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U.S. Eleventh Circuit
I've Been Injured on the Railroad: Now What?
By Robyn Hagan Cain on August 31, 2012 4:02 PM
A lawyer generally needs to plead the facts of a tort claim with specificity, but a plaintiff can survive summary judgment in a Federal Employers' Liability Act (FELA) claim, even when a few facts are missing.
The Eleventh Circuit Court of Appeals ruled this week that a railroad employee can proceed with his claim against Norfolk Southern Railway Company (Norfolk Southern), even though he couldn't identify the rail car that allegedly caused his injury.
The Eleventh Circuit recounted the facts behind the appeal with a musical flare:
On July 23, 2009, Connie Strickland had been "working on the railroad / All the live-long day." In fact, he claims he was working his customary twelve-hour shift when, towards the end of that shift, he suffered a massive shoulder injury as a result of a faulty handbrake. Strickland, however, could not identify the rail car on which the handbrake was installed. Nonetheless, he filed suit against his employer, Norfolk Southern.
Strickland sued under FELA, alleging that Norfolk Southern was negligent in failing to provide him with safe and adequate equipment, tools, assistance, and the like. He also claimed, under FELA and the Federal Safety Appliance Act (FSAA), that "inefficiencies" of the handbrake in question caused his injury and that Norfolk Southern was liable.
Norfolk Southern moved for summary judgment, contending that there was insufficient evidence to support Strickland's claims, and that it had no way to defend itself against the claims because Strickland could not identify the particular rail car on which he was injured.
Noting that an employee may recover under the FELA if his employer's negligence "played any part, even the slightest, in producing the injury or death for which damages are sought," Strickland argued that summary judgment is disfavored in FELA actions. Strickland claimed that the determining factor in his action was neither whether he could identify a "mechanical defect or broken part" in the handbrake at issue, nor whether he could identify the number of the car on which the handbrake was installed; instead, the issue was whether his testimony alone constituted sufficient evidence to survive summary judgment.
The district court ruled that it was not, and granted Norfolk Southern's request for summary judgment.
The Eleventh Circuit Court of Appeals reversed and remanded the case this week.
The appellate court wrote, "No authority exists for the proposition that the failure to identify the rail car, standing alone, provides a sufficient basis for summary judgment in Norfolk Southern's favor. While Strickland's failure to identify a specific rail car may hinder Norfolk Southern's defense, Norfolk Southern cited no authority ... that would have supported the granting of a motion for summary judgment on such a basis. Nor were we able to locate any controlling or persuasive authority authorizing such action."
The court further observed that Strickland had satisfied the "featherweight" standards of a FELA action to survive summary judgment.
Connie Strickland v. Norfolk Southern Railway Company (Eleventh Circuit Court of Appeals)
Missing Evidence Isn't Deal Breaker in Defective Design Case (FindLaw's Fifth Circuit Blog)
Third Circuit Affirmed on LIA Federal Preemption (FindLaw's Third Circuit Blog)


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Expert witnesses could face new risks
The longstanding principle that an expert witness is immune from being sued was overturned in the recent Supreme Court decision of Jones v Kaney. Having lost their immunity, experts are now exposed to the risk of being sued in respect of evidence given in court, says Dental Protection
Kevin Lewis, Dental Director of Dental Protection said: "Time will tell if the removal of expert witness immunity will lead to a significant increase in claims against expert witnesses. Members of Dental Protection are protected by an indemnity that extends to expert witness work and we will be closely monitoring the impact of this recent decision."
"As a matter of good practice, expert witnesses should follow the relevant guidelines and rules, including the Civil Procedure Rules and the General Dental Council's guidance. Provided they follow these guidelines and standards, allegations of negligence can be rebutted.
Mr Lewis added: "We would advise members who are involved in expert witness work to keep us fully informed about the type and extent of professional work they are doing, so that they have access to the appropriate indemnity at all times."

redpajama_set_name: RedPajamaCommonCrawl


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Alfa Laval/
Alfa Laval first to launch a premium separator range for single-use pharmaceutical processing
Tue, Jan 11, 2022 08:30 CET
Alfa Laval is the first manufacturer to introduce a new unique single-use separator range – Alfa Laval CultureOne Maxi – for biopharma processing that will cover the range from lab scale up to large production. All product-contact parts in the separator system can be replaced after each batch, eliminating the risk of cross-contamination, and increasing process hygiene and safety.
In 2020, Alfa Laval launched the first premium separator for single-use biopharma processing in small scale production. Based on the positive market reception the company is now expanding the offering to a range of single-use separators covering the scope from small lab production up to large scale processing.
Until recently, single-use disc-stack separators did not exist on the market. This forced manufacturers to choose less efficient alternatives for cell harvesting. Now the unique single-use range, based on Alfa Laval's 130 years of experience in separation technology and developed in close contact with Alfa Laval's biopharma customers, eliminates the need for onsite cleaning and sterilization – and thereby the associated consumption of chemicals, water and energy.
"Today 'health and safety' is at the top of everyone's agenda, so is the importance of more sustainable living. I am pleased to announce the launch of this new product range that addresses these points. Single-use systems enable our pharmaceutical customers to produce more medicines and bring them to market safely and quickly. In addition, all product-contact parts in the CultureOne range are made from recyclable material. which is good for society," says Nish Patel, President of the Food & Water Division.
Did you know… Alfa Laval CultureOne™ is used in processes for harvesting fragile cell cultures which are later used for injectable drugs for treating life-threatening illnesses including cancer and to counter organ transplant rejection.
This is Alfa Laval
Alfa Laval is a world leader in heat transfer, centrifugal separation and fluid handling, and is active in the areas of Energy, Marine, and Food & Water, offering its expertise, products, and service to a wide range of industries in some 100 countries. The company is committed to optimizing processes, creating responsible growth, and driving progress to support customers in achieving their business goals and sustainability targets.
Alfa Laval's innovative technologies are dedicated to purifying, refining, and reusing materials, promoting more responsible use of natural resources. They contribute to improved energy efficiency and heat recovery, better water treatment, and reduced emissions. Thereby, Alfa Laval is not only accelerating success for its customers, but also for people and the planet. Making the world better, every day.
Alfa Laval has 16,700 employees. Annual sales in 2020 were SEK 41.5 billion (approx. EUR 4 billion). The company is listed on Nasdaq Stockholm.
www.alfalaval.com
Johan Lundin
Eva Schiller
Tel: + 46 46 36 71 01
Alfa Laval Alfa Laval CultureOne Maxi
PR_COne_220111_ENG
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Intelligent, innovative, professional and cooperative staff team is the source of the power of asia-pacific group. The company's employees are rich and strong, with good education and professional training, fluent English communication skills. The company has established extensive business cooperation with 142 countries and regions around the world, contributing to China's reform and opening up and the development of China's electronics industry.
Clothing: Japanese, European and American brands.
Gift items: electronic products, gift pens.
Annual sales: USD 300 million.
Real estate equity, credit, bonds, trust financing.
Real estate insurance trust, securities arrangement.
Cooperate with international financial institutions in development and agency.
Financial investment insurance and other commodities.
Provide investment research and consulting services such as global asset distribution.
Environmental science and technology biology research.
To develop green energy industry with international professional organizations.
Research and development of contaminated water and soil purification projects.
@2018 Asia Holdings Enterprise Ltd.


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Framingham Stop & Shop plaza has new owner. Are changes coming to the plaza?
Jeff Malachowski
MetroWest Daily News
FRAMINGHAM – The Stop & Shop plaza on Old Connecticut Path has a new owner.
Needham-based real estate development company RK Centers announced this week it has purchased the shopping center at 235 Old Connecticut Path for $23 million from Regency Centers.
Ken Fries, director of acquisitions for RK Centers, said the company attempted to purchase the 80,000-square-foot shopping center last year. However, the owners had a deal with another company. That agreement fell through and RK Centers recently agreed to purchase the plaza.
"We resurrected the deal," said Fries.
The facility is anchored by Stop & Shop and also houses a liquor store, credit union and Sport Clips.
Changes to the plaza?
No immediate changes are expected at the facility. Company officials plan to meet with the tenants of the shopping center in the coming weeks and months to discuss their current and future needs. The company typically meets with tenants prior to making any changes at the site, said Fries.
The center does have 5,440 square feet of space for lease. More information is available at https://rkcenters.s3.amazonaws.com/New%20England/Framingham%20S%26S.pdf.
Continued acquisitions
RK Centers has completed more than $114 million in acquisitions the past 18 months, including investing in eight new properties totaling about 410,000 square feet of primarily open air regional and community shopping centers in New England and Florida.
"We're active," said Fries.
The company last year purchased a portion of the shopping center at 400 Cochituate Road – which abuts RK Centers' latest addition. That facility consists of approximately 178,000 square feet and houses Home Goods, Panera and Game Stop. RK Centers owns about 1.2 million square feet of retail space within 12 miles in the Framingham-Natick market.
More:The Framigham Mall has a new owner. What changes can shoppers expect?
"We like to own properties that are next to ones that we own," said Fries.
In the summer, RK Centers purchased a shopping center on Rte. 20 in Marlborough, which abuts the RK Center plaza, which opened in 1995 and is anchored by a Hannaford supermarket.
The new acquisition – dubbed RK Center II – is home to Chipotle, Mattress Firm, Great Clips, Subway and Sullivan Tire. There is more than 17,000 square feet available for lease.
More:A shopping center on Rte. 20 in Marlborough has a new owner. What changes are coming to the plaza?
The company is planning a rebranding effort at the RK Center II, which includes new signage and some new tenants in the near future. Fries said this summer he expects that plaza will be full by the middle of 2021.
Jeff Malachowski can be reached at 508-490-7466 or jmalachowski@wickedlocal.com. Follow him on Twitter @JmalachowskiMW.
© 2021 www.metrowestdailynews.com. All rights reserved.


Hlevel is proud to announce winning two design awards at this year's AIA SWFL Design Awards 2018.
The event was held at the historic and recently renovated site of The Sidney & Berne Davis Art Center, which is a must visit place in itself. The jury was nobody less than the renowned architecture firm Schulman & Associates from Miami (http://www.shulman-design.com/). We were looking forward to meeting and listening to Mr. Schulman's keynote speech but unfortunately, he had to cancel his appearance. We hope he can make it next time!
The Merit Award for Interior Design went to the Design for the new Pyure Organics HQ here in Naples, FL. We were fortunate to work with the owner on the renovation of an old warehouse and transform it into a trendy and fun workplace. The use of sustainable and organic materials was key to emphasize the company's mission to promote their mission of a healthier lifestyle. Btw, their Stevia-derived sugar substitute is going mainstream now and I spotted it in big chain stores. Way to go!
The Design Awards are given each year to AIA SWFL members to encourage excellence in architecture, to elevate public consciousness of good design, and to recognize those owners, designers, and contractors whose work enriches the built environment. The program recognizes both great design and outstanding individuals who contribute to the advancement of the profession.The list of all the winning projects and design awards will be posted on the local AIA SWFL site http://www.aiaflasw.org/ .


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Ephratah es un pueblo ubicado en el condado de Fulton en el estado estadounidense de Nueva York. En el año 2000 tenía una población de 1.693 habitantes y una densidad poblacional de 16.7 personas por km².

Geografía
Ephratah se encuentra ubicado en las coordenadas .

Demografía
Según la Oficina del Censo en 2000 los ingresos medios por hogar en la localidad eran de $33,810, y los ingresos medios por familia eran $36,324. Los hombres tenían unos ingresos medios de $28,566 frente a los $21,607 para las mujeres. La renta per cápita para la localidad era de $14,656. Alrededor del 15.3% de la población estaban por debajo del umbral de pobreza.

Referencias

Enlaces externos

Localidades del condado de Fulton (Nueva York)
Pueblos de Nueva York

redpajama_set_name: RedPajamaWikipedia


In a stand mixer bowl, stir together warm water and honey until the honey has dissolved. Add yeast and stir to combine. Allow to rest 5-10 minutes until yeast is foamy. Turn the mixer on low speed. Gradually add flour, baking powder, salt yogurt and egg. Increase speed to medium-low and continue mixing the dough for 2-3 minutes, or until the dough is smooth. Remove dough from the mixing bowl and use your hands to shape it into a ball. Grease the mixing bowl with cooking spray, then place the dough back in the bowl and cover with a damp towel. Place in a warm location and allow to rise for 1 hour, until the dough has nearly doubled in size. Once the dough is ready, transfer it to a floured work surface. Cut the dough into 5 separate pieces. Use your hands to spread dough piece so it is flat and ¼ inch thick. Heat a large cast iron skillet over medium-high heat. Add a piece of the rolled-out dough to the pan and cook for 1 minute, or until the dough begins to bubble and the bottoms turns lightly golden. Flip the dough and cook on the second side for 30-60 seconds, or until the bottom is golden. Transfer the naan to a separate plate and cover with a towel. Repeat until all pieces of naan are cooked. In the meantime, preheat the oven to 400 degrees. Place carrots, zucchini/squash, cauliflower and chickpeas on a large baking sheet and coat with olive oil. In a small bowl, mix together oregano, cumin, paprika, coriander, turmeric, salt, black pepper and crushed red pepper flakes. Sprinkle over vegetables and toss to coat. Roast for 20 minutes, or until tender and crispy. Spread hummus on each piece of naan. Top with roasted vegetables, olives, feta and fried egg (if using). Sprinkle with parsley and serve.


Every year as Halloween rolls around, we dust off the costumes, but when it comes to your children, do they get to choose their costume? The move to break gender barriers is on at even this young age, so let them choose what they want to be—boys can be Disney princesses and girls can be Spider-Man. Halloween is time for fun and anything goes. There's no need to draw gender lines when it comes to having fun with a kid's costume.
From a little girl who wanted to smash the gender barrier with her version of the Hulk costume to a young boy sporting Frozen's Elsa's costume, there's more to see below.
This little girl is a big fan of the Avengers, and her favorite is Hulk.
Even though Party City had a lot of princess costumes, this girl wanted to be Sully from Monsters Inc. She chose her costume from the boy's section.
A little girl would be lucky to have supportive parents who are okay with her liking superheroes.
For Halloween, this little girl wanted to be Shrek.
This little girl wanted to be Jack Skellington for Halloween.
This shows that girls can save themselves and not just have to wait for a knight to come along.
Darth Vader being carried around by her Storm Trooper dad.
Because Captain America wants to watch The Little Mermaid.
Let your child be their favorite character.
Two little girls decide to ignore the gender rules and dressed as Winter Soldier and Agent Phil Coulson.
"My daughter went as Ash Ketchum last year!" this girl's mom proudly says.
Girls can like reptiles too, and this grade schooler wanted to be the Crocodile Hunter.
Girls want to be Stormtroopers too.
This four-year-old little boy wanted to be his favorite character, Elsa.
Say hello to Spider-Man and her long, dangling earrings.
This girl wanted to wear her Rocket Raccoon costume early.
Buzz Lightyear to the rescue, with her headband and glittery, purple boots.
Darth Vader with Cinderella at her feet.
Superman taking a break with her drink.
Teenage Mutant Ninja Turtle's Leonardo gets a makeover.
This little girl obviously does not like girly costumes.
This beautiful girl is dressed as Iron Man.
Remember These Halloween Costume Ideas from the '80s and '90s?


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"DEADLY TEN wants you to Meet the Weedjies LIVE this Saturday 05/25!"
This past weekend, Full Moon was there (and hopefully, so were you!) for the LIVE casting session for DEADLY TEN's first feature film HALLOWEED NIGHT: MEET THE WEEDJIES. Did you catch it? Producer Charles Band and director Danny Draven ushered in a slew of LA's finest young actors, deliberating as to which of these lucky thespians would get the chance to star in our insane little movie. A cut-down highlights reel will appear on the site later this week. Check it out and stay tuned for the OFFICIAL final casting announcement coming soon!
Here's what's NEXT from DEADLY TEN:
THIS COMING SATURDAY - 05/25 - at 12 pm PST, DEADLY TEN dives back into the stream, giving fans an exclusive and LIVE peek behind the scenes of Tom Devlin's wild FX shop, where Tom will be in the final stages of creating the titular HALLOWEED NIGHT beasties themselves: THE WEEDJIES! Tom already has some of these cannabis-crazed inter-dimensional creatures produced, and you'll get your FIRST glimpses of what our new "ganja ghoulies" look like. AND we'll watch Tom deep in the process of MAKING a monster! All you have to do is visit www.DeadlyTen.com, sign up for FREE and you'll have instant FREE access to the weird "wizards behind the curtain" of not only this film, but ALL of the new genre films that will make up the DEADLY TEN roster!
ALSO don't forget that we've already cast a cavalcade of celebrity actors, oddballs and influencers to appear in the movie (check out that wild lineup HERE), and you can come hang out with all of them - and all of us - and actually BE IN the movie by contributing to our HALLOWEED NIGHT Indiegogo campaign! We'll put you up in the official Las Vegas HALLOWEED NIGHT hotel, you'll appear in the movie during the berserk party scene AND you can hang with us for a couple of days and party after the cameras have stopped rolling! Check out the campaign HERE. See you in Sin City!
Ten movies. Ten directors. Limitless possibilities. Join the DEADLY TEN action today!


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Meet us there
Learn about IAI
IAI H2O FOUNDATION
Clean Water Solutions
Contract Operations
Dredging & Dewatering
Contract Operations, Maintenance & Management
IAI offers integrated Contract Operations, Maintenance & Management Services to reduce operating costs and improve the performance of drinking water and wastewater treatment utilities. Our team of certified operators provides operations, maintenance and management services, with the support and added benefit of in-house engineering, mechanical maintenance, and construction management capabilities. Depending on the needs of the facility, our contract operations services may be provided on a short-term, technical assistance basis, or by long-term contract.
Certified Operators
IAI H2O FOUNDATION is Formed to Give Back
September 1, 2022 | Leave a Comment
Dana Trierweiler, P.E., IAI's President & CEO, has announced the formation of a 501(c)(3) charitable organization: the IAI H2O FOUNDATION. The foundation is fully funded by IAI and seeks to do good and promote both human and environmental causes in the communities where we work.
Lyons to Lead IAI's Engineering & Technical Services Division
February 9, 2022 | 4 Comments
Brad Lyons, P.E., and Emily Perrin, E.I.T., have recently joined the Engineering & Technical Services team at IAI, bringing new perspectives and energy to our water and wastewater engineering design and improvements projects. Read on to learn a little about Brad and Emily, and say hello, by dropping a note in the comments!
Baldwin WWTP Featured in Treatment Plant Operator Magazine
A recent upgrade to the headworks of the Baldwin Wastewater Treatment Plant, operated and maintained by IAI since 2017, has been featured in the September 2021 issue of Treatment Plant Operator magazine.
info@iaiwater.com
7888 Childsdale Ave. NE,
Rockford, Michigan 49341
Infrastructure Alternatives, Inc. is at Village of Parma.
IAI is proud to serve as the Engineer for the Village of Parma's upcoming wastewater pump stations and lagoons improvements. The project is explained in this article, featuring IAI Senior Project Engineer, Jill Harless, P.E. ... See MoreSee Less
$2M will help Parma upgrade wastewater treatment plant
www.mlive.com
The project will replace two pump stations, officials said.
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Since its establishment in 1988 by 40 founding members, the HRDF has developed, executed, implemented and also participated in a number of projects and activities at national and international levels on a wide and versatile range of issues. They include STIs & HIV/AIDS training; Information, Education and Communication (IEC); community-based reproductive health services; development of technical training materials for service providers; promoting children's rights; improving the socioeconomic status of women; orientation programs for refugees and post earthquake programs. Through these projects and activities, the HRDF has accumulated a remarkable experience and know-how in project development, implementation and assessment and also partnership and coordination skills with various international organizations. Since 1997, HRDF has been one of the internationally accredited executing agencies of UNFPA. Additionally, HRDF has developed and implemented programs that support asylum seekers, refugees and victims of human trafficking.


Four botanicals that will bring your Gin & Tonic to an entirely new level.
Packaged in glass tubes with cork, including a recipecard for the best combinations of gin, tonic and botanical.
Forbidden fruits: physalis, cinnamonapple, mulberry and goji berry.
Gentlemen's cut: cardamom, black malabarpepper, cassiabark and candied ginger.
Ladies kiss: rosebuds, limepomelo, coriander and juniper.


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< Anurag Behar
The storm in agriculture
September | 2010
We will have to make sustainable agriculture as big a global priority as countering terrorism or driving economic growth.
Whether Thomas Malthus will have the last laugh will be known in around 50 years. For most of the past few decades, powered by the confidence of the Green Revolution, we have been laughing at the Malthusian paranoia of population growth outstripping food production. World population has grown from around three billion in 1960 to around 6.8 billion today. But food production has kept pace.
Despite this achievement, the number of hungry, undernourished people in the world has grown from around 900 million to roughly one billion-a fall in the percentage, but an absolute increase. This is a failure, and most of us recognize it as such. Availability of food is not really the issue; it's a market and governance failure. And our slowness in solving the problem is strange and reprehensible.
This delay is not because of a lack of recognition of the problem. Globally, feeding the hungry is a key issue, not only for governments, but also for civil society. However slowly, the world's might is working on this, driven by ethical, political and emotional concerns.
Yet, most of us do not realize that this equilibrium on the food front, with one big recognized problem to solve (with seemingly known solutions), is the calm before a storm.
To peep into the eye of this storm, here's a thought experiment: Let's go back to 1960, and in that pre-Green Revolution world, look at ways to increase food production, with the knowledge that world population would increase by around four billion in 50 years. How would we feed the extra mouths?
Now let's impose some constraints on this experiment: As we try to boost food production, we cannot damage and deplete underground aquifers, nor overground water bodies, meaning we cannot draw more water than the rate of recharge. We cannot leach the soil. We cannot use fertilizers that increase the yield but pollute the life chain, damaging health, biodiversity and the soil. We cannot use pesticides that also pollute the life chain and environment, and eventually make the pests resistant. We cannot cut down more forests to increase agricultural land. We cannot mono-crop our farms, opening them to unknown risks. We cannot use so-called "high-yielding varieties", which are really "highly responsive varieties" - highly responsive to more irrigation and more fertilizers. We would still have to grow enough food for another four billion people.
But we did not do it this way. The Green Revolution had none of these constraints. In fact, world agriculture continues to operate with only tenuous consideration (if at all) for these issues.
But we have no choice but to have these constraints. That's why the storm is brewing. The damage to environment and life from irrigation-profligate, fertilizer- and pesticide-intensive, mono-cropped, land-hungry agriculture has made feeding 6.8 billion mouths unsustainable. We do not see this deep damage every day; and so, we never ask the question-"how can we feed the 6.8 billion, with no damage to life and environment?" In fact, some of the key architects of the Green Revolution were the first to point out these problems with the way the Revolution actually unfolded.
To sense the full intensity of this brewing storm, we need to consider three more crucial (and closely entwined) fronts.
First, world population will grow to around nine billion by 2050. So this "constrained" agriculture-let's call it sustainable agriculture-will have to produce enough food for all these people. As of now, we don't even know how to do it for the 6.8 billion.
Second, we have to consider both the cyclical effects of current agriculture methods on climate change and vice versa. Depending on how you measure it, between 15% and 20% of man's greenhouse gas (GHG) footprint comes from agriculture-around the same amount that comes from industry.
Estimates vary, but there seems to be reasonable consensus that climate change will affect - though unevenly - global crop yields. There will be a significant fall in yields, without factoring in the effect of the chronic water scarcity that will develop.
Third, as populations grow out of poverty (around three billion people over the next few decades), and become wealthier, the demand profile of food changes, accordingly driving a change in agriculture output. The shift is to more protein-intensive food, i.e., from grains to meat and milk-based products. This significantly increases the ecological strain from agriculture. For example, the GHG footprint of the average Indian food basket is less than 1 tonne per capita, and that of the average American around 8 tonnes per capita.
The minority conscious of this brewing storm believes that with intense effort, we can deal with it, because we have the understanding and the technology. But how can this happen, when the majority of us are not even conscious of the problem? Place that in the context of how long it is taking to solve the one problem regarding food that we recognize globally - that of feeding the hungry billion.
If we don't want Malthus to have the last laugh, we will have to make sustainable agriculture (what that could be is the subject of another column) as big a global priority as countering terrorism or driving economic growth.
Anurag Behar is the Chief Sustainability Officer of Wipro Limited, CEO for Azim Premji Foundation & Vice Chancellor, Azim Premji University. The Foundation and the University established by it are not-for-profit organizations committed to the vision of "contributing towards a just, equitable, humane and sustainable society". They run institutions and programs in India for improving school education and in related fields of human development. The field work of the Foundation is in collaboration with various state governments, to help improve equity and quality of the public education system. The current geographical focus of this work is in 7 states of India, which have over 350,000 schools. The University's teaching and research programs are also focused on the fields of Education and Development.
Anurag has been closely involved with efforts to improve education in India for the past eleven years. He has been a vocal advocate for the critical importance of public systems, in particular the public education system. His years in business have given him an insider's view in to both the possibilities and limits of markets. For the past few years he has also been engaged with environmental and ecological issues. He writes a fortnightly column for the newspaper Mint, on Education and Ecology, available on www.livemint.com.
He has led the social and ecological initiatives of Wipro Ltd for the past eleven years. He continues to provide oversight to this work as the Chief Sustainability Officer of Wipro.
Anurag has earlier played leadership roles in business. As the CEO of Wipro Infrastructure Engineering, he led the business from being No. 20 in the world to being the No. 1 in 5 years. The business has operations in Europe, India, Brazil and China. He led Wipro's investments in two strategic diversifications - in the Clean Energy and Water sectors. Earlier he has been responsible for multiple functions of Wipro including Brand, Quality and Innovation. He has also worked with GE Medical Systems, including being part of the team that built the leadership position of Wipro GE Healthcare in South Asia.
Anurag has served on the Board of Wipro GE Healthcare Ltd and of the TERI University. He serves on various government & industry councils, such as the National Mission on Teachers and Teacher Education, the Government of India implementation committee for the Justice Verma Commission, and with the CII's National Climate Change Council. He has been honored by the World Economic Forum, by being recognized as a 'Young Global Leader'.
He has an MBA from XLRI, Jamshedpur and a BE in Electrical & Electronics Engineering from National Institute of Technology, Trichy. He enjoys long distance running.


At the point when genuine fluid streams past a solid body or a solid boundary wall, the fluid particles adhere to the wall and state of no slip happens. This implies that the velocity of fluid near to the wall will be same as that of wall. On the off chance that the wall is stationary, the speed of fluid at the boundary will be zero. Further far from the limit, the velocity will be higher and as a consequence of this variety of velocity, and gradient of velocity will exist. The speed of fluid increments from zero on the stationary limit to the free stream velocity of the fluid in the direction normal to the boundary. This velocity from zero to free stream velocity in the perpendicular direction to the wall happens in a restricted locale in the region of solid boundary. This narrow locale of fluid is called Boundary Layer. Three fundamental parameters (portrayed underneath) that are utilized to describe the size and state of a boundary layer are the nominal boundary layer thickness, the displacement thickness, and the momentum thickness. In our proposition, we have gotten the boundary layer parameters and velocity profiles on different types of rough surfaces by using wind tunnel. The emery papers of distinctive grain sizes have been considered as rough surfaces. This paper summarizes a select set of recent investigations involving the computations of effects of roughness, mainstream velocity and distance from leading edge on turbulent boundary layer along with the correlations.
Surface Roughness, Velocity Profile, Boundary layer, Turbulent Flow, Correlation, Wind Tunnel.


During this Project, a downlink cellular traffic offloading framework with social-aware device-to-device (D2D) content sharing and proactive caching is studied. Within the considered system model, each user equipment (UE) is intelligent to determine which content(s) to request/cache and to share in step with its own preference. Because the central controller, the bottom station (BS) will establish cellular transmissions and/or incentivize D2D communications for content dissemination (as well as proactive caching). By taking into consideration wireless options, social characteristics, and device intelligence, we tend to formulate a welfare maximization problem integrating power management, channel allocation, link scheduling, and reward style. To resolve this complicated drawback, we propose a completely unique mechanism that consists of a newly developed optimization approach, called basis transformation method, for the joint resource management, and a specially devised pricing scheme for the reward determination. Theoretical and simulation results examine the specified properties of our proposed mechanism, and demonstrate its superiority in improving social welfare, network capacity, and utility of the BS.


Someone in the IRC room spoke of a forum that was once written in under 2 KB of code. A simple minimalistic forum that had no user account system, but still had enough functionality to support the notion of threads and posts.
Almost jokingly, I said I bet I could do it in 1KB. But I gave it a shot anyway, and behold, here it is, slightly under 1KB at 964 bytes!
It even creates the schema the first time you access the script. Of course you have to first have a database called 'd' and update the MySQL account credentials at the beginning to match your own. Magic quotes need to be enabled to prevent SQL injection!
I have this script running here if you want to see what it looks like in action. You'll have to pardon the graffiti, though. As you can imagine there is no such thing as a moderator on this forum.


Members of the city's Sikh community were at the Calgary airport on Tuesday to welcome the first two families out of an eventual 65 who are coming to Canada as refugees from Afghanistan, where they faced religious persecution.
The Manmeet Singh Bhullar Foundation is spearheading the effort to help the Sikh and Hindu families get out of Afghanistan, with support from community members and the World Sikh Organization of Canada.
"Sikhs and Hindus have endured increasing religious persecution and today face a difficult if not unlivable situation in many parts of Afghanistan," the WSO said in a release.
..."They were just happy to leave Afghanistan and that their life is saved. They're happy to practise their religion, out in the open," she said.
"They didn't have any human rights there. They weren't allowed to even leave their houses."


text:
\section{Introduction}
\setcounter{equation}{0}

String theory as a possible candidate for unification of all known interactions offers a framework for description of both gauge interactions and gravity. Analyzing the relation between world-sheet diffeomorphisms and transformations of the background fields for open bosonic string \cite{mebo1, mebo2, ljdbs} it is concluded that Kalb-Ramond field gets one additional term that is in fact a field strength of some gauge field. In sigma-model action it looks like that gauge fields are attached at the string endpoints moving along $Dp$-brane. Finiteness of the gauge theories (UV cutoff) demands existence of some minimal length. Consequently, noncommutativity naturally arose in open bosonic string theory in the presence of the constant background fields \cite{open string non-commutativity, sazda1, sazda2, sazda3}.

The fact that noncommutativity appears together with gauge theory produces a new line of investigation in quantum field theory - noncommutative gauge theories \cite{nc1, nc2, nc3}, but not noncommutative gravity.

The open bosonic string in the presence of the constant background fields gives constant noncommutativity \cite{open string non-commutativity, sazda1, sazda2, sazda3}, but, consequently, Jacobi identity is zero and associativity is not broken. Closed string in the presence of the constant background fields remains commutative.

Noncommutativity in open string theory comes from the boundary conditions (see \cite{sazda1, sazda2, sazda3}). Coordinates and their canonically conjugated momenta are mixed in the boundary conditions, and because they obey standard Poisson algebra, at the end we get noncommutativity of the initial coordinates. All these facts tell us about the way how we can reach noncommutativity in the bosonic closed string case. Kalb-Ramond field must be, at least, linearly coordinate dependent, and the generalized T-dualization procedure is a machinery \cite{T-duality explained 1, T-duality explained 2, Luest T-duality and geometry, T-duality procedure 1, T-duality procedure 2, Generalized Buscher procedure, Gereralized Buscher procedure 2, Generalized Buscher procedure 3, Auxiliary action Buscher procedure}. The noncommutativity relations are coordinate dependent and produce nonzero Jacobi identity - nonassociativity appears in the closed string theory \cite{Luest T-duality and geometry, Inversion of equations of motion, Generalized Buscher procedure 3, nasrad1, nasrad2}.

The noncommutativity and nonassociativity can be considered also within superstring theory \cite{book1, book2}. In Ref.\cite{nasrad3} we considered one special case of the type II superstring theory in pure spinor formulation \cite{pure spinor formalism papers 1, pure spinor formalism papers 2, pure spinor formalism papers 3, pure spinor formalism papers 4, Vertex operators} - all physical background fields are constant except Ramond-Ramond (RR) field strength. The RR field strength consists of the constant part and linearly coordinate dependent one, which is infinitesimal. In accordance with consistency conditions, we have chosen constant part of RR field strength to be symmetric and cooordinate dependent part to be antisymmetric tensor.

The motivation for this choice of background fields is the quest for the anticommutation relation between fermionic coordinates suggested in \cite{Vertex operators, original paper 2}. Formally, this case is similar to the bosonic string case with coordinate dependent Kalb-Ramond field (weakly curved background). The difference is that in the superstring case noncommutativity parameter depends both on the bosonic and fermionic coordinates. Also we obtained that Jacobiator is nonzero. Both noncommutativity and nonassociativity parameters are proportional to the infinitesimal tensor from RR field strength.

In this article we consider the same action as in \cite{nasrad3}, but we will not imply the additional restrictions on the constant and coordinate dependent part of RR field strength as in \cite{nasrad3}. The fundamental difference in relation to the choice of background field in \cite{nasrad3} is in the fact that action with RR field strength without restrictions does not possess translational isometry. In that sense this case can be considered as general one comparing with \cite{nasrad3}.

We will use the generalized T-dualization procedure \cite{Generalized Buscher procedure, Auxiliary action Buscher procedure} along bosonic directions. Because this general case cannot be deduced to the form of the bosonic string with linearly dependent Kalb-Ramond field, as it could in the case \cite{nasrad3}, we obtained more complicated form of T-dual transformation laws and, consequently, the generalization of $\beta_\mu$ functions in the form of $N(\xi)$ functions. Besides the complexity of the T-dual transformation laws we succeeded to find expressions for noncommutativity and nonassociativity as well as the form of the T-dual theory.

At the end we give some concluding remarks.
In the appendices we present the derivation of $N(\xi)$ functions and show their properties.

\section{General type II superstring action and  choice of background fields}
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In this section we will shortly present how we derive the action of type II superstring in pure spinor formulation with all constant background fields except RR field strength from the general form of that action given in \cite{Vertex operators, pure spinor formalism papers 1, pure spinor formalism papers 2, pure spinor formalism papers 3, pure spinor formalism papers 4}.

\subsection{General form of the pure spinor type II superstring action}

The general form of the type II superstring action in pure spinor formalism is derived and given in \cite{Vertex operators}. It consists of two parts and can be represent as their sum
\begin{equation}
S=S_0 + V_{SG}\, ,
\end{equation}
where $S_0$ describes the motion of string in flat background
\begin{equation} \label{S_0 action}
S_0 = \int_{\Sigma}d^2 \xi \left( \frac{k}{2} \eta_{ \mu \nu } \partial_m x^\mu \partial_n x^\nu \eta^{m n} - \pi_\alpha \partial_- \theta^\alpha + \partial_+ \bar{\theta}^\alpha \bar{\pi}_\alpha \right)
+S_\lambda +S_{ \bar{\lambda} }\, ,
\end{equation}
while the second one contains all possible interactions
\begin{equation}
V_{SG} =  \int_{\Sigma}d^2 \xi (X^T)^M A_{MN} \bar{X}^N.
\end{equation}
The second part of the action is expressed in terms of the integrated form of massless type II supergravity vertex operator $V_{SG}$. The actions $S_{\lambda}$ and $S_{\bar{\lambda}}$ in (\ref{S_0 action}) are {free-field} actions for pure spinors
 \begin{equation}
 S_\lambda = \int d^2 \xi \omega_\alpha \partial_- \lambda^\alpha, \quad S_{\bar{\lambda}} = \int d^2 \xi \bar{\omega}_\alpha \partial_+ \bar{\lambda}^\alpha\, .
 \end{equation}
Here, $\lambda^\alpha$ and $\bar{\lambda}^\alpha$ are pure spinors whose canonically conjugated momenta are $\omega_\alpha$ and $\bar{\omega}_\alpha$, respectively.

The vectors $X^M$ and $X^N$ and matrix $A_{MN}$ are of the form
\begin{equation}
X^M = \left(\begin{matrix}
\partial_+ \theta^\alpha\\
\Pi_+^\mu\\
d_\alpha\\
\frac{1}{2} N_+^{\mu \nu}
\end{matrix} \right),
\quad \bar{X}^M = \left( \begin{matrix}
\partial_- \bar{\theta}^\lambda\\
\Pi_-^\mu\\
\bar{d}_\lambda\\
\frac{1}{2} \bar{N}_-^{\mu \nu}
\end{matrix} \right), \quad
A_{MN} = \begin{bmatrix}
A_{\alpha \beta} & A_{\alpha \nu} & {E_\alpha}^\beta & \Omega_{\alpha, \mu \nu} \\
A_{\mu \beta} & A_{\mu \nu} & \bar{E}_\mu^\beta & \Omega_{\mu, \nu \rho}\\
{E^\alpha}_\beta & E_\nu^\alpha & P^{\alpha \beta} & {C^\alpha}{}_{\mu \nu}\\
\Omega_{\mu \nu, \beta} & \Omega_{\mu \nu, \rho} & {\bar{C}^{\beta}{}_{\mu \nu}} & S_{\mu \nu, \rho \sigma}
\end{bmatrix},
\end{equation}
where notation is taken from Refs.\cite{Vertex operators, nasrad3}. Every component of the matrix $A_{MN}$ is function of bosonic, $x^\mu$, and fermionic, $\theta^\alpha$ and $\bar{\theta}^\alpha$, coordinates. For more details about derivation of the components consult \cite{Vertex operators}. The superfields $A_{\mu \nu}$, $\bar{E}_\mu^\alpha$, $E_\mu^\alpha$ and $P^{\alpha \beta}$ are known as physical superfields, superfields that are in the first row and the first column are known as auxiliary because they can be expressed in terms of physical ones \cite{Vertex operators}. Remaining superfields $\Omega_{\mu, \nu \rho}\  (\Omega_{\mu \nu, \rho})$, $C^\alpha{}_{\mu \nu}\  ({\bar{C}^\beta{}_{\mu\nu}})$ and $S_{\mu\nu,\rho\sigma}$, are curvatures (field strengths) for physical fields.   Components of $X^M$ and $\bar{X}^N$ are of the form
\begin{equation}
\Pi_+^\mu = \partial_+ x^\mu + \frac{1}{2}\theta^\alpha (\Gamma^\mu)_{\alpha \beta}\partial_+\theta^\beta, \quad
\Pi_-^\mu = \partial_- x^\mu + \frac{1}{2} \bar{\theta}^\alpha (\Gamma^\mu)_{\alpha \beta} \partial_- \bar{\theta}^\beta,
\end{equation}

\begin{align}
d_\alpha &= \pi_\alpha - \frac{1}{2} (\Gamma_\mu \theta)_\alpha \left[ \partial_+ x^\mu +\frac{1}{4} (\theta \Gamma^\mu \partial_+ \theta)
\right],  \nonumber\\
\bar{d}_\alpha &= \bar{\pi}_\alpha - \frac{1}{2}(\Gamma_\mu \bar{\theta})_\alpha \left[ \partial_- x^\mu +\frac{1}{4}(\bar{\theta} \Gamma^\mu \partial_- \bar{\theta} )
\right],
\end{align}

\begin{equation}
N_+^{\mu \nu} = \frac{1}{2} \omega_\alpha {( \Gamma^{[\mu\nu]}
)^\alpha}_\beta \lambda ^\beta, \quad \bar{N}_-^{\mu\nu} = \frac{1}{2} \bar{\omega}_\alpha {(  \Gamma^{ [\mu\nu ]  }     )^\alpha}_\beta \bar{\lambda}^\beta.
\end{equation}

 The world-sheet is spanned by $\xi^m = (\xi^0 = \tau, \xi^1 = \sigma)$, while world-sheet light-cone partial derivatives are defined as $\partial_\pm = \partial_\tau \pm \partial_\sigma$. Superspace contains bosonic $x^\mu \  (\mu = 0,1,...,9)$ and fermionic $\theta^\alpha,\  \bar{\theta}^\alpha \  (\alpha = 1,2,...,16)$ coordinates. Variables $\pi_\alpha$ and $\bar{\pi}_\alpha$ are canonically conjugated momenta to the fermionic coordinates $\theta^\alpha$ and $\bar{\theta}^\alpha$, respectively.

 \subsection{Choice of the background fields}

 In this particular case we will use the supermatrix $A_{MN}$ where all physical background fields, except RR field strength $P^{\alpha \beta}$, are constant. RR fields strength will have linear coordinate dependence on bosonic coordinate $x^\mu$. Consequently, supermatrix $A_{MN}$ is of the following form

 \begin{equation}
 A_{MN} = \begin{bmatrix}
 0 & 0 & 0 & 0 \\
 0 & k(\frac{1}{2}g_{\mu \nu} + B_{\mu \nu}) & \bar{\Psi}_\mu^\beta & 0\\
 0 & -\Psi_\nu^\alpha & \frac{2}{k}(f^{\alpha\beta} + C_\rho^{\alpha\beta} x^\rho)& 0\\
 0 & 0 & 0 & 0
 \end{bmatrix},
 \end{equation}
where $g_{\mu \nu}$ is symmetric tensor, $B_{\mu \nu}$ is Kalb-Ramond antisymmetric field, $\Psi_\mu^\alpha$ and $\bar{\Psi}_\mu^\alpha$ are Mayorana-Weyl gravitino fields and $f^{\alpha \beta}$ and $C_\rho^{\alpha \beta}$ are constant tensors. Let us stress this will be a classical analysis and we will not calculate the dilaton shift under T-duality transformation.

From the consistency conditions given in Ref.\cite{Vertex operators}, following this choice of background fields, it follows
\begin{align} \label{constraint}
\gamma^\mu_{\alpha \beta} C_\mu^{\beta \gamma} = 0, \quad \gamma^\mu_{\alpha \beta} C_\mu^{\gamma \beta} = 0.
 \end{align}

Because all background fields are expanded in powers of $\theta^\alpha$ and $\bar\theta^\alpha$, $\theta^{\alpha}$ and $\bar{\theta}^{\alpha}$ terms in $X^M$ and $\bar{X}^N$ will be neglected. Taking into account all imposed assumptions and approximations, the full action $S$ is getting the form
\begin{equation}\label{Action full S}
\begin{gathered}
S        =          \int_{\Sigma}   d^2   \xi          \left[     \frac{k}{2}   \Pi_{ +\mu \nu } \partial_+   x^\mu  \partial_-   x^\nu          -           \pi_\alpha  ( \partial_-   \theta^\alpha   +   \Psi_\nu^\alpha   \partial_-  x^\nu )   +              (   \partial_+   \bar{ \theta }^\alpha +   \partial_+   x^\mu \bar{ \Psi }_\mu^\alpha  )   \bar{ \pi }_\alpha    \right.\\
\left.             +          \frac{2}{k} \pi_\alpha   (   f^{ \alpha\beta }   +C_\rho^{\alpha\beta} x^\rho   ) \bar{ \pi }_\beta          \right],
\end{gathered}
\end{equation}
where $\Pi_{ \pm \mu \nu } = B_{\mu \nu} \pm \frac{1}{2} G_{\mu \nu}$, and $G_{\mu \nu} = \eta_{\mu \nu} + g_{\mu \nu}$ is metric tensor. The actions $S_{\lambda}$ and $S_{\bar{\lambda}}$ are fully decoupled from the rest and they will not be analyzed from now on.

It is easy to notice that fermionic momenta play the roles of the auxiliary fields in full action. They can be integrated out finding equations for motion for both $\pi_\alpha$ and $\bar{ \pi }_\alpha$

\begin{alignat}{2} \label{Equations for fermionic momenta 1}
\bar{ \pi }_\beta   &   =
&&\frac{k}{2}
\left( F^{-1}  (x)   \right)_{ \beta \alpha}
\left(       \partial_- \theta^\alpha     +    \Psi_\nu^\alpha    \partial_-   x^\nu     \right) , \\
\label{Equations for fermionic momenta 2}
\pi_\alpha    &   =
-   &&\frac{k}{2}
\left(     \partial_+   \bar{ \theta }^\beta     +     \partial_+   x^\mu    \bar{ \Psi }_\mu^\beta   \right)
\left( F^{-1}  (x)   \right)_{ \beta \alpha} \, ,
\end{alignat}
where $F^{\alpha\beta}(x)$ and $(F^{-1}(x))_{\alpha\beta}$ are of the form
\begin{equation}
F^{\alpha\beta}(x)=f^{\alpha\beta}+C_\mu^{\alpha\beta} x^\mu\, ,\quad (F^{-1}(x))_{\alpha\beta}=( f^{ -1 } )_{ \alpha\beta }  - ( f^{ -1 } )_{ \alpha\alpha_1 }   C_\rho^{\alpha_1 \beta_1}    x^\rho   ( f^{ -1 } )_{ \beta_1\beta }\, .
\end{equation}
For practical reasons, we assume that $C^{\alpha\beta}{}_\mu$ is infinitesimal. This assumption is in accordance with constraints (\ref{constraint}).
Substituting equations (\ref{Equations for fermionic momenta 1}) and (\ref{Equations for fermionic momenta 2}) into (\ref{Action full S}) the final form of action is

\begin{align} \label{Action final S}
S       =
k    \int_{\Sigma}    d^2    \xi
\left[     \Pi_{ +\mu \nu }   \partial_+     x^\mu    \partial_-   x^\nu
+     \frac{1}{2}      (  \partial_+  \bar{ \theta }^\alpha  +   \partial_+   x^\mu   \bar{ \Psi }_\mu^\alpha     )
\left( F^{-1}  (x)   \right)_{ \alpha\beta }
(    \partial_-    \theta^\beta      + \Psi_\nu^\beta      \partial_-  x^\nu         )
\right] .
\end{align}
Let us note that we did not impose any conditions on tensors $f^{\alpha\beta}$ and $C^{\alpha\beta}_\mu$ as we did in Ref.\cite{nasrad3}. The case considered in this article is more general than the case studied in \cite{nasrad3}, because action does not possess translational symmetry.

\section{T-dualization}
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Here we will make T-dualization of all bosonic directions aiming to find T-dual transformation laws - relations between T-dual coordinates and canonical variables of the original theory. The T-dual transformation laws will be used to calculate Poisson brackets of the T-dual coordinates.

\subsection{Implementation of the generalized T-dualization procedure}

In implementing of T-dualization procedure we will use {\it generalized Buscher T-dualization procedure} \cite{Generalized Buscher procedure}. The standard Buscher procedure \cite{T-duality procedure 1,T-duality procedure 2} is made to be used along directions on which background fields do not depend (isometry directions), while generalized Buscher procedure can be applied to theories with coordinate dependent background fields along all directions. The generalized T-dualization procedure follows three steps - introduction of covariant derivatives, invariant coordinates and additional gauge fields, which produces additional degrees of freedom. The starting and T-dual theory must have the same number of degrees of freedom. In order to achieve that we eliminate all excessive degrees of freedom demanding that field strength of gauge fields $(F_{+ -} = \partial_+ v_- - \partial_- v_+)$ vanishes by addition of Lagrange multipliers. Then we fix the gauge symmetry (shift symmetry) and action is left with gauge fields and their derivatives. Finding equations of motion for gauge fields, expressing in terms of the Lagrange multipliers and inserting those equations into action we obtain T-dual action, where Lagrange multipliers have roles of T-dual coordinates.

T-duality can be performed also in the cases of the absence of shift symmetry \cite{Auxiliary action Buscher procedure}. Then we replace original action with translation invariant auxiliary action. Form of the auxiliary action is exactly the same as the form of action where translation symmetry was localized and gauge fixed. It produces correct T-dual theory only if original action can be salvaged from it.

Action (\ref{Action final S}) is not translational invariant. Consequently, we make the following substitutions

\begin{alignat}{2}
&\partial_\pm x^\mu     &&\rightarrow       v_\pm^\mu, \\
&x^\rho                  &&\rightarrow       \Delta V^\rho    =     \int_{P} d { \xi^\prime }^m v_m^\rho (\xi^\prime)\label{V expresion},\\
&S                    &&\rightarrow     S  +  \frac{k}{2}    \int_{\Sigma}       d^2       \xi          \left[ v_+^\mu \partial_- y_\mu   -  v_-^\mu   \partial_+ y_\mu
\right],
\end{alignat}
and insert them in action (\ref{Action final S}). The result is auxiliary action convenient for T-dualization procedure
\begin{equation}\label{Auxiliary action S_{aux}}
\begin{gathered}
S_{aux}       =    k    \int_{\Sigma}    d^2    \xi
\left[ \Pi_{ +\mu \nu } v_+^\mu v_-^\nu    +    \frac{1}{2} (      \partial_+     \bar{ \theta }^\alpha      +     v_+^\mu    \bar{ \Psi }_\mu^\alpha     )         \left( F^{-1}  ( \Delta V )   \right)_{ \alpha\beta }   (      \partial_-\theta^\beta     + \Psi_\nu^\beta  v_-^\nu       ) \right. \\
\left.  +      \frac{1}{2}(     v_+^\mu    \partial_- y_\mu           -         v_-^\mu       \partial_+      y_\mu       )
\right].
\end{gathered}
\end{equation}
Let us note that path $P$ starts from $\xi_0$ and ends in $\xi$. In this way action becomes non-local.

Finding equations of motion for Lagrange multipliers

\begin{equation} \label{x form v}
\partial_- v_+^\mu - \partial_+ v_-^\mu = 0 \quad v_\pm^\mu = \partial_\pm x^\mu,
\end{equation}
and inserting them into (\ref{V expresion}) we have
\begin{equation} \label{X from V}
\Delta V^\rho = \int_{P} d { \xi^\prime }^m \partial_m x^\rho (\xi^\prime) = x^\rho (\xi) - x^\rho (\xi_0) = \Delta x^\rho.
\end{equation}
In absence of translational symmetry, in order to extract starting action from auxiliary one, we impose $x^\rho (\xi_0) =0$ as a constraint. Taking all this into account, we get the starting action (\ref{Action final S}).

Euler-Lagrange equations of motion for gauge fields $v_\pm(\kappa)$ give the following ones

\begin{align} \label{eq of motion for v_+}
\begin{gathered}
-\frac{1}{2}   \partial_- y_\mu  (\kappa)   =
\Pi_{ +\mu \nu }   v_-^\nu (\kappa)  +
\frac{1}{2}  \bar{ \Psi }_\mu^\alpha     \left( F^{-1}  ( \Delta V )   \right)_{ \alpha\beta }
(    \partial_-  \theta^\beta  (\kappa)     +  \Psi_\nu^\beta v_-^\nu  (\kappa)  )  \\
- \frac{1}{2}        \int_{\Sigma}           d^2          \xi
\big[    \partial_+     \bar{ \theta }^\alpha (\xi)     +     v_+^{\nu_1}  (\xi)   \bar{ \Psi }_{\nu_1} ^\alpha    \big]
( f^{ -1 } )_{ \alpha\alpha_1 }     C_\mu^{\alpha_1 \beta_1}      ( f^{ -1 } )_{ \beta_1\beta }
N (\kappa^+) \big[     \partial_-\theta^\beta (\xi)    + \Psi_{\nu_2} ^\beta  v_-^{\nu_2}   (\xi)     \big], \\
\end{gathered}\\
\begin{gathered}
\frac{1}{2} \partial_+ y_\mu  (\kappa)  =
\Pi_{ +\nu \mu }  v_+^\nu (\kappa)
+\frac{1}{2}    (    \partial_+  \bar{ \theta }^\alpha  (\kappa)  +  v_+^\nu (\kappa)  \bar{ \Psi }_\nu^\alpha  )    \left( F^{-1}  ( \Delta V )   \right)_{ \alpha\beta }   \Psi_\mu^\beta  \\
- \frac{1}{2}        \int_{\Sigma}           d^2          \xi
\big[    \partial_+     \bar{ \theta }^\alpha (\xi)     +     v_+^{\nu_1}  (\xi)   \bar{ \Psi }_{\nu_1} ^\alpha    \big]
( f^{ -1 } )_{ \alpha\alpha_1 }     C_\mu^{\alpha_1 \beta_1}      ( f^{ -1 } )_{ \beta_1\beta }
N (\kappa^-)  \big[     \partial_-\theta^\beta (\xi)    + \Psi_{\nu_2} ^\beta  v_-^{\nu_2}  (\xi)     \big].
\end{gathered} \label{eq of motion for v_-}
\end{align}
Here, function $N(\kappa^\pm)$ is obtained from variation of term containing $\Delta V^\rho$ in expression for $ F^{-1}  ( \Delta V )$ (details are presented in Appendix \ref{appendix A}). They represent the generalization of beta functions introduced in Ref.\cite{nasrad3}

\begin{align}
N({\kappa^+}) =&
\delta      \Big(      { \xi^\prime }^- \big( ( { { \xi^\prime }^+ })^{-1}
(\kappa^+) \big)   - \kappa^-
\Big)
\left[    H( \xi^+   - \kappa^+  )  -  H(\xi_0^+    -   \kappa^+)    \right], \\
N(\kappa^-)
=&
\delta      \Big(      { \xi^\prime }^+ \big( ( { { \xi^\prime }^- })^{-1}
(\kappa^-) \big)   - \kappa^+
\Big)
\left[    H( \xi^-   - \kappa^-  )  -  H(\xi_0^-    -   \kappa^-)    \right],
\end{align}
where more details on Dirac delta function and step function are given in Appendix \ref{appendix A}. As we see the expressions for derivatives of $y_\mu$ are more complex comparing with those in \cite{nasrad3}, where translational symmetry is present.

Assuming that $C_\mu^{\alpha \beta}$ is an infinitesimal, we can iteratively invert equations of motion (\ref{eq of motion for v_+}) and (\ref{eq of motion for v_-}) \cite{Inversion of equations of motion}. Separating variables into two parts, one finite and one infinitesimal proportional to $C_\mu^{\alpha \beta}$, we have

\begin{align}
\label{v_-^n as function of y}
\begin{gathered}
v_-^\nu  (\kappa)        =
-   \frac{1}{2}  \bar{\Theta}_-^{\nu \nu_1}
\Bigg\{ \Bigg.
\partial_-     y_{\nu_1}  (\kappa)       +     \bar{ \Psi }_{\nu_1}^\alpha     ( F^{ -1 } ( \Delta V  ) )_{\alpha\beta}   \partial_-   \theta^\beta (\kappa)
 \\
\begin{aligned}
&+ \frac{1}{2}  \Psi_{\nu_1}^\alpha  ( f^{- 1 } )_{ \alpha\alpha_1 }  C_\rho^{\alpha_1 \alpha_2} \Delta V^\rho ( f^{- 1 } )_{ \alpha_2\alpha_3 }     \Psi_{\nu_2}^{\alpha_3}   \bar{\Theta}_-^{\nu_2 \nu_3}
\Big(   \partial_-  y_{\nu_3} (\kappa)   + \bar{ \Psi }_{\nu_3} ^{ \beta_1 }     ( f^{- 1 } )_{ \beta_1\beta }      \partial_-    \theta^{ \beta } (\kappa)  \Big)   \\
&-       \int_{\Sigma}          d^2 \xi
\Big[    \partial_+     \bar{ \theta }^\alpha (\xi)     +     \frac{1}{2} \Big( \partial_+ y_{\mu_1} (\xi) -  \partial_+ \bar{ \theta }^{\gamma_1} (\xi)  ( f^{- 1 } )_{ \gamma_1\gamma_2 } \Psi_{\mu_1}^{\gamma_2}
\Big)  \bar{\Theta}_-^{\mu_1 \nu_1}
\bar{ \Psi }_{\nu_1} ^\alpha    \Big] ( f^{ -1 } )_{ \alpha\alpha_1 }     C_{\nu_1}^{\alpha_1 \beta_1}  \\
&\quad\times ( f^{ -1 } )_{ \beta_1\beta }
N (\kappa^+)
\Big[     \partial_-\theta^\beta (\xi)    -\frac{1}{2} \Psi_{\nu_2} ^\beta \bar{\Theta}_-^{\nu_2 \mu_2}
\Big( \partial_- y_{\mu_2} (\xi) + \bar{ \Psi }_{\mu_2}^{\gamma_3}  ( f^{- 1 } )_{ \gamma_3\gamma_4 } \partial_- \theta^{\gamma_4}  (\xi)
\Big)
\Big] \Bigg. \Bigg\},
\end{aligned}
\end{gathered} \\
\label{v_+^n as function of y}
\begin{gathered}
 v_+^\mu (\kappa)  =
\frac{1}{2} \bar{\Theta}_-^{\mu_1 \mu}
\Bigg\{ \Bigg.
\partial_+   y_{\mu_1}    (\kappa)   -      \partial_+ \bar{ \theta }^\alpha (\kappa) ( F^{ -1 } ( \Delta V  ) )_{\alpha\beta} \Psi_{\mu_1}^\beta
 \\
\begin{aligned}
&+\frac{1}{2} \Big( \partial_+    y_{\mu_2} (\kappa)     -   \partial_+   \bar{ \theta }^\alpha (\kappa)  ( f^{- 1 } )_{ \alpha\alpha_1 } \Psi_{\mu_2}^{\alpha_1}     \Big)
\bar{\Theta}_-^{\mu_2 \mu_3}
\bar{ \Psi }_{\mu_3}^{\beta_3}     ( f^{- 1 } )_{ \beta_3\beta_2 } C_\rho^{\beta_2 \beta_1} \Delta V^\rho ( f^{- 1 } )_{ \beta_1\beta }     \Psi_{\mu_1}^{\beta}  \\
&+       \int_{\Sigma}          d^2 \xi
\Big[    \partial_+     \bar{ \theta }^\alpha (\xi)     +     \frac{1}{2} \Big( \partial_+ y_{\mu_2} (\xi) -  \partial_+ \bar{ \theta }^{\gamma_1} (\xi)  ( f^{- 1 } )_{ \gamma_1\gamma_2 } \Psi_{\mu_2}^{\gamma_2}
\Big)  \bar{\Theta}_-^{\mu_2 \nu_1}
\bar{ \Psi }_{\nu_1} ^\alpha    \Big] ( f^{ -1 } )_{ \alpha\alpha_1 }     C_{\mu_1}^{\alpha_1 \beta_1}     \\
&\quad\times ( f^{ -1 } )_{ \beta_1\beta }
N (\kappa^-)
\Big[     \partial_-\theta^\beta (\xi)    -\frac{1}{2} \Psi_{\nu_2} ^\beta \bar{\Theta}_-^{\nu_2 \mu_3}
\Big( \partial_- y_{\mu_3} (\xi) + \bar{ \Psi }_{\mu_3}^{\gamma_3}  ( f^{- 1 } )_{ \gamma_3\gamma_4 } \partial_- \theta^{\gamma_4}  (\xi)
\Big)
\Big] \Bigg. \Bigg\}.
\end{aligned}
\end{gathered}
\end{align}
Tensor $\bar{\Theta}_-^{\mu\nu}$ is inverse tensor to $\bar{\Pi}_{+\mu\nu} = \Pi_{ +\mu \nu } + \frac{1}{2} \bar{ \Psi }_\mu^\alpha (f^{-1})_{\alpha\beta}\Psi_\nu^\beta $

\begin{equation}
\bar{\Theta}_-^{\mu\nu} \bar{\Pi}_{+\nu\rho} = \delta^\mu_\rho,
\end{equation}
where
\begin{gather}
\bar{\Theta}_-^{\mu\nu} = \Theta_-^{\mu\nu} - \frac{1}{2} \Theta_-^{\mu\mu_1} \bar{ \Psi }_{\mu_1}^\alpha (\bar{f}^{-1})_{\alpha\beta} \Psi^\beta_{\nu_1} \Theta_-^{\nu_1\nu},\\
\bar{f}^{\alpha\beta} = f^{\alpha \beta} + \frac{1}{2} \Psi_\mu^\alpha \Theta_-^{\mu\nu} \bar{ \Psi }_\nu^\beta,\\
\Theta_-^{\mu\nu} \Pi_{ +\mu \rho } = \delta^\mu_\rho, \qquad \Theta_- = -4 (G_E^{-1} \Pi_- G^{-1})^{\mu\nu}.
\end{gather}
Effective metric tensor is defined as $G_{E \mu\nu} \equiv G_{\mu \nu} -4(BG^{-1}B)_{\mu\nu} $.

In above expressions $\Delta V$ is a quantity in the zeroth order in $C^{\alpha\beta}_\mu$

\begin{align}
\begin{gathered}
\Delta V^\rho  =  \int d\xi^+ v_+^\rho+\int d\xi^- v_-^\rho\\
=\frac{1}{2} \int_{P} d \xi^+ \bar{\Theta}_-^{\rho_1 \rho} \left[ \partial_+ y_{\rho_1}     -  \partial_+ \bar{ \theta } ^\alpha ( f^{- 1 } )_{ \alpha\beta } \Psi_{\rho_1}^\beta
\right]
- \frac{1}{2} \int_{P} d \xi^- \bar{\Theta}_-^{\rho \rho_1}
\left[    \partial_- y_{\rho_1}  +  \bar{ \Psi }_{\rho_1}^\alpha ( f^{- 1 } )_{ \alpha\beta } \partial_- \theta^\beta
\right] .
\end{gathered}
\end{align}

Using (\ref{eq of motion for v_+}) and (\ref{eq of motion for v_-}) and inserting them into (\ref{Auxiliary action S_{aux}}), we get T-dual action

\begin{align}    \label{S_{T-dual}}
\begin{gathered}
S_{T-dual}    =     k \int_{P} d^2 \xi  \Bigg[
\frac{1}{4} \bar{\Theta}_-^{\mu \nu}  \partial_+ y_\mu    \partial_- y_\nu \Bigg.  \\
\begin{aligned}
&+\frac{1}{8}  \bar{\Theta}_-^{\mu \mu_1} \bar{ \Psi }_{\mu_1}^\alpha   ( f^{- 1 } )_{ \alpha\alpha_1 }   C_\rho^{\alpha_1 \beta_1} \Delta V^\rho ( f^{- 1 } )_{ \beta_1\beta }     \Psi_{\nu_1}^{\beta} \bar{\Theta}_-^{\nu_1 \nu}  \partial_+ y_\mu    \partial_- y_\nu  \\
&
+ \frac{1}{2} \partial_+ \bar{ \theta }^\alpha \Big( \Big. (F^{-1} ( \Delta V  ) )_{\alpha\beta}    + \frac{1}{2} ( f^{- 1 } )_{ \alpha\alpha_1 }   C_\rho^{\alpha_1 \alpha_2} \Delta V^\rho ( f^{- 1 } )_{ \alpha_2\alpha_3 }   \Psi_\mu^{ \alpha_3 }  \bar{\Theta}_-^{\mu \nu} \bar{ \Psi }_{\nu}^{\beta_1} ( f^{- 1 } )_{\beta_1\beta}   \\
&\quad - \frac{1}{2} ( f^{- 1 } )_{\alpha\alpha_1}  \Psi_\mu^{ \alpha_1 }  \bar{\Theta}_-^{\mu \nu} \bar{ \Psi }_{\nu}^{\beta_1} ( f^{- 1 } )_{\beta_1\beta}
+ \frac{1}{2} ( f^{- 1 } )_{\alpha\alpha_1}  \Psi_\mu^{ \alpha_1 }  \bar{\Theta}_-^{\mu \nu} \bar{ \Psi }_{\nu}^{\beta_3} ( f^{- 1 } )_{ \beta_3\beta_2 }   C_\rho^{\beta_2 \beta_1} \Delta V^\rho ( f^{- 1 } )_{ \beta_1\beta }  \\
&\quad\Big. -\frac{1}{4}    ( f^{- 1 } )_{ \alpha\alpha_1 } \Psi_\mu^{ \alpha_1 } \bar{\Theta}_-^{\mu \mu_1} \bar{ \Psi }_{\mu_1}^{\alpha_2}
( f^{- 1 } )_{ \alpha_2\alpha_3 }  C_\rho^{\alpha_3 \beta_3}
\Delta V^\rho
( f^{- 1 } )_{ \beta_3\beta_2 }  \Psi_{\nu_1}^{ \beta_2 } \bar{\Theta}_-^{\nu_1  \nu} \bar{ \Psi }_\nu^{\beta_1}  ( f^{- 1 } )_{ \beta_1\beta }
\Big) \partial_- \theta^\beta    \\
& +\frac{1}{4}  \partial_+ y_\mu   \bar{\Theta}_-^{\mu  \mu_1}  \bar{ \Psi }_{\mu_1}^\alpha  \Big( (F^{-1} ( \Delta V  ) )_{\alpha\beta}    +   \frac{1}{2}   ( f^{- 1 } )_{ \alpha\alpha_1 }   C_\rho^{\alpha_1 \beta_3}
\Delta V^\rho ( f^{- 1 } )_{ \beta_3\beta_2 } \Psi_{\nu_1}^{\beta_2}   \bar{\Theta}_-^{\nu_1  \nu} \bar{ \Psi }_\nu^{\beta_1}  ( f^{- 1 } )_{ \beta_1\beta }
\Big)   \\
&\quad\times \partial_- \theta^\beta  \\
&- \frac{1}{4} \partial_+ \bar{ \theta }^\alpha        \Big(  (F^{-1} ( \Delta V  ) )_{\alpha\beta}  +\frac{1}{2}  ( f^{- 1 } )_{ \alpha\alpha_1 } \Psi_\mu^{\alpha_1}  \bar{\Theta}_-^{\mu \mu_1} \bar{ \Psi }_{\mu_1}^{\alpha_2}
( f^{- 1 } )_{ \alpha_2\alpha_3 } C_\rho^{\alpha_3 \beta_1} \Delta V^\rho ( f^{- 1 } )_{ \beta_1\beta } \Big)  \Psi_{\nu_1}^\beta \bar{\Theta}_-^{\nu_1 \nu}   \\
&\quad\Bigg. \times   \partial_- y_\nu  \Bigg].
\end{aligned}
\end{gathered}
\end{align}
Let us note that above we kept terms up to to the first order in $C^{\alpha\beta}_\mu$.

T-dual action contains all terms as initial action (\ref{Action final S}) up to the change $x^\mu\to y_\mu$. Consequently, T-dual background fields are of the form

\begin{align}\label{Background fields transformations}
\begin{gathered}
{}^\star\Pi_{ +}^{\mu \nu } = \frac{1}{4} \bar{\Theta}_-^{\mu \nu} + \frac{1}{8} \bar{\Theta}_-^{\mu \mu_1} \bar{ \Psi }_{\mu_1}^\alpha \Big[\Big. (F^{-1} ( \Delta V  ) )_{\alpha\beta} +  ( f^{- 1 } )_{ \alpha\alpha_1 }   C_\rho^{\alpha_1 \beta_1} \Delta V^\rho ( f^{- 1 } )_{ \beta_1\beta } \\
\begin{aligned}
&- \frac{1}{2} ( f^{- 1 } )_{\alpha\alpha_1}  \Psi_{\mu_2}^{ \alpha_1 }  \bar{\Theta}_-^{\mu_2 \nu_2} \bar{ \Psi }_{\nu_2}^{\beta_1} ( f^{- 1 } )_{\beta_1\beta} + \frac{1}{2} ( f^{- 1 } )_{ \alpha\alpha_1 }   C_\rho^{\alpha_1 \alpha_2} \Delta V^\rho ( f^{- 1 } )_{ \alpha_2\alpha_3 }   \Psi_{\mu_2}^{ \alpha_3 }  \bar{\Theta}_-^{\mu_2 \nu_2} \bar{ \Psi }_{\nu_2}^{\beta_1} ( f^{- 1 } )_{\beta_1\beta} \\
&+\frac{1}{2} ( f^{- 1 } )_{\alpha\alpha_1}  \Psi_{\mu_2}^{ \alpha_1 }  \bar{\Theta}_-^{\mu_2 \nu_2} \bar{ \Psi }_{\nu_2}^{\beta_3} ( f^{- 1 } )_{ \beta_3\beta_2 }   C_\rho^{\beta_2 \beta_1} \Delta V^\rho ( f^{- 1 } )_{ \beta_1\beta } \\
&-\frac{1}{4}    ( f^{- 1 } )_{ \alpha\alpha_1 } \Psi_{\mu_2}^{ \alpha_1 } \bar{\Theta}_-^{\mu_2 \mu_3} \bar{ \Psi }_{\mu_3}^{\alpha_2}
( f^{- 1 } )_{ \alpha_2\alpha_3 }  C_\rho^{\alpha_3 \beta_3}
\Delta V^\rho
( f^{- 1 } )_{ \beta_3\beta_2 }  \Psi_{\nu_3}^{ \beta_2 } \bar{\Theta}_-^{\nu_3  \nu_2} \bar{ \Psi }_{\nu_2}^{\beta_1}  ( f^{- 1 } )_{ \beta_1\beta } \Big.\Big] \Psi_{\nu_1}^\beta \bar{\Theta}_-^{\nu_1 \nu},
\end{aligned}
\end{gathered}\\
\label{Background fields transformation 2}
\begin{gathered}
{}^\star(F^{-1} ( x  ) )_{\alpha\beta}  = (F^{-1} ( \Delta \bar{ y }  ) )_{\alpha\beta}  + \frac{1}{2} ( f^{- 1 } )_{ \alpha\alpha_1 }   C_\rho^{\alpha_1 \alpha_2} \Delta V^\rho ( f^{- 1 } )_{ \alpha_2\alpha_3 }   \Psi_\mu^{ \alpha_3 }  \bar{\Theta}_-^{\mu \nu} \bar{ \Psi }_{\nu}^{\beta_1} ( f^{- 1 } )_{\beta_1\beta} \\
\begin{aligned}
&- \frac{1}{2} ( f^{- 1 } )_{\alpha\alpha_1}  \Psi_\mu^{ \alpha_1 }  \bar{\Theta}_-^{\mu \nu} \bar{ \Psi }_{\nu}^{\beta_1} ( f^{- 1 } )_{\beta_1\beta} + \frac{1}{2} ( f^{- 1 } )_{\alpha\alpha_1}  \Psi_\mu^{ \alpha_1 }  \bar{\Theta}_-^{\mu \nu} \bar{ \Psi }_{\nu}^{\beta_3} ( f^{- 1 } )_{ \beta_3\beta_2 }   C_\rho^{\beta_2 \beta_1} \Delta V^\rho ( f^{- 1 } )_{ \beta_1\beta } \quad\ \  \\
&-\frac{1}{4}    ( f^{- 1 } )_{ \alpha\alpha_1 } \Psi_\mu^{ \alpha_1 } \bar{\Theta}_-^{\mu \mu_1} \bar{ \Psi }_{\mu_1}^{\alpha_2}
( f^{- 1 } )_{ \alpha_2\alpha_3 }  C_\rho^{\alpha_3 \beta_3}
\Delta V^\rho
( f^{- 1 } )_{ \beta_3\beta_2 }  \Psi_{\nu_1}^{ \beta_2 } \bar{\Theta}_-^{\nu_1  \nu} \bar{ \Psi }_\nu^{\beta_1}  ( f^{- 1 } )_{ \beta_1\beta },
\end{aligned}
\end{gathered}
\end{align}
\begin{equation}
{}^\star \bar{ \Psi }^{\mu\alpha} = \frac{1}{2} \Theta_-^{\mu\nu}\bar{ \Psi }_\nu^\alpha, \qquad {}^\star \Psi_{\nu\beta} = -\frac{1}{2}\Psi_\mu^\beta \Theta_-^{\mu\nu}.
\end{equation}
Comparing background field of T-dual theory with background fields from \cite{nasrad3} we immediately notice that background fields have become more complex. However, this is just an illusion. In both cases background field are exactly the same only difference is that here we did not introduce tensor $\breve{\Pi}_{+\mu\nu} = \Pi_{+\mu\nu} + \frac{1}{2}\bar{ \Psi }^\alpha_\mu F^{-1}(\Delta V) _{\alpha \beta} \Psi^\beta_\nu$    and its inverse, therefore we are missing ingredients to express our fields in more compactified format.

\subsection{T-dualization of T-dual theory}

Since the initial theory is not symmetric under translations, T-dual action that is obtained from auxiliary action (\ref{Auxiliary action S_{aux}}) and it is now invariant to translations of T-dual coordinates. Consequently, we can dualize T-dual theory by generalized Buscher procedure. We start with the introduction of following substitutions

\begin{align}
\partial_\pm y_\mu       \rightarrow       &   D_\pm y_\mu  = \partial_\pm y_\mu +  u_{\pm \mu}  \rightarrow D_\pm y_\mu =  u_{\pm \mu}, \\
\Delta \bar{ y }^\rho       \rightarrow     &   \Delta \bar{ u }^\rho, \\
\Delta \bar{ u }^\rho  =
&\frac{1}{2} \int_{P} d \xi^+ \bar{\Theta}_-^{\rho_1 \rho} \left[ u_{+ \rho_1}     -  \partial_+ \bar{ \theta } ^\alpha ( f^{- 1 } )_{ \alpha\beta } \Psi_{\rho_1}^\beta
\right] \nonumber \\
- &\frac{1}{2} \int_{P} d \xi^- \bar{\Theta}_-^{\rho \rho_1}
\left[    u_{- \rho_1}  +  \bar{ \Psi }_{\rho_1}^\alpha ( f^{- 1 } )_{ \alpha\beta } \partial_- \theta^\beta
\right]\, ,\\
S \rightarrow & S + \frac{1}{2}   (u_{+ \mu}  \partial_-x^\mu  - u_{- \mu}\partial_+ x^\mu  ) \, .
\end{align}
From the first line we see that gauge is fixed choosing $y(\xi) = const$. Inserting these substitutions into (\ref{S_{T-dual}}) we obtain

\begin{align}    \label{S_{gauge fix}}
\begin{gathered}
S_{gauge fix}    =     \kappa \int_{P} d^2 \xi  \Bigg[
\frac{1}{4} \bar{\Theta}_-^{\mu \nu}  u_{ + \mu}    u_{- \nu} \Bigg.  \\
\begin{aligned}
&+\frac{1}{8}  \bar{\Theta}_-^{\mu \mu_1} \bar{ \Psi }_{\mu_1}^\alpha   ( f^{- 1 } )_{ \alpha\alpha_1 }   C_\rho^{\alpha_1 \beta_1} \Delta \bar{ u }^\rho ( f^{- 1 } )_{ \beta_1\beta }     \Psi_{\nu_1}^{\beta} \bar{\Theta}_-^{\nu_1 \nu}  u_{ + \mu}    u_{- \nu}  \\
&
+ \frac{1}{2} \partial_+ \bar{ \theta }^\alpha \Big( \Big. (F^{-1} ( \Delta \bar{ u }  ) )_{\alpha\beta}    + \frac{1}{2} ( f^{- 1 } )_{ \alpha\alpha_1 }   C_\rho^{\alpha_1 \alpha_2} \Delta \bar{ u }^\rho ( f^{- 1 } )_{ \alpha_2\alpha_3 }   \Psi_\mu^{ \alpha_3 }  \bar{\Theta}_-^{\mu \nu} \bar{ \Psi }_{\nu}^{\beta_1} ( f^{- 1 } )_{\beta_1\beta}   \\
&\quad - \frac{1}{2} ( f^{- 1 } )_{\alpha\alpha_1}  \Psi_\mu^{ \alpha_1 }  \bar{\Theta}_-^{\mu \nu} \bar{ \Psi }_{\nu}^{\beta_1} ( f^{- 1 } )_{\beta_1\beta}
+ \frac{1}{2} ( f^{- 1 } )_{\alpha\alpha_1}  \Psi_\mu^{ \alpha_1 }  \bar{\Theta}_-^{\mu \nu} \bar{ \Psi }_{\nu}^{\beta_3} ( f^{- 1 } )_{ \beta_3\beta_2 }   C_\rho^{\beta_2 \beta_1} \Delta \bar{ u }^\rho ( f^{- 1 } )_{ \beta_1\beta }  \\
&\quad\Big. -\frac{1}{4}    ( f^{- 1 } )_{ \alpha\alpha_1 } \Psi_\mu^{ \alpha_1 } \bar{\Theta}_-^{\mu \mu_1} \bar{ \Psi }_{\mu_1}^{\alpha_2}
( f^{- 1 } )_{ \alpha_2\alpha_3 }  C_\rho^{\alpha_3 \beta_3}
\Delta \bar{ u }^\rho
( f^{- 1 } )_{ \beta_3\beta_2 }  \Psi_{\nu_1}^{ \beta_2 } \bar{\Theta}_-^{\nu_1  \nu} \bar{ \Psi }_\nu^{\beta_1}  ( f^{- 1 } )_{ \beta_1\beta }
\Big) \partial_- \theta^\beta    \\
& +\frac{1}{4}  u_{ + \mu}   \bar{\Theta}_-^{\mu  \mu_1}  \bar{ \Psi }_{\mu_1}^\alpha  \Big( (F^{-1} ( \Delta \bar{ u }  ) )_{\alpha\beta}    +   \frac{1}{2}   ( f^{- 1 } )_{ \alpha\alpha_1 }   C_\rho^{\alpha_1 \beta_3}
\Delta \bar{ u }^\rho ( f^{- 1 } )_{ \beta_3\beta_2 } \Psi_{\nu_1}^{\beta_2}   \bar{\Theta}_-^{\nu_1  \nu} \bar{ \Psi }_\nu^{\beta_1}  ( f^{- 1 } )_{ \beta_1\beta }
\Big)   \\
&\quad\times \partial_- \theta^\beta  \\
&- \frac{1}{4} \partial_+ \bar{ \theta }^\alpha        \Big(  (F^{-1} ( \Delta \bar{ u }  ) )_{\alpha\beta}  +\frac{1}{2}  ( f^{- 1 } )_{ \alpha\alpha_1 } \Psi_\mu^{\alpha_1}  \bar{\Theta}_-^{\mu \mu_1} \bar{ \Psi }_{\mu_1}^{\alpha_2}
( f^{- 1 } )_{ \alpha_2\alpha_3 } C_\rho^{\alpha_3 \beta_1} \Delta \bar{ u }^\rho ( f^{- 1 } )_{ \beta_1\beta } \Big)  \Psi_{\nu_1}^\beta \bar{\Theta}_-^{\nu_1 \nu}   \\
&\quad \times   u_{- \nu}\\
 &+ \frac{1}{2}   (u_{+ \mu}  \partial_-x^\mu  - u_{- \mu}\partial_+ x^\mu  )  \Bigg. \Bigg].
\end{aligned}
\end{gathered}
\end{align}
Using equations of motion for Lagrange multipliers, we return to the T-dual action. Finding equations of motion for gauge fields, we have

\begin{align}
\label{T^2 equations of motion 1}
u_{+ \mu}(\kappa)   =  &\phantom{-\ }2\bar{\Pi}_{+ \nu \mu} \partial_+ x^\nu (\kappa)
-  \partial_+ x^\nu (\kappa) \bar{ \Psi }_\nu^\alpha  (f^{- 1 } )_{ \alpha\alpha_1 }     C_\rho^{\alpha_1 \beta_1}  \Delta x^\rho (f^{- 1 } )_{ \beta_1\beta } \Psi_\mu^\beta      \nonumber \\
&+ \partial_+ \bar{ \theta }^\alpha (\kappa) (F^{-1} ( \Delta \bar{ x }  ))_{\alpha \beta} \Psi_\mu^\beta \nonumber  \\
&- \int_{\Sigma} d^2 \xi \Big(
\partial_+ \bar{ \theta }^\alpha (\xi) +\partial_+x^{\mu_1} (\xi) \bar{ \Psi }_{\mu_1}^\alpha
\Big)
( f^{ -1 } )_{ \alpha\alpha_1 }     C_\mu^{\alpha_1 \beta_1}      ( f^{ -1 } )_{ \beta_1\beta } N(\kappa^-) \nonumber \\
&\quad\times
\Big(
\partial_- \theta^\beta (\xi) + \Psi_{\nu}^\beta \partial_- x^\nu (\xi)
\Big), \\
\label{T^2 equations of motion 2}
u_{- \nu}(\kappa)    =  &-2 \bar{\Pi}_{+\nu \mu}\partial_- x^\mu (\kappa)
+ \bar{ \Psi }_\nu^\alpha (f^{- 1 } )_{ \alpha\alpha_1 }     C_\rho^{\alpha_1 \beta_1}  \Delta x^\rho (f^{- 1 } )_{ \beta_1\beta } \Psi_\mu^\beta \partial_- x^\mu (\kappa)  \nonumber\\
&- \bar{ \Psi }_\nu^\alpha (F^{-1} ( \Delta \bar{ x }  ))_{\alpha \beta} \partial_- \theta^\beta  (\kappa) \nonumber \\
&+ \int_{\Sigma} d^2 \xi
\Big(
\partial_+ \bar{ \theta }^\alpha (\xi) +\partial_+x^{\mu} (\xi) \bar{ \Psi }_{\mu}^\alpha
\Big)
( f^{ -1 } )_{ \alpha\alpha_1 }     C_\nu^{\alpha_1 \beta_1}      ( f^{ -1 } )_{ \beta_1\beta } N(\kappa^-) \nonumber \\
&\quad\times
\Big(
\partial_- \theta^\beta (\xi) + \Psi_{\nu_1}^\beta \partial_- x^{\nu_1} (\xi)
\Big)\, .
\end{align}
Here we have that $\Delta x^\mu = x(\xi) - x(\xi_0)$, and inserting these equations into the gauge fixed action, keeping all terms linear with respect to $C_\rho^{\mu\nu}$ and selecting $\xi_0$ such that $x(\xi_0) = 0$, we obtain our original action (\ref{Action final S}).

\section{Non-commutative relations}
\setcounter{equation}{0}

In this chapter we will establish a relationship between Poisson brackets of original and T-dual theory using results from the previous one. Original theory is a geometric one, which means that canonical variables $x^\mu(\xi)$ and $\pi_\mu(\xi)$ satisfy standard Poisson algebra

\begin{equation}
\{ x^\mu (\sigma), \pi_\nu (\bar{\sigma})  \} = \delta^\mu_\nu \delta(\sigma - \bar{\sigma}), \quad \{ x^\mu(\sigma) , x^\nu(\bar{\sigma}) \} = 0, \quad \{ \pi_\mu(\sigma), \pi_\nu(\bar{\sigma})  \} = 0.
\end{equation}
We will find Poisson structure of T-dual theory using relations (\ref{eq of motion for v_+}) and (\ref{eq of motion for v_-}) and expressing them in terms of the coordinates and momenta of the initial theory. Replacing gauge fields with solutions of equations of motion for Lagrange multipliers, we get T-dual transformation laws in Lagrangian form. Because we implement here canonical approach, the next step is removing of all terms that are proportional to $\partial_\tau x^\mu(\xi)$. The most of the terms of this type will get incorporated into expression for canonical momenta $\pi_\mu(\xi)$, but term that is non-local and which is dependent on function $N(\xi^\pm)$ remains. One way of removing this term is to first use equations of motion for coordinate $x^\mu(\xi)$, and then replace remaining $\partial_\tau x^\mu$ term with canonical momentum.  By doing all the steps that were outlined, we have following relationship between T-dual coordinate and variables of starting theory

\begin{align} \label{sigma derivative of y}
\begin{gathered}
\partial_{\sigma} y_\nu (\sigma) =2B_{\nu \mu} \partial_{\sigma} x^\mu - G_{\nu \mu}
(\bar{\Pi}_+ +\bar{\Pi}_+^T)^{-1 \nu_1 \mu}
\Bigg[
\frac{\pi_{\nu_1}}{k}    - \frac{1}{2} \bar{ \Psi }_{\nu_1}^\alpha \left( F^{-1} (x) \right)_{\alpha \beta} \partial_- \theta^\beta  \Bigg. \\
\begin{aligned}
& - \frac{1}{2} \partial_+ \bar{ \theta }^\alpha \left( F^{-1} (x) \right)_{\alpha \beta} \Psi_{\nu_1}^\beta    - \Big[ \Pi_{+ \mu_1 \mu_2} + \frac{1}{2} \bar{ \Psi }_{\mu_1}^\alpha \left( F^{-1} (x) \right)_{\alpha \beta} \Psi_{\mu_2}^\beta
\Big]       (\delta_{\nu_2}^{\mu_1} \delta_{\nu_1}^{\mu_2} - \delta_{\nu_1}^{\mu_1} \delta_{\nu_2}^{\mu_2}   )  \partial_{\sigma}x^{\nu_2}  \\
&+\frac{1}{2}
\bar{ \Psi }_{\mu_1}^\alpha ( f^{ -1 } )_{ \alpha\alpha_1 }     C_\rho^{\alpha_1 \beta_1}   x^\rho(\sigma)   ( f^{ -1 } )_{ \beta_1\beta }   \Psi_{\mu_2}^\beta (\delta_{\nu_2}^{\mu_1} \delta_{\nu_1}^{\mu_2} - \delta_{\nu_1}^{\mu_1} \delta_{\nu_2}^{\mu_2}   )    (\bar{\Pi}_+ +\bar{\Pi}_+^T)^{-1 \rho \nu_2}   \\
&\quad\times
\Big[ \frac{\pi_\rho}{k} - \frac{1}{2} \bar{ \Psi }_\rho^\gamma (f^{-1})_{\gamma \gamma_1} \partial_- \theta^{\gamma_1} - \frac{1}{2} \partial_+ \bar{ \theta }^\gamma (f^{-1})_{\gamma \gamma_1} \Psi_\rho^{\gamma_1} + \bar{\Pi}_{+\rho \rho_1} \partial_{\sigma} x^{\rho_1 } - \bar{\Pi}_{+\rho_1 \rho} \partial_{\sigma} x^{\rho_1 }
\Big]
\Bigg].
\end{aligned}
\end{gathered}
\end{align}

To find Poisson bracket between T-dual coordinates, we can start by finding Poisson bracket of sigma derivatives of T-dual coordinates and then integrating twice (see \cite{nasrad3}). Implementing this procedure we have that Poisson bracket for sigma derivatives is given as

\begin{align} \label{sigma derivative Poisson bracket}
\begin{gathered}
\{\partial_{\sigma_1} y_{\nu_1} (\sigma_1), \partial_{\sigma_2} y_{\nu_2} (\sigma_2)  \} = \\
\begin{aligned}
&= \frac{2}{k} (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_1 \mu_2} \Big[ G_{\nu_1 \mu_1} B_{\nu_2 \mu_2} \partial_{\sigma_2} \delta(\sigma_1 - \sigma_2)    -   B_{\nu_1 \mu_1}G_{\nu_2\mu_2} \partial_{\sigma_1}     \delta(\sigma_1- \sigma_2)
\Big]  \\
&+ \frac{1}{k} \bar{ \Psi }_{\nu_3}^\alpha (f^{-1})_{\alpha \alpha_1} C_\rho^{ \alpha_1 \beta_1} (f^{-1})_{\beta_1 \beta} \Psi_{\nu_4}^\beta ( \delta_{\mu_3}^{\nu_3} \delta_{\mu_4}^{\nu_4}  + \delta_{\mu_3}^{\nu_4}\delta_{\mu_4}^{\nu_3}     ) (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_3 \mu_1} (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_4 \mu_2}  \\
&\quad\times \Big[
G_{\nu_1 \mu_1} B_{\nu_2 \mu_2}  x^\rho (\sigma_1) \partial_{\sigma_2} \delta(\sigma_1 - \sigma_2)    -   B_{\nu_1 \mu_1}G_{\nu_2\mu_2} x^\rho (\sigma_2) \partial_{\sigma_1}     \delta(\sigma_1- \sigma_2)
\Big].
\end{aligned}
\end{gathered}
\end{align}
Then we integrate with respect to $\sigma_1$ ($\sigma_2$), where we set boundaries as $\sigma_0$ ($\bar{\sigma}_0$) and $\sigma$ ($\bar{\sigma}$). Extracting only Poisson bracket terms that contain $\sigma $ and $\bar{\sigma}$, we have

\begin{align} \label{Poisson brackets T-dual}
\begin{gathered}
\{ y_{\nu_1} (\sigma),  y_{\nu_2} (\bar{\sigma})  \} = \frac{2}{k} (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_1 \mu_2} \Big[ G_{\nu_1 \mu_1} B_{\nu_2 \mu_2}     +   B_{\nu_1 \mu_1}G_{\nu_2\mu_2}
\Big] H(\sigma - \bar{\sigma}) \\
\begin{aligned}
&+ \frac{1}{k}\bar{ \Psi }_{\nu_3}^\alpha (f^{-1})_{\alpha \alpha_1} G_\rho^{ \alpha_1 \beta_1} (f^{-1})_{\beta_1 \beta} \Psi_{\nu_4}^\beta ( \delta_{\mu_3}^{\nu_3} \delta_{\mu_4}^{\nu_4}  + \delta_{\mu_3}^{\nu_4}\delta_{\mu_4}^{\nu_3}     ) (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_3 \mu_1} (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_4 \mu_2} \\
&\times    \Big[ G_{\nu_1 \mu_1} B_{\nu_2 \mu_2} x^\rho (\bar{\sigma})    +   B_{\nu_1 \mu_1}G_{\nu_2\mu_2} x^\rho (\sigma)
\Big]H(\sigma - \bar{\sigma}) .
\end{aligned}
\end{gathered}
\end{align}
Here, $H(\sigma - \bar{\sigma})$ is same step function defined in Appendix \ref{appendix A}. It should be noted that these Poisson brackets are zero when $\sigma = \bar{\sigma}$. However, in cases where string in curled around compactified dimension, that is cases where $\sigma - \bar{\sigma} = 2\pi$, we have following situation

\begin{align}
\begin{gathered}
\{ y_{\nu_1} (\sigma + 2\pi),  y_{\nu_2} (\sigma)  \} =\frac{2}{k} (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_1 \mu_2} \Big[ G_{\nu_1 \mu_1} B_{\nu_2 \mu_2}     +   B_{\nu_1 \mu_1}G_{\nu_2\mu_2}
\Big] \\
\begin{aligned}
&+ \frac{1}{k}\bar{ \Psi }_{\nu_3}^\alpha (f^{-1})_{\alpha \alpha_1} C_\rho^{ \alpha_1 \beta_1} (f^{-1})_{\beta_1 \beta} \Psi_{\nu_4}^\beta ( \delta_{\mu_3}^{\nu_3} \delta_{\mu_4}^{\nu_4}  + \delta_{\mu_3}^{\nu_4}\delta_{\mu_4}^{\nu_3}     ) (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_3 \mu_1} (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_4 \mu_2} \\
&\times    \Big[4\pi  G_{\nu_1 \mu_1} B_{\nu_2 \mu_2}  N^\rho +   \big(  G_{\nu_1 \mu_1} B_{\nu_2 \mu_2}    +   B_{\nu_1 \mu_1}G_{\nu_2\mu_2}  \big) x^\rho (\sigma)
\Big]    .
\end{aligned}
\end{gathered}
\end{align}
We used fact that $H(2\pi) = 1$. The symbol $N^\mu$ denotes winding number around compactified coordinate, if is defined as

\begin{equation}
x^\mu(\sigma + 2 \pi) - x^\mu(\sigma) = 2\pi N^\mu.
\end{equation}
Let us note that if we choose $x^\mu(\sigma) = 0$ than Poisson bracket has linear dependence on winding number. In cases where we don't have any winding number, we still have non-commutativity that is proportional to background fields.

Using the expression for sigma derivative of $y_\nu$ (\ref{sigma derivative of y}) and expression for Poisson bracket of sigma derivatives (\ref{sigma derivative Poisson bracket}), we can find non-associative relations. Procedure is the same as for finding Poisson brackets of T-dual theory, we find Poisson bracket of sigma derivatives and integrate with respect to sigma coordinate, this time integral is done trice. Going along with this procedure we have following final result

\begin{align}
\begin{gathered}
\{  y_\nu (\sigma)  ,  \{ y_{\nu_1} (\sigma_1),  y_{\nu_2} (\sigma_2)  \} \} = \frac{G_{\nu \mu}}{k^2} (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \rho \mu} \\
\begin{aligned}
&\times \bar{ \Psi }_{\nu_3}^\alpha (f^{-1})_{\alpha \alpha_1} C_\rho^{ \alpha_1 \beta_1} (f^{-1})_{\beta_1 \beta} \Psi_{\nu_4}^\beta( \delta_{\mu_3}^{\nu_3} \delta_{\mu_4}^{\nu_4}  + \delta_{\mu_3}^{\nu_4}\delta_{\mu_4}^{\nu_3}     ) (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_3 \mu_1}   (\bar{\Pi}_+ + \bar{\Pi}_+^T)^{-1 \mu_4 \mu_2}
\\
& \times\Big[ G_{\nu_1 \mu_1} B_{\nu_2 \mu_2} H(\sigma - \sigma_2)    +   B_{\nu_1 \mu_1}G_{\nu_2\mu_2} H(\sigma - \sigma_1)
\Big]H(\sigma_1 - \sigma_2) .
\end{aligned}
\end{gathered}
\end{align}
Since Jacobi identity is non-zero for T-dual theory we have that coordinate dependent RR field produces non-associative theory. However putting $\sigma_1=\sigma_2=\bar{\sigma}$ and $\sigma= \bar{\sigma} +2\pi$ we have that Jacobi identity disappears

\begin{equation}
\{  y_\nu (\bar{\sigma} + 2\pi)  ,  \{ y_{\nu_1} (\bar{\sigma}),  y_{\nu_2} (\bar{\sigma})  \} \} = 0.
\end{equation}

\section{Conclusion}
\setcounter{equation}{0}

In this article we examined type II superstring propagating in presence of coordinate dependent RR field. This choice of background was in accordance with consistency conditions for background field and all calculations were made in approximation that are linear with respect to coordinate dependent part of RR field. We have also excluded parts that were non-linear in fermionic coordinates and neglected pure spinor actions. Using equations of motion for fermionic momenta we obtained action that was expressed in terms of bosonic coordinates, their derivatives and derivatives of fermionic coordinates. Unlike \cite{nasrad3} we do not impose any conditions on the constant and coordinate dependent part of RR field strength, so, it is not possible to deduce this case to the form of the weakly curved background one.

Action with our choice of background fields did not possess translation symmetry, therefore we needed to use Buscher procedure that was extended to such cases. By substituting starting action with auxiliary action we gave up on locality in order to be able to find T-dual theory. Finding equations of motion of newly introduced Lagrange multipliers we were able to salvage starting action giving us assurance that auxiliary action we selected would produce correct T-dual theory. After this we found equations of motion for gauge fields and by inserting them into action, we found T-dual theory.

Having found T-dual theory, we applied T-dual procedure once again as a more thorough way of checking if action we obtained was in fact correct T-dual of starting action. Unlike starting action, T-dual action possessed translation symmetry and was non-local from the start by virtue of having dual coordinate $\Delta V^\mu$. Applying steps of generalized Buscher procedure \cite{Generalized Buscher procedure, Auxiliary action Buscher procedure} we obtained starting action, again confirming that our choice of auxiliary action was correct.

We obtained non-commutativity relations in context of T-dual theory, where we used T-dual transformation laws as a bridge between Poisson brackets of starting theory and T-dual theory. T-dual transformation laws were expressed as functions of coordinates and momenta of original theory and using their standard Poisson algebra, we got non-commutativity in T-dual theory. From expression for Poisson brackets (\ref{Poisson brackets T-dual}) we can see that non-commutativity is proportional to infinitesimal part of RR field as well as to symmetrised inverse of field $\bar{\Pi}$. Non-commutativity relations are zero in case when $\sigma = \bar{\sigma}$, while in case where $\sigma = \bar{\sigma} + 2\pi$ we see the emergence of winding numbers.

Taking into account Poisson brackets of sigma derivatives and expression for sigma derivative of T-dual coordinate we were able to find non-associative relation for T-dual theory. In general case this relation was non-zero and it was proportional to infinitesimal constant $C_\rho^{\mu \nu}$. In special case when we put  $\sigma_1=\sigma_2=\bar{\sigma}$ and $\sigma= \bar{\sigma} +2\pi$ we noticed that non-associativity relation disappears. During the implementation of the T-dualization procedure and calculations, we obtained generalization of $\beta_\mu$ functions in the form of the $N$-functions.

It should be noted that since we did not preform T-dualization along fermionic coordinates their Poisson structure would remain the same as in original theory. Furthermore, since background fields do not depend on fermionic coordinates it should be expected, as in the case of bosonic coordinates \cite{Generalized Buscher procedure 3}, that T-duality would leave Poisson brackets between fermionic fields the same. We expect that, if proposed non-commutative relations from \cite{Vertex operators, original paper 2} are even possible, we would need at least RR field that depends both on fermionic and bosonic coordinates.

redpajama_set_name: RedPajamaArXiv


text:
The Grove Pub – New Plans Revealed
Plans to convert the former The Grove Pub in Nottingham into social housing have been submitted.
The historic pub on Castle Boulevard in the city has been empty for years. Now a joint venture between Bmor and Carlton Street Trading could see it converted and extended to create 27 one-and two-bedroom social housing apartments for key workers. Plans include extending the building over the current car park.
The Grove – Leonard Design Architects
The scheme will preserve the existing character of the building while adding contemporary architectural points of interest.
Leonard Design have devised the scheme, that will preserve the existing character of the building while adding contemporary architectural points of interest.
James O'Brien, head of planning at Bmor, said: "A key milestone has been achieved with the planning submission for The Grove and we're delighted to have reached this stage."
"The site is quite challenging in terms of the space available and protecting its heritage. This has meant that the plans have been through many iterations so we're hopeful that this design will not only get the green light but also provide much needed social housing in Nottingham city centre."
The redevelopment is essential to the building's survival and its regeneration will be an essential part of injecting new life into this part of Nottingham.
Sam Burt, director at Nottingham firm Carlton Street Trading, added: "Developments such as The Grove are prime examples of how we can bring derelict heritage buildings back into use for the benefit of the community. The building has been boarded up for many years with the external facades starting to show signs of decay, so we really hope we'll soon be able to give it a new lease of life. The redevelopment is essential to the building's survival and its regeneration will be an essential part of injecting new life into this part of Nottingham."
Next Waterside Apartments Practical Completion


We offer dismounting of individual machines as well as entire production lines.
And of course we also provide installation of your new machinery.
We have experience with relocation of entire factories both national and international. In one of these relocation operations we moved Gumlink from Denmark to Turkey.


text:
The Monetary Policy Committee (MPC) is an internal committee of the Reserve Bank of New Zealand (RBNZ) and is responsible for formulating monetary policy in New Zealand, directed towards the economic objectives of achieving and maintaining stability in the general level of prices over the medium term, and supporting maximum sustainable employment.
The global economic disruption caused by the spread of COVID-19 has been catastrophic, but the effects on the developed worlds' share markets have largely been mitigated by the aggressive implementation of monetary policy tools.
In New Zealand, the RBNZ's monetary policy tools include changing the Official Cash Rate (OCR), the Large Scale Asset Purchasing Programme (LSAP), Term Lending Programme and Purchases of Foreign Assets.
Changing the Official Cash Rate (OCR) sends a powerful signal to the market for lower wholesale interest rates, which passes through to NZ Banks to lower their lending and borrowing rates. The intended effect is lower borrowing rates to stimulate investment by businesses and encourage consumers to spend and/or invest in productive assets rather than cash deposits. Lower interest rates, all things being equal, lowers the value of the New Zealand Dollar which is positive for New Zealand's exporting primary sector, and increased spending generally has an inflationary effect on pricing which helps the RBNZ achieve its inflation policy target.
Changes to the OCR has been the primary monetary policy tool used by the RBNZ, until the COVID-19 pandemic. The OCR was maintained at 0.25% at the August 2020 MPC Meeting, which is consistent with the RBNZ's commentary at the March 2020 meeting indicating to the market that it will likely be maintained at this level for 12 months. The MPC agreed that, "any future move to a lower or negative OCR, if complemented by a Funding for Lending Programme, could provide an effective way to deliver monetary stimulus in addition to the expanded Large Scale Asset Purchasing (LSAP) program, if needed."
The LSAP programme is a monetary policy tool that involves the RBNZ undertaking large scale purchases of New Zealand Government bonds on the secondary market. Purchasing of listed bonds increases the demand on a limited supply of listed securities, increasing the price of these securities, which applies downward pressure on government bond yields (price & yield are inversely related). Government Bonds are widely respected as a risk-free investment, so when lenders and borrowers are calculating the appropriate interest rate to apply to a transaction, they often use a government bond yield for a particular term plus a risk margin. As the yield on government bonds drop, so does the yield on newly issued bonds, term deposits and lending etc.
The initial size of the LSAP programme was NZD $30 Billion over a 12-month period, starting with weekly purchases of NZD $750 million per week via an auction process. On the 25th of March 2020 the RBNZ started its LSAP program. It was expanded in May 2020 to $60 Billion NZD over 12 months to include NZ Government Bonds, Local Government Funding Agency Bonds and NZ Government Inflation-Indexed Bonds (previously excluded), and expanded again in the August MPC Meeting to NZD $100 Billion.
In the RBNZ August Monetary Policy Statement the MPC discussed the expansion of the LSAP programme for the purpose of lowering wholesale interest rates which will pass through to retail interest rates for borrowers & lenders, along with lowering the exchange rate (value of the NZD).
Alternative Monetary Policy Tools
According to the RBNZ, "A negative OCR influences activity in the economy through channels similar to those for a positive OCR. It would lower short-term benchmark rates, flowing through to lower lending and borrowing rates for households and firms, and put downward pressure on the exchange rate." The experience internationally with negative interest rates showed that retail deposit rates tend not to fall below 0% p.a. This will likely be similar for bank lending rates in a negative OCR environment as retail lending rates are priced at a margin above a benchmark rate and bank funding costs.
A Term Lending Programme would involve the RBNZ providing credit facilities directly to lending institutions in New Zealand. According to the RBNZ, "A term lending programme may be increasingly useful for supporting the pass-through of monetary stimulus if the OCR were reduced. The programme could help to ensure that bank lending rates remained responsive to declines in the policy rate even as retail deposit rates approached zero."
Purchases of foreign assets creates additional demand for foreign currency in exchange for New Zealand Dollars (NZD), asserting downward pressure on the value of the NZD. Benefits of the RBNZ purchasing foreign assets includes lower interest rates for borrowers, leading to increased consumption from retail consumers and capital expenditure from businesses, along with a weaker NZD supporting NZ exporters.
The RBNZ has a variety of tools available for supporting the NZ economy, and its widely anticipated that further action will be needed in the coming months. Lower interest rates and a weaker NZD is largely positive for listed NZ companies and the value of existing bonds in client portfolios.
The prospect of a rise in inflation and future interest rates
By the end of 2019, the world was already showing signs typical of a late-cycle phase. Material structural imbalances were unfolding including spluttering regional and global demand, over-indebtedness in major pockets, and weak inflationary impulses. The onset of COVID-19 has dramatically devastated the world, and central banks and governments have quickly implemented enormous emergency liquidity and accommodation measures to prevent the world from descending into a deep recession and potential depression. Meanwhile, three key megatrends have conspired to temper worldwide growth and inflation.
Aging demographics – the older generation increasing in proportion to many countries' populations, means rising public financing obligations, and changing workforce dynamics.
Technology innovation (resultant increasing industrial efficiency, decreased production costs) and the altering of the human/physical capital balance – producing headwinds for global spending levels, economic growth and inflation.
Massive (and ever growing) debt burdens, which traditionally lower additional credit creation, spending and investment – incentivising central banks to keep rates lower for longer.
To be sure, inflation could become an issue down the track. The enormous fiscal and monetary easing alongside with re-emerging supply chains and disillusionment with globalisation in favour of local independence could all provide the impetus for rising prices. One possible scenario sees a global economic recovery brought about by vaccine development and widespread distribution, lockdown removals and the effects of stimulus combining to resemble the periods following World War II. Such an optimistic scenario differs markedly from where the world is currently. We have witnessed the sharpest fall in U.S. growth expectations and the fastest collapse in the U.S. labour market of all time. Treasury yield curves in New Zealand and the U.S. at the time of writing remain decidedly flat, with the market concerned about a prolonged global recession (or even depression) from the fallout of the COVID-19 shock. The pathway to recovery from here may be potentially longer than expected, by vaccine development and widespread distribution, lockdown removals and the effects of stimulus combining to resemble the periods following World War II. Such an optimistic scenario differs markedly from where the world is currently. We have witnessed the sharpest fall in U.S. growth expectations and the fastest collapse in the U.S. labour market of all time. Treasury yield curves in New Zealand and the U.S. at the time of writing remain decidedly flat, with the market concerned about a prolonged global recession (or even depression) from the fallout of the COVID-19 shock. The pathway to recovery from here may be potentially longer than broadly expected.
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Pensions freedom age to increase from 55 to 57