use of lethal force in this matter."
"This lack of transparency impedes the public scrutiny which is necessary to hold government officials accountable in a free society," the statement added. "It also interferes with the ability of Ashli's family to obtain justice for their loss."
The family's lawyer closed the statement with a plea for justice and transparency.
"My law firm and I represent Ashli's husband and family members," Roberts said. "We will continue to investigate this matter. We intend to take appropriate legal action when our investigation has been completed."
House Sergeant At Arms 'Slips Up' & May Have Just Revealed Name of Ashli Babbitt's Shooter


text:
ACS:Law Now Using Dubious Legal Theories To Threaten Slyck.com
Viacom's Real Intent? To Pretend The DMCA Requires Filtering
Switzerland So Neutral It Won't Even Let In Violent Video Games
from the overdoing-it-a-bit dept
Mon, Mar 22nd 2010 5:59am — Mike Masnick
An anonymous reader sends in word that Switzerland appears to be following in the footsteps of Venezuela by getting close to banning all violent video games in the country (yes, even for adults). It's not quite there yet -- as the Swiss National Council has basically just given itself the right to put in place such a ban, but is still debating the actual extent of the ban. However, it appears that many expect all video games rated at a mature or adult level will likely be banned. I'm curious why none of the countries that ban such video games are also willing to ban R-rated movies as well.
Filed Under: switzerland, violent video games
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Social Networking Software (profile), 22 Mar 2010 @ 6:18am
Who gets to decide what is actually considered violent? If you listen to my grandmother play poppit you would assume she was playing an incrediably violent game. Is it the gore? The Killing? The Fights? In my opinion this is something that should be left up to the individual, the government should not have any part of it.
Michael, 22 Mar 2010 @ 6:53am
Re: Slippery Slope
But we are protecting the children! Since you don't agree with this ban, you must want to create violent offenders that harm children! What kind of person are you!
The people that come up with this are clearly not thinking as rationally as you are. It's really just amazing how many people seem to think this kind of thing is a good idea.
Marcus Carab (profile), 22 Mar 2010 @ 9:48am
Agreed. As a kid I always thought it was funny how Mortal Kombat stripped out the blood from the home console versions - as if that changed the fact that the game was about brutally beating/dismembering/impaling/beheading each other. And then you used the cheat code to turn blood back on, but you didn't even really notice or care, it was more for the satisfaction of knowing and using a cheat code.
Believe it or not, to this day I have never once shot a fireball or done a flying kick at anyone.
Adam (profile), 22 Mar 2010 @ 6:42am
To what end?
Ok, the Swiss want to ban violent video games. Why? What purpose do you hope to serve?
Any time you make something illegal that a large number of people want to do, you end up hurting. Not helping. See Prohibition.
PaulT (profile), 22 Mar 2010 @ 6:59am
Re: To what end?
Not to mention, how can you possibly ban them? Oh, you can stop authorised dealers from selling them, but Switzerland isn't a large country and it's bordered by 4 countries that haven't banned such games. Said borders do not have border controls - you can hop on a train to France, Germany, Austria or Italy, stock up on banned games and be back in a couple of hours. Even that's assuming that the Swiss don't simply download the games.
With this kind of issue, I always recall my childhood in the UK. The "video nasties" list was basically a shopping list of must-see titles, and I managed to buy pirated copies of nearly all of them - this being the 80s, where VHS was the only real option and I managed to get most of them sent by mail from Cyprus or Greece while under 16 years old! How in God's name can you expect to effectively ban a game with today's technology?
The only reason for this is a misguided "protect the children" stance, which will be ineffective since it's often parents who are buying the games for their kids in the first place. Nice black market you're creating there, Switzerland, I hope your police enjoy the pointless extra work you're shovelling their way...
Hulser (profile), 22 Mar 2010 @ 7:26am
Re: Re: To what end?
How in God's name can you expect to effectively ban a game with today's technology?
It's precisely because of today's technology that they will be able to ban video games. Sure, Switzerland's borders are porous, but with much of today's DRM requiring a connection (sometimes constant) to the game company servers, there will be pressure on the game companies to restrict access based on country of origin. DRM isn't just a tool for protecting "IP"; it can also be used for censorship. Sure, this restriction can be easily circumvented, but the point is that the ban will have a dramatic effect on the freedoms of the Swiss.
Re: Re: Re: To what end?
"with much of today's DRM requiring a connection (sometimes constant) to the game company servers"
*PC* games do. Most of the games being targeted will be on consoles which have no such DRM. Sure, you have to hack the console to play a pirated copy, but the Swiss authorities have just provided a great reason to do so.
Maybe such a tactic will be used in the next generation of consoles, but this is next to useless for the current gen.
Re: Re: Re: Re: To what end?
Oh, and I might as well add - even if such DRM did exist, do you really believe that the copies floating around the P2P networks would have said DRM intact? I somehow doubt it...
Re: Re: Re: Re: Re: To what end?
I acknowledged that the DRM could be circumvented. I hope you're not, but you seem to be implying that censorship is OK as long as it can be circumvented by the technically literate. The danger in this attitude, obviously, is that people don't fight back when they have the chance (when a new law is being proposed) and when they figure out how to lock down the DRM even tighter, it's already too late.
Re: Re: Re: Re: Re: Re: To what end?
Erm, I don't believe I've said a word supporting censorship. At least I hope not, because I sure as hell don't...
My point was that said censorship is pretty pointless. I was able to circumvent it quite easily while living on an island, under the age of 16 in an era when the only way to distribute material was on a brick-sized piece of plastic that had to pass through customs. You described ways in which technology could be used to try and enforce the bans, I merely pointed out that this would not only be ineffective but also create a thriving black market, on and offline.
Of course I support efforts to fight said censorship, and hopefully it will fizzle out like the whole "video nasties" thing (most of those movies are now available on DVD in the UK, uncut). Meanwhile, Swiss citizens should fight this every step of the way.
*PC* games do. Most of the games being targeted will be on consoles which have no such DRM.
I'm not a console gamer, but don't most big budget games require some kind of authentication to the central servers? Maybe even just to log into voice chat or to record your achievements? Maybe I'm defining DRM as little more loosely that you are, but I consider this as a form of DRM. Ostensibly, it's adding value to your gaming experience, but there's no denying that this kind of feature also gives quite a bit of control to the game company (or its publisher), the kind of control that can be used to censor a game.
PaulT (profile), 22 Mar 2010 @ 10:12am
I can see where you're coming from but no, they're not required to authenticate. You do need to access servers to play games online via official servers and to record achievements, but I think that a lot of gamers would be willing to give up perks if it means the difference between playing the game at all or not (I'm sure that unofficial servers can be set up for online play if needed - they exist for WoW so I assume they will exist for console games).
It's still DRM, but it's minimal and usually makes no difference to whether you can play the game once the console's hacked. Again, this may change in future generations but there's no way to stop a player using the current gen (and remember, DRM is typically removed from pirated copies of PC games, so it's useless there as well).
Hulser (profile), 22 Mar 2010 @ 11:27am
You do need to access servers to play games online via official servers and to record achievements, but I think that a lot of gamers would be willing to give up perks if it means the difference between playing the game at all or not
But you're making a distinction between official server and unofficial servers. So, let me qualify my original statement. Today's DRM implemented in many PC and console games requires a connection (sometimes constant) to the game company's official servers in order to play legally. This is what lead me to believe that you were implying that the censorship was OK because it could be circumvented. Or else why even bring up that it can be circumvented? What relevance does this have on the issue of whether it's ethical or just for Switzerland to censor computer games?
Deborah Hall, 22 Mar 2010 @ 11:23pm
I think the police will love this extra little job, compared to most countries, I don't think they have an awful lot to do.
And, of course it will make way for a rampant 'black ' Market - good for the economy, like the cannabis production...
bugmenot (profile), 2 Apr 2010 @ 8:35am
Doubt a rampant black market will evolve...
You have Germany to the north, France to the west, Italy to the south, and Austria and Liechtenstein about an hour a way... not hard to buy any game there legally and probably cheaper than it is in Switzerland anyway.
D., 26 Feb 2012 @ 12:03pm
And we will download them. At the time you wrote your comment, it was already decided that private copies - that is downloading something (video game, movie, song...) for your own enjoyment - were not illegal. Thus, nothing stops us from hopping on the pirate bay and just grab the titles.
Two years later, and the ban is still not in effect. There's some discussion going on, and for now minors do not have the right to buy games 18+ (PEGI classification).
Ima Fish (profile), 22 Mar 2010 @ 6:50am
I think this is a good thing for the video game industry. Now they can put stickers on their games: Banned In Europe!
I was listening to a horror podcast the other day, where one of the presenters was remembering the time he rented a copy of Faces Of Death. He was way too young to be doing so at the time, but he couldn't resist the "banned in 37 countries" on the cover :)
Planespotter (profile), 22 Mar 2010 @ 7:13am
The Swiss do make me chuckle... before long they'll be giving every man over 18 a gun to keep at home to defend his country from the hoards of cheese eating, cuckoo clock loving waiting at the border... oh they already do that!
errr... maybe they'll ban the building of minarets on Mosques... bugger!
Oh the Swiss... they just mad.
MBraedley (profile), 22 Mar 2010 @ 7:56am
Dammit, you beat me to it!
And made a joke while you were at it.
Anonymous Coward, 22 Mar 2010 @ 7:34am
WILL SOMEBODY PLEASE THINK OF THE CHILDREN...
that woun't be allowed to play awesome games!
NAMELESS.ONE, 22 Mar 2010 @ 7:48am
bambi and the 7 dwarfs
thats what you will be playing should this continue
DO YOU want your kids to be fruity lil faggits?
The reason why they won't ban R rated movies is because the movie industry lobbyists have more money than the game industry lobbyists.
Music Lover In GA, 22 Mar 2010 @ 7:52am
YES -- We must ban the kids...
That way I won't get pwned the minute I try to play a multiplayer game. Banning kids will make it fairer for 40 year olds like me....
Atkray (profile), 22 Mar 2010 @ 8:20am
Re: YES -- We must ban the kids...
.....and the heavens parted and I saw the light.
Rikuo (profile), 22 Mar 2010 @ 7:52am
the irony
Well, lets look at what's happening here.
The only argument I can see going for these kinds of bans is "protect the children" i.e. they see violence in a video game and think its okay to do it in real life. In video games, you for example pull a trigger and an enemy is dead.
What about kiddy cartoons like spongebob etc? Their violence is often much greater. There are explosions and such, and the characters are unharmed in the next scene. That can be interpreted as teaching kids that violence is okay, there are no consequences. Let's blow up that bully who's always picking on me! It's all right, he'll be magically unharmed in a few minutes.
mike allen (profile), 22 Mar 2010 @ 9:59am
how many Swiss
play second life? nuff said.
Txknight (profile), 23 Mar 2010 @ 6:03am
can we just deport the Swedish females? they can have the rest of the country
e zahne, 10 Feb 2011 @ 3:02pm
For kids or not for kids
I work in game design and I think the (flawed) logic here is that video game are for kids, and movies are for adults, thus violent movies are ok, but violent games are not.


text:
\section{Introduction}
\label{sec:intro}
In the context of general relativity wormholes act as tunnel-like structures  connecting two different
regions in spacetime. This phenomenon necessitates solving Einstein's equations in a reversed manner
to obtain solutions admitting wormholes. Studies on this topic can be divided into two classes: one
relating to the Euclidean wormholes \cite{Ruz:2013hfa,ArkaniHamed:2007js,Hawking:1987mz,Hawking:1988ae}
and the other concerned with the Lorentzian ones. Historically, the notion of wormhole physics may be
traced back to 1916 by Flamm \cite{Flamm}, soon after the discovery of the Schwarzschild solution.
Einstein and Rosen \cite{Einstein:1935tc} proposed a mathematical construction in order to eliminate
coordinate or curvature singularities, eventually introduced a bridge-like structure connecting two
identical sheets known as the \emph{Einstein-Rosen bridges}. This mathematical  representation of
physical space was not successful as a model for particles rather it emerged as the prototype wormhole
in gravitational physics. Subsequently, Wheeler \cite{WH,Fuller:1962zza} revived the subject in the
1950s where the Kruskal-Szekeres coordinates were employed to describe the geometry of the
Schwarzschild wormhole, although these wormholes were at the quantum scale. Wheeler coined the
term \emph{wormhole} and later his solutions were transformed into Euclidean wormholes by Hawking
\cite{Hawking:1988ae} and others.

Interest in traversable Lorentzian wormholes has been on the incline recently  following  the
stimulating work of Morris and Thorne \cite{MM}. In this proposal it is possible for  observers to
freely traverse wormholes and  time travel is admissable. They initially introduced concepts as
pedagogic tools for teaching general relativity where the Einstein field equations are solved by
constructing the spacetime metric first and then deducing the stress-energy tensor components. In order
to construct such traversable wormhole solutions demands the existence of exotic matter whose
stress-energy tensor components violate the null, weak, and the strong energy conditions
\cite{MM,Morris:1988tu}, at least in a neighborhood of the wormhole throat. For a more detailed review
the reader may consult  \cite{MV,Lobo:2007zb} and references therein. While the introduction of exotic
matter may appear unpalatable such matter fields exist in the quantum theory of the gravitational field
(namely the Casimir effect and Hawking evaporation \cite{Klinkhammer}) as well as in scalar-tensor
theories. In fact wormhole geometries violate the averaged energy conditions \cite{MV}.

Historically various attempts have been made to avoid appealing to exotic matter but all were in vain
within the context of general relativity. An advance in this discussion was  to consider minimizing the
violation of the energy conditions, namely, the \emph{volume integral quantifier}
\cite{Visser:2003yf,Kar:2004hc},
which quantifies the total amount of  matter violating the energy conditions. In this regard  Nandi
\emph{et al.} \cite{Nandi:2004ku} considered an exact integral quantifier for matter violating the
averaged null energy condition (ANEC). Kuhfittig \cite{Kuhfittig:2003pu} reported  that the region
consisting of exotic matter can be made arbitrarily small. Therefore, it is not an easy task to search
for promising candidates for exotic matter because all classical forms of matter are believed to obey
the standard energy-conditions. Dark energy models with exotic equations of state have been proposed
due to the formation and the evolution of the present structures in the Universe. While observational and
experimental support is presently lacking, strong theoretical arguments for dark matter have been advanced
principally to address the anomalous accelerated expansion of the universe problem. Consequently, much
effort has been made to obtain stable wormhole solutions within these new paradigms. These include models
supported by the phantom energy \cite{Lobo:2005us,Lobo:2005yv,Zaslavskii:2005fs}, the cosmological constant
\cite{Rahaman:2006xa,Lemos:2003jb,Cataldo:2008ku}, generalized or modified Chaplygin gas
\cite{Chakraborty:2007zi,Jamil:2008wu,Kuhfittig:2009mx}. However, in some alternative or modified theories
of gravity, the requirement of exotic matter can be minimized or even completely avoided. For instance, it
was shown that the matter threading the wormhole throat satisfies all of the energy conditions by Harko
\emph{et al.} \cite{Harko:2013yb}, and it is the higher order curvature terms, interpreted as a
gravitational fluid, that support the wormhole geometry. In \cite{MontelongoGarcia:2010xd}, wormhole
solutions have also been found with matter satisfying the null energy  condition were nonminimal
curvature-matter coupling in a generalized $f(R)$ modified theory of gravity. These kind of solutions were
also found in various modified theories, e.g., Einstein-Gauss-Bonnet \cite{Mehdizadeh:2015jra},
Born-Infeld gravity \cite{Shaikh:2018yku}, Einstein-Cartan \cite{Mehdizadeh:2017tcf}, and trace of the
energy-momentum tensor squared gravity \cite{Moraes:2017dbs}.

The detection of gravitational waves (GWs) by the advanced Laser Interferometer Gravitational Wave
Observatory (aLIGO) \cite{TheLIGOScientific:2014jea} and Advanced Virgo \cite{TheVirgo:2014hva} detectors
offers exciting opportunities towards the study of the nature of black holes. The detection of GWs from
five binary black holes (BBHs) demonstrated that stellar-mass black holes really exist in our universe.
However, the complete structure of the spacetime inside the light ring and near-horizon is still opaque
from the current observations. Thus, the physics in strong gravitational field, e.g., near black holes is
still an important topic not only in theoretical but also observational investigations.
Analysing the physical nature of black holes requires the actual detection of the event horizon. To confirm
the presence of event horizons a number  of tests have been performed that help reveal exciting physics and
astrophysics possibilities \cite{Broderick:2009ph,Broderick:2015tda,Narayan:2008bv}. The evidence is
compelling however not conclusive \cite{Abramowicz:2002vt}. Another important phenomenological feature of
black holes is their shadow. The concept of the rotating black hole shadow was suggested by Bardeen
\cite{Bardeen:1973gb}, with the idea of the optical image of black hole appearing due to the strong
gravitational lensing effect. Black holes are  expected to cast shadows on the bright background. Current
observations suggest that most galaxies contains supermassive black holes at their centers
\cite{Rees:1984si,Kormendy:1995} and that galaxies are rotating. This means that the black hole at the
center of a galaxy also possesses a spin and in this environment it is interesting to investigate the
nature of the black hole by analyzing the shadow that they cast on the bright background. Motivated by
present observational missions \cite{Doeleman}, the study of the black hole shadow has received
significant attention. Various configurations of black hole solutions, such as the shadow of the
Schwarzschild black hole \cite{Synge:1966,Luminet:1979}, have been investigated. The investigation of the
shadow for several black holes in the context of modified theories of gravity and higher-dimensional
theories have received attention in
\cite{Takahashi:2005hy,Bambi:2008jg,Hioki:2009na,Wei:2013kza,Bambi:2010hf,Amarilla:2010zq,Amarilla:2011fx,Amarilla:2013sj,Yumoto:2012kz,Abdujabbarov:2012bn,Atamurotov:2013sca,Li:2013jra,Cunha:2015yba,Johannsen:2015qca,Abdujabbarov:2016hnw,Amir:2016cen,Kumar:2017vuh,Singh:2017xle,Papnoi:2014aaa,Amir:2017slq,Singh:2017vfr}.
Shadow casting by the Kerr-like black holes in modified gravity theory has been addressed recently in
\cite{Wang:2018prk}. Different approaches to investigate the black hole shadow has been addressed so far in
the literature, e.g., photon regions based description of shadow \cite{Grenzebach:2014fha}, Hioki and Maeda
approach to calculate the observables of shadow \cite{Hioki:2009na}, new method to perform
general-relativistic ray-tracing for shadow images \cite{Younsi:2016azx}, coordinate-independent method
\cite{Abdujabbarov:2015xqa}, in presence of plasma \cite{Perlick:2015vta}, analytic description of shadow
\cite{Tsupko:2018apb}.

The main motivation of the paper is to investigate the shadows of Kerr-like wormholes obtained by Bueno
\emph{et al.} \cite{Bueno:2017hyj}, where the Kerr black hole turns out to be a wormhole solution that
reproduces Kerr's spacetime away from the throat. The same procedure outlined was followed by  Damour and
Solodukhin to obtain the Schwarzschild-like wormhole \cite{Damour:2007ap}. The detection of ringdown
frequencies from the black holes provides precise tests that astrophysical black holes are verily described
by the Kerr spacetime. Therefore, we conduct an  analysis of shadow for the Kerr-like wormholes. In
addition, it is expected that the shadow of the Kerr-like wormholes can be used to probe the true nature
of wormholes by Very Long Baseline Interferometry (VLBI) observations. In this direction a recent paper
has been devoted to the study of the shadow boundary associated with the outer spherical orbits
\cite{Nedkova:2013msa} and later this work was  developed by \cite{Shaikh:2018kfv}. Ellis wormholes have
been analyzed  by using the images of wormholes surrounded by optically thin dust in \cite{Ohgami:2015nra}.
The shadow of rotating wormholes in a plasma environment has been studied in the literature by the authors
\cite{Abdujabbarov:2016efm}. Recently, the shadow of a class of charged wormholes solutions in EMDA theory
has been studied in \cite{Amir:2018szm}.

The paper is organized as follows: after a brief introduction in Sect.~\ref{sec:intro}, we review the
Kerr-like wormhole solution and construct embedding diagrams to represent a wormhole in
Sect.~\ref{spacetime}. In Sect.~\ref{geodesics}, we evaluate the geodesic equations and derive the photon
trajectories around the wormhole in Sect.~\ref {orbit}. Section~\ref{shadow} is devoted  to constructing
the shadow images of Kerr-like wormholes. A discussion on the results is included in Sect.~\ref{conclusion}.

\section{Kerr-Like wormholes and embedding diagrams}
\label{spacetime}
We commence with the Kerr-like wormhole spacetime which was obtained as a toy model by performing a
modification on the Kerr metric  similar to  that of Damour and Solodukhin  for a Schwarzschild black
hole \cite{Damour:2007ap}. This spacetime class was introduced by Bueno \emph{et al.}
\cite{Bueno:2017hyj} and the metric in Boyer-Lindquist coordinates ($t, r, \theta, \phi$) is given by
\begin{eqnarray}\label{metric}
ds^2 & = & -\left(1-\frac{2Mr}{\Sigma}\right)dt^2 -\frac{4Mar\sin^2 \theta}{\Sigma} dt d\phi
+\frac{\Sigma}{\hat{\Delta}}dr^2   \nonumber \\ &+& \Sigma d \theta^2
+ \left(r^2+ a^2 +\frac{2Ma^2r \sin^2 \theta}{\Sigma} \right) \sin^2 \theta d\phi^2,
\end{eqnarray}
where $\Sigma$ and $\hat{\Delta}$ are expressed as follows
\begin{eqnarray}\label{root}
\Sigma = r^2 + a^2 \cos^2\theta, \quad \hat{\Delta}=r^2 + a^2 - 2 M(1+\lambda^2)r.
\end{eqnarray}
This spacetime contains a family of parameters where $a$ and $M$, respectively corresponds to the spin
and the mass of the wormhole and $\lambda^2$ is the deviation parameter which accounts for the deviation
from the Kerr spacetime. In other words, for any non vanishing $\lambda^2$  the new metric differs from
the Kerr metric. The Kerr spacetime may be recovered  when $\lambda^2 =0$. The throat of the Kerr-like
wormhole (\ref{root}) can be evaluated by equating the $\hat{\Delta}$ to zero, which gives
\begin{equation}
r_{+} = M (1+\lambda^2) + \sqrt{M^2(1+\lambda^2)^2 -a^2}.
\end{equation}
This expression represents a special surface or region that connects two different asymptotically flat
regions. Now we can construct the embedding diagrams to represent a Kerr-like wormhole and extract some
useful information by considering an equatorial slice, $\theta  = \pi/2$ and a fixed moment of time, $t =$
a constant. The metric has the form
\begin{equation}\label{em1}
ds^2=\frac{dr^2}{1-\frac{b(r)}{r}}+R^2 d \phi^2,
\end{equation}
where
\begin{equation}\label{em2}
R^2=r^2+a^2+\frac{2Ma^2}{r},~~\text{and}~~b(r)=2M(1+\lambda^2)-\frac{a^2}{r}.
\end{equation}
We embed the metric (\ref{em1}) into three-dimensional Euclidean space to visualize this slice and the
spacetime can be written in cylindrical coordinates as
\begin{equation}\label{em3}
ds^2=dz^2+dR^2 + R^2 d\phi^2=\left[\left(\frac{dR}{dr} \right)^2+\left(\frac{dz}{dr} \right)^2\right]dr^2+R^2 d \phi^2.
\end{equation}
The combination of (\ref{em1}) and (\ref{em3}) generate the equation for the embedding surface which is given by
\begin{equation}\label{em4}
\frac{dz}{dr}=\pm \sqrt{\frac{r}{r-b(r)}-\left(\frac{dR}{dr} \right)^2}.
\end{equation}
Now, plugging the value of (\ref{em2}) into (\ref{em4})  the above relation assumes the form
\begin{equation}
\frac{dz}{dr}=\pm \sqrt{\frac{M\left[2r^7\lambda_1 +2 a^2 r^3(2r^2+ a^2)
-4Ma^2 \lambda_1 r^4 -Ma^4(r^2+a^2)+2Ma^4 \lambda_1 r\right]}
{r^3(r^3+a^2r+2Ma^2)\left(r^2+a^2-2M\lambda_1 r\right)} },\label{2.9}
\end{equation}
where we have put $\lambda_1 = 1 + \lambda^2$ for convenience. Note that the integration of (\ref{2.9})
cannot be accomplished analytically. Invoking numerical techniques allows us to  illustrate the wormhole
shape given in Fig.~\ref{kerr-wormhole}.
\begin{figure*}
    \includegraphics[scale=0.98]{kerr-wormhole1.eps}
    \includegraphics[scale=0.91]{kerr-wormhole2.eps}
 \caption{\label{kerr-wormhole} Plot showing the embedding diagrams of the Kerr-like wormholes.
 (Left) Rotating Kerr-like wormhole: $z$ as a function of $r$ with $\phi$ direction for $M=1$ and $a=1$.
 (Right) Slowly rotating Kerr-like wormhole: plot of $z$ as a function of $\rho $ with $\phi$
 direction for  $M=1.2$, $a=0.01$ and $\lambda^2=0.01$.}
\end{figure*}
In the limit $a\rightarrow 0$, we obtain
\begin{equation}
z= \pm \sqrt{8M(1+\lambda^2) (r-2M-2M\lambda^2)},
\end{equation}
for the integral of (\ref{2.9}). In addition, on setting the deviation parameter to zero, i.e.,
$\lambda^2=0$, the Schwarzschild solution
\begin{equation}
z= \pm \sqrt{8M (r-2M)}.
\end{equation}
is regained. The problem may be simplified by considering a slowly rotating Kerr-like wormhole solution.
For this purpose we are interested in approximate solutions by considering a series expansion, say, around
$a$ and $\lambda^2$ in Eq.~\eqref{2.9}. The solution can be approximated as follows
\begin{equation}\notag
z= \pm \Big\{\sqrt{8M (r-2M)}-\frac{\lambda^2 \sqrt{2M} }{4 M^{3/2} r(r-2M)^{3/2}}
\left[\sqrt{2}\arctan \left(\frac{r-2M}{\sqrt{M}} \right)(r-2M)^{3/2}r a^2+ \chi  \right]
\end{equation}
\begin{equation}
+\frac{a^2 \sqrt{2M} }{16 r^2 M^{3/2} (r-2M)^{1/2}} \left[3\sqrt{2}\arctan \left(\frac{r-2M}{\sqrt{M}}  \right)(r-2M)^{1/2}r^2+\zeta  \right]\Big\},
\end{equation}
where
\begin{equation}
\zeta =16M^{5/2}-4 M^{3/2}r+6 r^2 M^{1/2},
\end{equation}
and
\begin{equation}
\chi = 24 M^{5/2}r^2-32M^{7/2}r+4M^{5/2}a^2-4 M^{3/2}r^3-8 a^2 M^{3/2}r+2 r^2 a^2 \sqrt{M}.
\end{equation}
Finally, let us introduce a new variable $\rho$, via
\begin{equation}\label{emb}
r=2M(1+\lambda^2)+\frac{\lambda^2-1}{2M}a^2+\frac{\rho^2}{2M}.
\end{equation}
The graphical representation of (\ref{emb}) with the $\phi$ direction can be seen from
Fig.~\ref{kerr-wormhole}, which shows the visual image of the  slowly rotating Kerr-like wormhole.

\subsection{ADM mass}
Now let us compute the ADM mass for the Kerr-like wormhole. We compute it for asymptotically flat
spacetime and it will be similar to that of axisymmetric spacetime. We consider the asymptotic flat
spacetime
\begin{eqnarray}
ds^2_{\Sigma} = \psi(r)dr^2+r^2 \chi(r)\left(d\theta^2+\sin^2\theta d\varphi^2\right),
\end{eqnarray}
where we have identified
\begin{equation}
    \psi(r)=\frac{1}{1-\frac{2M(1+\lambda^2)}{r}},\quad \text{and} \quad \chi(r)=1.
\end{equation}
In order to compute the ADM mass, we use the approach which used in \cite{Shaikh:2018kfv},
\begin{equation}\label{for}
    M_{ADM}=\lim_{r\to \infty} \frac{1}{2}\left[-r^2 \chi'+r(\psi -\chi) \right].
\end{equation}
On substituting the values in (\ref{for}) and after computing the limit we get the ADM mass for the
wormhole,
\begin{equation}\label{ADM}
    M_{ADM}=M(1+\lambda^2).
\end{equation}
Note that this is the mass of the Kerr-like wormhole as seen by an observer located at the
asymptotic spatial infinity.  We will use this mass to explain the physical processes throughout the paper.

\section{Geodesics in Kerr-like wormholes}
\label{geodesics}
The spacetime of rotating Kerr-like wormholes is generally characterized by the four constants of
motion, i.e., the Lagrangian $\mathcal{L}$, the energy $E$, the angular momentum $L_{z}$ and the Carter
constant $\mathcal{K}$. The geodesic equations of a test particle having rest mass $m_0$ can be derived
by using these conserved quantities and the Hamilton-Jacobi equation. We can derive the geodesic equations
for $t$ and $\phi$ coordinates with the help of conserved quantities, $E=-p_t$ and $L_z=p_{\phi}$, which
turns out
\begin{eqnarray}\label{u}
\Sigma \frac{d t}{d \sigma} &=&  -a \left(aE \sin^2 \theta - L_{z}\right)
+ \frac{(r^2 + a^2) \mathcal{P}}{r^2 + a^2 - 2 M r},
\nonumber \\
\Sigma \frac{d \phi}{d \sigma} &=& -\left(aE - L_{z}\csc^2 \theta \right)
+ \frac{a \mathcal{P}}{r^2 + a^2 - 2 M r},
\end{eqnarray}
where $\mathcal{P} = (r^2+a^2)E-aL_{z}$. The other geodesic equations, i.e., for $r$ and $\theta$
coordinates can be computed by using the Hamilton-Jacobi method. Since the geodesics of the test particle
in the background of Kerr-like wormholes spacetime (\ref{metric}) satisfy the Hamilton-Jacobi equation
\cite{Chandrasekhar:1992}, which is given by
\begin{equation}\label{HamJac}
\frac{\partial S}{\partial \sigma} = -\frac{1}{2} g^{\mu \nu}
\frac{\partial S}{\partial x^{\mu}} \frac{\partial S}{\partial x^{\nu}},
\end{equation}
where $\sigma$ is the affine parameter and $S$ is the Jacobian action with the following separable ansatz:
\begin{equation}\label{ansatz}
S = \frac{1}{2} m_0^2 \sigma -Et +S_r(r) +S_{\theta}(\theta) +L_z \phi.
\end{equation}
Here $S_r$ and $S_{\theta}$ are  functions of $r$ and $\theta$, respectively. On substituting
Eq.~(\ref{ansatz}) into Eq.~(\ref{HamJac}) and after some straightforward computations we obtain the
following forms of the geodesic equations
\begin{eqnarray}\label{u1}
\Sigma \frac{d r}{d \sigma} &=& \pm  \sqrt{\mathcal{R}},
\nonumber \\
\Sigma \frac{d \theta}{d \sigma} &=& \pm  \sqrt{\Theta},
\end{eqnarray}
where the terms $\mathcal{R}$ and $\Theta$ in (\ref{u1}) are expressed as follows
\begin{eqnarray}\label{quant}
\mathcal{R} &=& \frac{\left[r^2 + a^2- 2 M (1+\lambda^2) r \right]
\lbrace \mathcal{P}^2 -(r^2 + a^2- 2 M r)
\left[\mathcal{K}+ (L_{z}-a E)^2 +m_0^2r^2 \right] \rbrace }{r^2 + a^2- 2 M r},
\nonumber \\
\Theta &=& \mathcal{K} +\cos^2 \theta \left(a^2E^2-L_{z}^2\csc^2 \theta -m_0^2 a^2 \right).
\end{eqnarray}
These geodesic equations determine the trajectories of a test particle in background of the Kerr-like
wormholes spacetime. Physically, the quantity $E$ is the energy required for a distant observer to place
the test particle in orbit around the Kerr-like wormhole.

\section{Spherical photon orbits around Kerr-like wormholes}
\label{orbit}
Consider the  case of photons released from a bright source and which are moving towards the wormhole
that is placed between the observer and the light source. The possible trajectories of the photons
around the wormhole are: (i) falling into the wormholes, (ii) scattered away from the wormholes to
infinity, and (iii) critical geodesics which separate the first two sets, also known as unstable
spherical orbits. It turns out that in the observer's sky, the plunged photon geodesics form dark spots
whereas the scattered photon geodesics form bright spots. The critical photon geodesic trajectories form
a dark region in the observer's sky in the presence of a bright background which is referred to as the
\emph{wormhole hole shadow}.

Our principal objective is to evaluate these critical geodesics or unstable spherical orbits. In order
to obtain the boundary of the wormhole shadow, it is necessary to work out the radial motion of photons
around the wormholes. Here, we consider a photon as a massless test particle, therefore $m_0=0$. The
radial geodesic equation can be rewritten as
\begin{equation}\label{rad}
 \left(\Sigma \frac{dr}{d\sigma}\right)^2 + V_{eff} =0,
\end{equation}
where $V_{eff}$ represents the effective potential that describes the trajectories of the photons around
the wormhole. However, the different bounds of the effective potential determine the various
trajectories depending on the magnitude of the angular momentum. Now we express the effective potential
of the photons in terms of two independent impact parameters such that $\xi=L_{z}/E$ and
$\eta=\mathcal{K}/E^2$. The effective potential can be written as follows
\begin{eqnarray}
\label{Veff}
V_{eff} &=& -\frac{E^2 \left[r^2 + a^2- 2 M(1+\lambda^2)r\right]}{r^2 + a^2 -2 Mr}
\Big[(r^2+a^2-a\xi)^2 \nonumber\\ &&
-(r^2 + a^2- 2 M r) \left[\eta + (\xi -a)^2 \right] \Big].
\end{eqnarray}
It is easy to observe that the effective potential has a dependency of the deviation parameter $\lambda^2$
that affects the trajectories of photons.
\begin{figure*}
\includegraphics[scale=0.6]{eff1.eps}
\includegraphics[scale=0.6]{eff2.eps}
\caption{\label{eff} Plot illustrating the nature of effective potential in Kerr-like wormholes by
varying the impact parameter $\xi$ and the deviation parameter $\lambda^2$.}
\end{figure*}
We plot effective potential with radius for the Kerr-like wormhole in Fig.~\ref{eff} by varying the
parameter $\xi$ as well as the deviation parameter $\lambda^2$. We use the ADM mass ($M_{ADM}$) to plot
the effective potential of the Kerr-like wormholes. We find that the effective potential has different
potential barriers according to the variation of parameters which increase with parameter $\xi$ as well
as with the deviation parameter $\lambda^2$. On the other hand, the boundary of the shadow can be
determined by the unstable spherical photon orbits corresponding to the highest maximum value (supremum)
of the effective potential $V_{eff}$. The following standard conditions can be used to determine the
unstable spherical photon orbits
\begin{equation}\label{condition1}
V_{eff} = 0, \quad  V_{eff}'=0,
\end{equation}
where prime ($'$) represents derivatives with respect to $r$. In terms of $\mathcal{R}$, the unstable
spherical photon orbits conditions transform as follows
\begin{equation}\label{condition}
\mathcal{R} = 0, \quad  \mathcal{R}'=0.
\end{equation}
Now on using Eqs.~(\ref{quant}) and (\ref{condition}), we immediately obtain the expressions of the
impact parameters
\begin{eqnarray}\label{imptp}
\xi &=&\frac{a^2(r+M)+r^2 (r-3 M)}{a(M-r)},
\nonumber \\
\eta &=& \frac{4M a^2 r^3-r^4 (r-3 M)^2}{a^2(M-r)^2},
\end{eqnarray}
where $r$ is the radius of unstable spherical photon orbits. Interestingly, Eq.~(\ref{imptp}) determines
the critical locus of the impact parameters which can be considered as the set of unstable photon orbits.
As it can be seen from Eq.~(\ref{imptp}) that the impact parameters have a dependency on the spin $a$
and the mass $M$. When we compare our computed expressions of the impact parameters with the Kerr
spacetime, we find them indistinguishable. However, there is a dependency of deviation parameter
$\lambda^2$ on the impact parameters through the ADM mass by using the relation,
$M = M_{ADM}/(1 +\lambda^2)$. If we compute the impact parameters for $a = 0$ (nonrotating case),
we obtain the following relation
\begin{equation}
    \eta = 27M^2 - \xi^2 \quad \text{with} \quad r = 3M.
\end{equation}
This result is similar to that of the Schwarzschild spacetime one. Although we are using the ADM
mass which turns out that there is a dependency on deviation parameter $\lambda^2$. The apparent
image or shadow of the wormhole can be obtained by looking for the unstable photon orbits which can
be discussed more explicitly in the next section.

\section{Shadow of Kerr-like wormholes}
\label{shadow}
In this section, our main goal is to construct and characterize the shadow of the Kerr-like wormholes.
We turn our attention towards the observer's sky to detect the optical images cast by the Kerr-like
wormholes. In preparation for the investigation of the shadow,  consider a plane passing through the
center of the wormhole and it's normal joining the center of the wormhole and the line of sight of an
observer. We introduce new coordinates ($\alpha,\beta$) \cite{Bardeen:1973gb}, widely known as
celestial coordinates that span a two-dimensional plane also known as celestial plane. Note that the
coordinates $\alpha$ and $\beta$ corresponds to the apparent perpendicular distance of the image as
seen from the axis of symmetry and the apparent perpendicular distance of the image from its
projection on to the equatorial plane, respectively. With this construction, we obtain the projection
of wormhole's throat on the observer's sky. The celestial coordinates for a distant observer can be
written \cite{Bardeen:1973gb} in the form
\begin{eqnarray}
\label{alp-bet}
\alpha &=& \lim_{r \rightarrow \infty} \left(-r^2 \sin \theta_{0} \frac{d \phi}{dr} \right),
\nonumber \\
\beta &=& \lim_{r \rightarrow \infty} \left(r^2 \frac{d \theta}{dr} \right),
\end{eqnarray}
where $\theta_{0}$ represents the inclination angle between the rotation axis of the wormhole and the
direction to the observer. By using Eqs.~(\ref{u}), (\ref{u1}), (\ref{quant}), and (\ref{alp-bet}), the
celestial coordinates transform into
\begin{eqnarray}
\label{alp-bet1}
\alpha &=& -\xi \csc \theta_{0}, \nonumber \\
\beta &=& \pm \sqrt{\eta +a^2 \cos^2 \theta_{0} -\xi^2 \cot^2 \theta_{0}}.
\end{eqnarray}
It is clear from Eq.~(\ref{alp-bet1}) that the shapes of the Kerr-like wormhole's shadow depend not
only on its spin $a$ but also on its inclination angle $\theta_0$. When the observer is located in the
equatorial plane ($\theta_{0}=\pi /2$) of the wormhole,  the expressions in Eq.~(\ref{alp-bet1}) reduce
to
\begin{eqnarray}\label{eqtc}
\alpha &=& -\xi, \nonumber\\
\beta &=& \pm \sqrt{\eta}.
\end{eqnarray}
\begin{figure}
  \includegraphics[scale=0.65]{nonrot.eps}
  \caption{\label{nshad} Plot illustrating the shadow images of the nonrotating wormholes by varying
  the deviation parameter $\lambda^2$. Here $\lambda^2=0$ corresponds to the Schwarzschild black hole
  case ($M_{ADM}$ is set equal to $1$ for both of the spacetimes).}
\end{figure}
A dark region in the observer's sky can be obtained when the impact parameters $\eta$ and $\xi$
attains all the possible values. This dark region is known as the shadow of the wormhole. The
nonrotating wormhole shadow can be constructed by the following expression
\begin{eqnarray}\label{nonr}
\alpha^2 + \beta^2 = \frac{2 r^2 \left(r^2-3 M^2\right)}{(M-r)^2},
\end{eqnarray}
which implies that the shadow casts by a nonrotating wormhole ($a=0$) has a circular shape with a
radius $\sqrt{\frac{2 r^2 \left(r^2-3 M^2\right)}{(M-r)^2}}$. In order to plot the shadows, we consider
the ADM mass ($M_{ADM}$) of the wormhole. The shadows of nonrotating wormhole can be seen from
Fig.~\ref{nshad}. The figure shows that the radius of shadow decreases with a small change in deviation
parameter $\lambda^2$. Moreover, the radius of shadow is smaller than that of Schwarzschild black hole
(cf. Fig.~\ref{nshad}). In contrast for a rotating wormhole the sum of $\alpha^2 + \beta^2$, takes the
complicated form
\begin{eqnarray}\label{rot}
\alpha^2 + \beta^2 &=& \frac{a^2 (M + r)^2 +2 r^2 (r^2 -3 M^2)}{(M-r)^2}.
\end{eqnarray}
The presence of spin $a$ in the expression (\ref{rot}) results in manifestly different shapes of the
shadow of the Kerr-like wormhole in comparison with the nonrotating one. It is noticeable that the
expression (\ref{rot}) depends on deviation parameter $\lambda^2$ while the ADM mass of the wormhole is
considered. This is because as we pointed out we shall refer to the ADM mass as the physical mass of the
wormhole viewed by an observer located at spatial infinity. In order to see it more clearly, we construct
shapes of the Kerr-like wormholes shadows for nonzero values of the spin $a$, the deviation parameter
$\lambda^2$, and the inclination angle $\theta_0$. We plot the shadow images of the Kerr-like wormholes
for different values of the spin $a$, the deviation parameter $\lambda^2$, and the inclination angle
$\theta_0$ (cf. Figs.~\ref{shad} and \ref{shad-1}). Interestingly, we find that the shape of the shadow
is oblate instead of being circular when compare with the nonrotating case. This oblateness or distortion
in the shape arises because of the nonzero values of the spin $a$. In Fig.~\ref{shad}, we show the
variation of the spin $a$ while the Fig.~\ref{shad-1} depicts the effect of deviation parameter
$\lambda^2$ on the shape of the shadow. It is clearly observed that the presence of the deviation
parameter $\lambda^2$ influences the radius of the shadow.
\begin{figure*}
  \includegraphics[scale=0.34]{fig1a.eps}
  \includegraphics[scale=0.34]{fig1b.eps}
  \includegraphics[scale=0.34]{fig1c.eps}
  \includegraphics[scale=0.323]{fig1d.eps}\\
  \includegraphics[scale=0.34]{fig1e.eps}
  \includegraphics[scale=0.345]{fig1f.eps}
  \includegraphics[scale=0.34]{fig1g.eps}
  \includegraphics[scale=0.325]{fig1h.eps}
 \caption{\label{shad} Plot illustrating the shadow images of the Kerr-like wormholes by varying
 the spin $a$ for different values of deviation parameter $\lambda^2$ ($M_{ADM}=1$).}
\end{figure*}
\begin{figure*}
   \includegraphics[scale=0.34]{fig2a.eps}
   \includegraphics[scale=0.35]{fig2b.eps}
   \includegraphics[scale=0.335]{fig2c.eps}
   \includegraphics[scale=0.33]{fig2d.eps}\\
   \includegraphics[scale=0.34]{fig2e.eps}
   \includegraphics[scale=0.35]{fig2f.eps}
   \includegraphics[scale=0.335]{fig2g.eps}
   \includegraphics[scale=0.33]{fig2h.eps}
 \caption{\label{shad-1} Plot illustrating the shadow images of the Kerr-like wormholes by varying
 the deviation parameter $\lambda^2$. Here $\lambda^2=0$ corresponds to the Kerr black hole case
 ($M_{ADM}$ is set equal to $1$ for both of the spacetimes).}
\end{figure*}

An increase in the magnitude of spin $a$ increases the amount of distortion in the shadow of the
Kerr-like wormhole (cf. Figs.~\ref{shad} and \ref{shad-1}). On the other hand when we fix the values of
$a$ and at the same stage we do a change in $\lambda^2$ values that also increases the distortion in the
shape. The shape is maximally distorted when the observer is located in equatorial plane as can be
seen from Fig.~\ref{shad-1}. While we talk about the effect on the size or radius of the Kerr-like
wormhole's shadow, we find that the radius is continuously decreasing with a small change in the
magnitude of the deviation parameter $\lambda^2$ (cf. Fig.~\ref{shad-1}). We also include the case of
the Kerr black hole ($\lambda^2 =0$) by considering the same ADM mass ($M_{ADM} =1$) to see the
difference in their shadow images (cf. Fig.~\ref{shad-1}). We discover that the shadow images of the
Kerr-like wormholes are smaller in comparison to that of the Kerr black hole. In case of the Kerr
spacetime, one can only observe the effect of spin $a$ on shadow, but in our case we have an additional
parameter $\lambda^2$ which provides more images of the shadow so that extract more substantial
information from them. Note that the actual size of the wormhole's shadow is bigger as compare to
wormhole's geometrical size. Since the wormhole bends photon trajectories, therefore, the actual cross
section of the shadow is greater than that of the geometrical one.

\section{Conclusion}
\label{conclusion}
The discovery of quasar in 1960s  provided compelling evidence for the existence of supermassive black
holes located at least in some galactic binary systems in the centers of most of the large galaxies,
e.g., the Milky Way and Messier 87 ostensibly  have such objects, namely, Sgr A$^*$ and M87$^*$.
Supermassive black holes are considered as astrophysical black holes and they form from the
gravitational collapse of matter. Besides, the detection of ringdown frequencies from the black holes
provide precise tests that astrophysical black holes are accurately described by the Kerr spacetime.
Motivated by these tests, we construct the theoretical analysis of the shadow for the Kerr-like
wormholes. Therefore, observational investigation of the Kerr-like wormhole shadows will be very
interesting and a useful tool to demonstrate the true nature of it. The observation of the shadow also
provides a tentative way to determine the parameters governing the evolution of  the wormholes. As it
is well known one of the approaches to detect supermassive black holes is based on high resolution
imaging of them. The Event Horizon Telescope which functions on the Very Long Baseline Interferometry
technique, has been designed to resolve the problem of the detection of the supermassive black hole at
the center of the Milky Way. This technique is able to achieve the angular resolution comparable to
sub-millimeter wavelength diapason.

In this paper, we concentrate on the construction of the shadow cast by the Kerr-like wormholes. We
have evaluated the test particle geodesics and determined the trajectories of photons around the
Kerr-like wormhole. It has been noticed that the photons approaching the wormhole with sufficient
angular momentum form unstable spherical orbits around it. In further investigation, we introduced the
impact parameters that define the boundary of the shadow against the bright background. In order to
visualize the optical images of the shadow of the Kerr-like wormhole, the celestial coordinates are
evaluated. We have plotted these coordinates into the celestial plane to get the shadow images,
eventually discussed the nonrotating and rotating cases of the wormhole's shadows. We have discovered
that the radii of the nonrotating wormhole's shadows are smaller in comparison to that of the
Schawrzschild black hole. We have obtained different shapes of the shadow for the Kerr-like wormholes
by varying the parameters. We find  that the shapes of the Kerr-like wormhole's shadow are oblate or
distorted. Mainly, this distortion occurs due to the magnitude of the spin parameter $a$ and inclination
angle $\theta_0$. The shapes are more distorted for the extreme value of the spin $a$ and when the
observer is located into the equatorial plane. In addition, it is found that the radius of the shadow
images is also sensitive to value of the deviation parameter $\lambda^2$; a small change in $\lambda^2$
decreases the radius of the shadow substantially. As a consequence the radius decreases with deviation
parameter $\lambda^2$ in general. Our results provide the deviations when a comparison with the Kerr
spacetime is taking on account by using the same ADM mass for both of the spacetimes. We have also
discovered that the radii of the Kerr-like wormhole's shadows are smaller in comparison to that of the
Kerr black hole. This important study will be helpful to extract the essential information about the
Kerr-like wormhole and its existence as the astrophysical object. We are expecting that in upcoming years
the direct images of wormholes will be observe by the Event Horizon Telescope.

\acknowledgments
M.A., A.B., and S.H. would like to thank University of KwaZulu-Natal and the National Research
Foundation for financial support. We would like to thank the referees for useful comments and
suggestions.

redpajama_set_name: RedPajamaArXiv


"'I know the plans I have for you,' says the Lord. 'Plans to give you a hope and a future.'" Okay, Lord, I want to know what they are and I want to know RIGHT NOW! (stomping my feet and yelling and raising my fist at God) as if that's gonna make Him tell me! Don't you just feel like yelling and screaming and having a hissy fit when you don't understand what is happening to you?! God says we should have faith like a little child, well, sometimes I have the attitude and patience of a little child and want to rant and rave and ….you know what I mean, right? Please tell me it's not just me?!??
Did u read what I said in last month's blog about how this year is so much better than last? Well, it's now a month later and my husband has lost his job and we only have enough $ in the bank for the next 6 weeks or so. I start my last quarter at the community college to get my associates degree so there's no question that I'm going to finish. Besides, it's already paid for by financial aid.
On one hand there's the usual doubts and worries about not being able to eat and maybe being homeless. But then the strong side of me thunks me on the forehead and says, what are you thinking? God is in control and He has a plan. So just calm down and wait for it! Thankfully there have been some good devotionals in one book I have on my Kindle that have come at the right time and helped keep me from worrying too. Again, just like I said last month, God has the best timing.


Lost 3lbs this week so now i am on week 4 i dont know weather to do aam next week or not i still have around 4 stone to lose so would i be beteer staying on ss.
Hi Jessy - well done on your loss so far - FAB !!
Unless you get a note from your Doctor, you really should do AAM week.
You have lost well over a stone in your first 3 weeks - so you are doing really well.
AAM week should not slow your weight loss down, and in some people, they actually lose more the week after AAM.
I think AAM is a good idea to get you used to eating, and being satisfied with a small portion of food.
It will really help in the long-term.
I didn't do AAM last time I did the diet, and didn't do management either- and look where I am now! I am heavier than when I started last time, so I would strongly advise anyone to do this diet by the book!!
Well done, the small amount you eat doesnt affect the weight loss.
Step 1 Sole Source + Week three starts today !


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Q: Removing Spotlight Is it possible to remove spotlight from the menu bar? I have too many menu bar items running all the time and I'm trying to remove what I can to see everything regardless of what app is open.

A: You can do this by running a command in the terminal: sudo chmod 600 /System/Library/CoreServices/Search.bundle/Contents/MacOS/Search.  Then logout and back in.
Source.

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