text:
Sun, 26 Jul 2020 01:22:02 GMT
3.8: Ionic Bonding: Symbolizing and Naming Transition Metal Cations
https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FCourses%2FHeartland_Community_College%2FCHEM_120%253A_Fundamentals_of_Chemistry%2F03%253A_Molecules_and_Compounds%2F3.08%253A_Transition_Metals
Heartland Community College
CHEM 120: Fundamentals of Chemistry
3: Ionic and Covalent Compounds
Symbolize and name transition metal cations.
Section 3.5 presented a pattern-based "charge shortcut" for predicting the charges of the ions that result when main group elements ionize. Recall that all main group elements found within the same column in the periodic table have the same number of valence electrons, and, consequently, will form ions with the same charge. However, this charge pattern only applies to main group elements. Transition metals, which are the elements found in Groups 3 - 12, do not have readily-apparent reactivity patterns or trends, with one exception: Because all of the elements in the "B-Block" of the periodic table are metals, they achieve stable electron configurations by losing electrons and, therefore, ionize to form cations.
The remaining aspects of transition metal ionizations are relatively complex. The electron configurations of transition metals utilize d orbitals, in addition to the s and p orbitals that were discussed in Section 2.5. As a result, transition metals are able lose inner shell electrons, in addition to their valence electrons. This atypical behavior allows transition metals to lose more than three total electrons, which is energetically-unfavorable for main group elements. Additionally, most transition metals are able to achieve stable electron configurations through multiple ionization pathways. For example, iron (Fe) can lose two electrons to produce an ion symbolized as Fe+2. However, iron is equally likely to ionize by losing three electrons, resulting in the formation of an Fe+3 cation. As there is no consistency for the ionization of individual transition metals, developing a column-based charge trend that relates these elements to one another is impossible.
Naming transition metal cations is also complicated by their ability ionize through multiple pathways. In Section 3.3, cations were named by including the word "ion" after the name of the element that was ionized. Therefore, the ion symbolized as "Fe+2" should be named as an "iron ion." However, the ion symbolized as "Fe+3" should also be named as an "iron ion." As stated in Section 3.7, no two chemical formulas should share a common chemical name. Since the phrase "iron ion," could refer to either Fe+2 or Fe+3, this name is ambiguous and, therefore, is not chemically-correct.
There are two methods for distinguishing the names of transition metal cations.
The simpler, more modern approach, uses the IUPAC, or International Union of Pure and Applied Chemistry, system. This method indicates the charge of a transition metal cation by writing a corresponding Roman numeral in parentheses after the element name, but before the word "ion," in an ion name. The charges that can result upon the ionization of transition metals, as well as their corresponding Roman numerals, are shown below in Table \(\PageIndex{1}\). Therefore, using the IUPAC system, Fe+2 is called the "iron (II) ion," and Fe+3 is named as the "iron (III) ion." Incorporating a Roman numeral into the name of a transition metal cation removes its ambiguity and results in a chemically-acceptable name.
Table \(\PageIndex{1}\): Possible Transition Metal Charges and Their IUPAC Roman Numeral Designations
+1 (I)
+2 (II)
+3 (III)
+4 (IV)
+5 (V)
+6 (VI)
+7 (VII)
The second system, called the common system uses two suffixes, "-ous" and "-ic," to distinguish the names of transition metal elements. The "-ous" suffix indicates the cation with the lesser relative cation charge, and an "-ic" suffix is used to refer to a cation with a larger charge. In most cases, the stem, or main portion, of the elemental name used in the common system is typically derived from the element's Latin name. For example, the Latin stem for "iron" is "ferr-." Therefore, using the common system, Fe+2 is called the "ferrous ion," and Fe+3 is named as the "ferric ion."
While these names are distinctive and, therefore, are considered chemically-correct, the common system has two significant limitations.
The common system only utilizes two suffixes and, consequently, can only distinguish the names of transition metals that have exactly two ionization pathways. Vanadium (V) can readily lose two, three, four, or five electrons to form V+2, V+3, V+4, and V+5, respectively. The common system cannot be distinguish these ions, as no suffix is available for the ions formed through the third and fourth ionization pathways. In contrast, the IUPAC system can be employed to unambiguously name these ions, as its Roman numerals are directly tied to the charges of the ions. Therefore, V+2, V+3, V+4, and V+5 are named as "vanadium (II) ion," "vanadium (III) ion," "vanadium (IV) ion," and "vanadium (V) ion," respectively, using the IUPAC system.
Additionally, the suffixes in the common system indicate the relative charges of two transition metals, but do not directly specify their exact charges. For example, the Latin stem for "copper" (Cu) is "cupr-." Therefore, using the common system, Cu+1 is called the "cuprous ion," and Cu+2 is named as the "cupric ion." The common names for both iron and copper use the "-ous" ending to refer to the cation with the lesser relative charge. However, iron's lesser charge is +2, but copper's smaller charge is +1. Finally, when iron ionizes to form a cation with a +2 charge, its common name ends in "-ous." When copper ionizes to form Cu+2, its common name ends in "-ic." These inconsistencies often result in confusion, which, again, can be completely avoided by using the IUPAC system.
Despite these limitations, the common system is still fairly prevalent, particularly in the health sciences. Table \(\PageIndex{2}\) provides the IUPAC and common names of several transition metal cations.
Table \(\PageIndex{2}\): IUPAC and Common Names of Selected Transition Metal Cations
chromium chrom- +2 chromium (II) ion chromous ion
+3 chromium (III) ion chromic ion
iron ferr- +2 iron (II) ion ferrous ion
+3 iron (III) ion ferric ion
cobalt cobalt- +2 cobalt (II) ion cobaltous ion
+3 cobalt (III) ion cobaltic ion
nickel nickel- +2 nickel (II) ion nickelous ion
+3 nickel (III) ion nickelic ion
copper cupr- +1 copper (I) ion cuprous ion
+2 copper (II) ion cupric ion
tin stann- +2 tin (II) ion stannous ion
+4 tin (IV) ion stannic ion
gold aur- +1 gold (I) ion aurous ion
+3 gold (III) ion auric ion
mercury mercur- +1 mercury (I) ion mercurous ion
+2 mercury (II) ion mercuric ion
lead plumb- +2 lead (II) ion plumbous ion
+4 lead (IV) ion plumbic ion
Finally, remember that these systems are only used for elements, like the transition metals, that can ionize to form more than one cation. Recall that the main group elements can only follow one ionization pathway. Therefore, the incorporation of a Roman numeral into a main group cation name is unnecessary, as the charge of its corresponding cation is unambiguous. For example, in Section 3.3, the ion symbolized as "Ca+2" was correctly named as a "calcium ion," not a "calcium (II) ion," because calcium will only ionize to form a cation with a +2 charge.
Use the IUPAC system to write an unambiguous ion name for Au+3.
The IUPAC system specifies the charge of a transition metal cation by writing a corresponding Roman numeral in parentheses after the element name, but before the word "ion," in an ion name. The element symbolized as "Au" is named "gold." The superscript in the ion symbol indicates that this ion of gold has a charge of +3, which is represented by a Roman numeral (III) in the IUPAC system. Therefore, the IUPAC name of Au+3 is the gold (III) ion.
Use the IUPAC system to write an unambiguous ion name for each of the following ions.
Cr+2
Pb+4
Answer a
The IUPAC system specifies the charge of a transition metal cation by writing a corresponding Roman numeral in parentheses after the element name, but before the word "ion," in an ion name. The element symbolized as "Cr" is named "chromium." The superscript in the ion symbol indicates that this ion of chromium has a charge of +2, which is represented by a Roman numeral (II) in the IUPAC system. Therefore, the IUPAC name of Cr+2 is the chromium (II) ion.
Answer b
The element symbolized as "Pb" is named "lead." This ion of lead has a charge of +4, which is represented by a Roman numeral (IV) in the IUPAC system. Therefore, the IUPAC name of Pb+4 is the lead (IV) ion.
Write the ion symbol for a nickel (II) ion.
The Roman numeral within the ion name is an IUPAC system designation that specifies the charge of a transition metal cation. The element named "nickel" is symbolized as "Ni". The Roman numeral (II) in the ion name indicates that this ion of nickel has a charge of +2, and this information is incorporated into the ion symbol as a superscript on the corresponding elemental symbol. Therefore, the ion named nickel (II) ion is symbolized as Ni+2.
Write the ion symbol for each of the following ions.
Mercury (II) ion
Cobalt (III) ion
The Roman numeral within the ion name is an IUPAC system designation that specifies the charge of a transition metal cation. The element named "mercury " is symbolized as "Hg". The Roman numeral (II) in the ion name indicates that this ion of mercury has a charge of +2, and this information is incorporated into the ion symbol as a superscript on the corresponding elemental symbol. Therefore, the ion named mercury (II) ion is symbolized as Hg+2.
The element named "cobalt" is symbolized as "Co". The Roman numeral (III) in the ion name indicates that this ion has a charge of +3. Therefore, the ion named cobalt (III) ion is symbolized as Co+3.
3.7: Ionic Bonding: Writing Chemical Names of Ionic Compounds Containing Main Group Elements
3.9: Ionic Bonding: Writing Chemical Formulas of Ionic Compounds Containing Transition Metals


text:
https://apnews.com/press-release/business-wire/space-exploration-technology-science-business-canyons-35821442854443479a24842ae6922de5
Press release content from Business Wire. The AP news staff was not involved in its creation.
PRESS RELEASE: Paid content from Business Wire
Blue Canyon Technologies Announces Reaction Wheel Milestone on NASA's CYGNSS Mission
December 15, 2021 GMT
BCT Nano Star Tracker (Photo: Business Wire)
LAFAYETTE, Colo.--(BUSINESS WIRE)--Dec 15, 2021--
Small-satellite manufacturer and mission services provider Blue Canyon Technologies LLC ("BCT" or "Blue Canyon"), a wholly-owned subsidiary of Raytheon Technologies, announced the five-year on-orbit milestone of its reaction wheels and star trackers on NASA's Cyclone Global Navigation Satellite System (CYGNSS) mission. Manufactured and operated by Southwest Research Institute (SwRI) for Principal Investigator Dr. Chris Ruf from the University of Michigan, the CYGNSS constellation includes 24 high-performance reaction wheels (RWp015) and eight star trackers provided by BCT.
"Our reaction wheel and tracker performance are key components to the mission's attitude controls," said Matt Pallas, Blue Canyon executive director of components. "We pride ourselves on delivering performance-proven products for each of our customer's unique mission needs."
Europe narrows hunt for next astronauts, eyes crewed flights
Study nixes Mars life in meteorite found in Antarctica
China plans space station completion, many launches in 2022
Final goodbye: Recalling influential people who died in 2021
The CYGNSS mission was extended three years to 2023, with plans to revisit and possibly extend through 2026. The mission consists of a constellation of eight low-Earth orbit microsatellites that make frequent measurements of the ocean surface to monitor the intensity and development of tropical cyclones.
"Capturing this data is critical in predicting the intensity of storms and mapping them accurately through the GPS signals received by the microsatellites," said SwRI's Jillian Redfern, CYGNSS project manager and mission operations manager.
Each of the eight satellites is equipped with Blue Canyon's three reaction wheels and one star tracker. The reaction wheels deliver three-axis attitude control with high-pointing accuracy, brushless DC motors, ultra-smooth bearings, and the advanced lubrication system provide low-jitter performance and a long service life, as shown in the CYGNSS mission. BCT's star trackers offer best-in-class performance on missions that require low mass and low power and lead the way in pointing performance.
At its manufacturing facility in Boulder, Colorado, Blue Canyon produces more than 30 reaction wheels weekly and has delivered over 1000 flight reaction wheels, of which 500 have successfully flown. BCT's reaction wheel design offers seven sizes to fit many different applications and has expanded product offerings into high torque and power-efficient control moment gyroscopes.
About Blue Canyon Technologies
Blue Canyon Technologies (BCT), a wholly-owned subsidiary of Raytheon Technologies, offers a diverse portfolio of innovative, reliable and affordable spacecraft that enable a broad range of missions and technological advancements. BCT's mission is to enable space missions to expand the frontiers of science and defense. BCT is currently supporting nearly 50 unique missions with over 90 spacecraft, all in production or recently delivered at their newly developed 80,000-square-foot facility in Lafayette, Colorado.
BCT has supported missions for the U.S. Air Force, NASA and the Defense Advanced Research Projects Agency, and provided the Attitude Control Systems for the first interplanetary CubeSats, which successfully traveled to Mars. The company has been recognized with awards from Inc. Magazine's 5000 Fastest Growing Private Companies, the 2020 Best in Biz Award and the 2020 Tibbetts Award.
For the latest news on Blue Canyon Technologies and for other company information, please visit www.bluecanyontech.com. You can follow the company on Instagram here or Twitter here.
About Raytheon Intelligence & Space
Raytheon Intelligence & Space delivers the disruptive technologies our customers need to succeed in any domain, against any challenge. A developer of advanced sensors, training, and cyber and software solutions, Raytheon Intelligence & Space provides a decisive advantage to civil, military and commercial customers in more than 46 countries around the world. Headquartered in Arlington, Virginia, the business generated $15 billion in pro forma annual revenue in 2020 and has 37,000 employees worldwide. Raytheon Intelligence & Space is one of four businesses that form Raytheon Technologies Corporation.
View source version on businesswire.com:https://www.businesswire.com/news/home/20211215005197/en/
Natalie Miller, 714-496-0839
KEYWORD: UNITED STATES NORTH AMERICA COLORADO
INDUSTRY KEYWORD: WHITE HOUSE/FEDERAL GOVERNMENT PUBLIC POLICY/GOVERNMENT TECHNOLOGY SATELLITE AEROSPACE MANUFACTURING
SOURCE: Blue Canyon Technologies LLC
PUB: 12/15/2021 10:00 AM/DISC: 12/15/2021 10:02 AM

redpajama_set_name: RedPajamaCommonCrawl


To add this calendar to your own electronic calendar (Google Calendar, iCal, etc.), click on the "+Google Calendar" button.
Please note that this is a Google calendar and the older Digital PTO calendar will no longer be updated. If calendar does not show please refresh your browser.


text:
Q: osticket staff id becomes 0 after closing the ticket I am new to the osticket,when someone creates ticket there is staffid but upon closing the ticket staffid against the ticket goes to zero.
structure of ost_ticket table is
ticket_id,ticketID,dept_id,sla_id,priority_id,topic_id,staff_id,team_id,email,name,subject,helptopic,phone,phone_ext,ip_address,status,isoverdue,isanswered,duedate,ropened,closed,lastmessage,lastresponse,created,updated.

As i want to know who closed the ticket and time duration taken by single staff member to close the ticket.
Thanks in advance for the help.

A: I got the solution over here
ost_ticket_event table over there log is maintained of
Assigned ticket
closed ticket
created ticket

along with staffid ,dept_id, team_id
also we can obtain the timestamp

redpajama_set_name: RedPajamaStackExchange


text:
Past Benefits
GALA FOR LIFE
2020 Virtual Benefit
posted by Stephanie Rybinski | 1370sc
The largest pro-life benefit in Canada went virtual May 30, 2020.
From the comfort of their homes, hundreds of Albertans who believe all human beings deserve human rights, tuned in to watch the virtual event. The evening covered:
- The problem (the harm of abortion): An honest look at the state of abortion in Canada.
- The solution (our part of the solution): To pass Canada's first pro-life law to protect girls, women and the preborn from the harm of abortion.
Featuring remarks from Conservative Party of Canada leadership candidates, annual award recipient and Executive Director, Stephanie Fennelly. The first thousand guests register received a Benefit-in-a-box gift packaged mailed to their doorstep.
6:00pm-7:00pm (MDT)
Stephanie Fennelly
Stephanie Fennelly is the Executive Director of Alberta's provincial pro-life group The Wilberforce Project. An honours graduate of the Edwards School of Business in Saskatoon, and currently working on her Masters, Stephanie is a passionate pro-life leader and a proud mother. Seen on CTV and The Miracle Channel, and covered on numerous news sources from the Toronto City News, Calgary Sun, CBC Reporter to Maclean's magazine. Stephanie will be sharing The Wilberforce Project's strategy to create the FIRST pro-life law in Canada.
The Calgary Herald writes "If a group like Wilberforce sells bundles of UCP memberships and succeeds in winning nominations, it will have real influence. Kenney would face internal pressure to alter the abortion system." Come hear Stephanie's strategy to do just that!
Leslyn Lewis
Lawyer, Toronto
www.LeslynLewis.ca
I am not a career politician. I am a mother who has been given much by this great country, and by my hardworking parents before me. I want to help the next generation succeed. I want my children to inherit an even better Canada than the one that has given me so much. Canadians deserve a Conservative party with the courage to hold fast to the foundational values of democracy. We must be a country where the freedom of religion, conscience and expression are upheld.
Member of Parliament for Hastings-Lennox & Addington in Eastern Ontario
www.DerekSloan.ca
Derek is a lawyer, husband to Jennifer and three children. Derek is a Conservative without apology. He knows that the damage to free speech, freedom of religion, and freedom of conscience happening in Canada cannot be understated. It's time for everyone concerned about these issues to stand up and support a candidate who will not just pay lip service but get in the line of fire to defend these freedoms.
Check out our past banquet pictures - click here.
Visit The Wilberforce Project's website
Or sign up:
Liquid syntax error: Error in tag 'subpage' - No such page slug
using a public theme by cStreet


text:
> Privacy, cookies, advertisements
Babymaxi respects the privacy of all users of the website and ensures that all personal data is treated confidentially. Your personal data is properly secured. If we receive or transfer certain critical information, such as payment data, we use a secure server.
Babymaxi uses the collected data to provide its clients with the following services:
1. Processing your order, payment and delivery to the correct delivery address.
2. To inform you about the development of Babymaxi and about special (personalized) offers and promotions. If you no longer would like to receive this information, you can let us know by sending an email to info@babymaxi.com.
3. To be able to request that you share your experiences with Babymaxi in order to be of even better service to you and others.
We will not sell your data to third parties and will only make it available to third parties that are involved in processing your order, evaluating the activities / services of Babymaxi, or optimizing its internet advertisements on other websites. Our employees and third parties engaged by us are obliged to respect the confidentiality of your data.
If you have any questions about the Privacy Policy of Babymaxi, please contact us. You have the right at all times to inspect, correct and/or delete the specified personal data.
When you visit the website, various data is collected to provide you with an optimal service. These small pieces of information are stored in form of cookies on your computer by your browser. Babymaxi uses the following cookies:
Functional cookies ensure that the website works properly. These cookies are placed by default and are not deleted if you do not accept the cookies. Functional cookies ensure, for example, that you can remain logged in on the website or that products stay in your shopping basket.
With analytical cookies from Google Analytics, Babymaxi gets insights how you use the website. These insights are used to improve the website. Analytical cookies make a minimal intrusion on your privacy. They contain no personal data, so Babymaxi cannot use cookies to identify you.
Babymaxi uses Google Adwords (Search, Remarketing for Search, Dynamic Remarketing, Regular Display Marketing, Shopping) and Microsoft Bing Ads to advertise its articles on other websites. To advertise on target, tracking cookies are placed to record the navigation behaviour of visitors.
These cookies make it possible to:
• Keep track of which ads you have already seen. This prevents you from seeing the same ads too often.
• Keep track of how many visitors click on the ads.
• Keep track of how many visitors buy a product after they clicked on an ad. This is necessary to be able to analyse the effectiveness of advertisements.
• Keep track of whether you have already purchased certain products from Babymaxi. You will then not see irrelevant advertisements.
Even if you do not accept cookies, you can still find advertisements from Babymaxi online. Not all ads use cookies. Cookies make it possible to show you more relevant advertisements instead.
Social media buttons and embedded content from social media sites such as YouTube, Facebook, Twitter, Instagram, Pinterest, LinkedIn, Google+ and other platforms often contain cookies. We do not know what these platforms do with these cookies. The information is not clear to us and we also have no influence on the placement or not of these cookies. For the placement of these buttons and embedded content (including the cookies) we need your permission according to the cookie legislation.
You can always change the settings of your browser so that you do not receive cookies while shopping on Babymaxi's website. Please note that you must adjust the settings separately for each browser and computer you use.
Advertisements, links to other websites
The Babymaxi website may contain advertisements from third parties or links to other sites. Babymaxi has no influence on the privacy policy of these third parties or their websites and is not responsible for this.


The FBI said Sol Pais, 18, is "considered to be extremely dangerous" and "made threats to commit an act of violence in the Denver metropolitan area" just days before the 20th anniversary of the attack that killed 13 people.
All schools in the Denver area were urged to tighten security because the threat was deemed "credible and general," said Patricia Billinger, a spokeswoman for the Colorado Department of Public Safety. Columbine and more than 20 other schools outside Denver lock their doors for nearly three hours Tuesday afternoon before Wednesday's complete closures were announced.
Authorities said Pais was last seen near Columbine -- in the Jefferson County foothills outside Denver -- wearing a black T-shirt, camouflage pants and black boots. They appealed for anyone seeing her to call an FBI tip line at 303 630-6227, and said she is too dangerous to be approached by civilians. The alert also said police who come into contact with her should detain her and evaluate her mental health.


In this episode, I interview Steve Shell (VP of Veterinary Channel Development) and Elyse Cannon (Claims Manager) about the details of their new policy. It offers policyholders broader choices of policy maximums (new unlimited option), deductibles (new annual option), and copays so they can customize a policy that fits their needs at a premium they can afford.
Thanks for sharing on the new Petplan Launches. The Expanded Coverage on pet insurance policy is good offer.


text:
You are here: Home / Movies / Blu-ray / House of Cards Season 2 Blu-ray Release Date and Pre-Orders
House of Cards Season 2 Blu-ray Release Date and Pre-Orders
April 20, 2014 by Sara Leave a Comment
With the last batch of Netflix April content showing up this week, it's only appropriate that Sony announced the House of Cards Season 2 Blu-ray release date. On June 17, House of Cards: The Complete Second Season will see a street date on both the Blu-ray and DVD format. All 13 episodes will be available on the four-disc Blu-ray and four-disc DVD sets. Pre-orders are hit-and-miss on Amazon; you should check this link
periodically and place your pre-order ASAP, as they may disappear again.
The House of Cards Season 2 Blu-ray and DVD box sets have collectible packaging and five bonus featurettes in addition to the 13 episodes. Two Houses explores the differences between the classic '90s British mini-series, as well as the history of how this project came together.
Table Read gives a behind-the-scenes look at table reads cut together with the actual scenes from the show, demonstrating how the scene changes from script to screen. Direct Address focuses on the way Francis talks directly to viewers, breaking the 4th wall, and the differences between how it's done in the original show versus how it is used in this series.
The last two featurettes are Politics for Politics Sake, which explores the universal themes of the show, including relationships and power, not just politics; and Line of Succession, in which fans can get a closer look at the creative process that goes into producing an episode.
In House of Cards Season 2, two-time Academy Award-winner Kevin Spacey returns as the newly appointed Vice President of the United States, along with Robin Wright, this year's Golden Globe winner for her role as his wife, Claire Underwood. In Season 2, the series continues to sizzle as the ruthless Underwoods stop at nothing to climb the political food chain.


Placed on a hillside, rising majestically above the 600 acre beach, Jade Mountain Resort on St. Lucia's south-western Caribbean coastline is a cornucopia of organic architecture. Celebrating St. Lucia's stunning scenic beauty, this exquisite resort has been innovatively designed to integrate with nature and is a hopeless romantic's dream.
The bold architectural design – individual bridges leading to exceptional infinity pool sanctuaries and rugged stoned-faced columns reaching towards the sky – makes Jade Mountain St. Lucia one of the Caribbean's most mesmerizing resort experiences.
Individual bridges lead to unique suites featuring a king size bed, living area, bath and rain shower all in one extravagantly sized living area. Without any telephones, radio or televisions, you can enjoy in sounds of nature, awaken with birdsong and beautiful smell of tropical flowers.
In Jade Mountain Resort you can expect grand sweeping spaces where bedroom, living area and an extravagant private infinity pool glide which reflects the changing colors of the sky, into one another forming extraordinary floating platforms out into nature.
The Jade Mountain Resort combines exquisite dining with spectacular views. Seasonal menus showcase modern fusion cuisine infused with bold Caribbean flavors. The Celestial Terrace offers a romantic spot for watching sunsets or star-gazing. You can also dine at any of the restaurants and with short walking you can go directly to the two lovely beaches.
This unique and luxurious hill side Jade Mountain Resort offers ultimate romantic retreat.


*VF and VH staterooms have solid steel verandah railings instead of clear-view Plexiglas railings; VH have shower only.
A $600 per person deposit, plus a $150 pp Non-refundable Booking Service Fee, along with a completed reservation form confirms your space. FULL PAYMENT is due on August 1, 2020 ("Final Payment Date") (or, if you book after August 1, 2020 at the time of booking). Passengers are not confirmed on the manifest and cruise tickets are not issued until your account is paid in full. The Conference Fee ($1,575) payment is due 30 days after initial booking.
The Surcharge for late boarding in Ushuaia ($499 for Conference Attendees; $1,099 for non-attendees) is collected when this service is requested and is immediately non-refundable.
A signed Insurance Waiver is due in the Insight Cruises office upon issuance and no later than the Final Payment Date. Your booking is subject to cancellation unless we receive this document.
Insight Cruises will match all published prices on HollandAmerica.com.
If you purchase the cruise on your own, the Conference Fee can be purchased separately. There is a 60% Conference Fee surcharge to do this. This surcharge covers all goods and services the cruiseline provides to guests traveling with our group. This option is capacity controlled.
If you would like to be the sole occupant of a cabin, there is a single-occupancy upcharge of 80% for cabins without a balcony and a 100% upcharge for all cabins with a balcony.
This option is for passengers who are coming on this event by themselves and wish to share a cabin with another passenger in our group. Many Insight Cruisers, male and female, are independent travelers. Some of our sharing guests find a new friend in their roommate; some find a source of new information and viewpoints; all find a great cruise fare!
For this cruise, we will guarantee we will find you a roommate, or you will have the cabin to yourself (!): IF you sign up for the SEMINAR PROGRAM AND you book at least 12 months in advance.
RESTRICTIONS: Only cabins without balconies are possible to share. (Please inquire if you wish to share a different category.) Share cabin assignments are generally made at time of ticket issuance — and shared cabin assignments are subject to change. If you do not quality for our GUARANTEED share (see paragraph just above), and can be matched, you will be matched with members of the same gender, and we factor in age and geography (in that order) where possible. Shares that are not initally guaranteed when booked remain not guaranteed until confirmed which will be no later than July 1, 2020. If you are unmatched, you may cancel on July 1 with no penalty — though the initial $150 non-refundable Booking Service fee and the late boarding fee (if you have selected this option), remain non-refundable. (Your cruise deposit, SEMINAR PROGRAM or facility fee, hotel nights, and air if booked with the cruiseline, would all be refundable if we can not find you a match.) Because of the limited number of accessible cabins, shares are not available for physically-challenged passengers.
For Inside/Oceanview cabins, $1,999; Verandah, $2,049; Suites, $2,099.
A $25 discount is given for each previous Insight Cruise attended. Minimum discount is $50 per person for previous Insight Cruisers. Maximum discount is 10% of the cruise fare.
Surcharge for late boarding in Ushuaia ($1,099 or $499) — this option is capacity controlled by Argentinian Customs. If you have signed up for our SEMINAR PROGRAM (which is $1,575) the addon fee for joining late in Ushuaia is $499; otherwise it' $1,099 plus a $200 Facility Fee (see next item).
Facility Fee ($200 pp) — If you have not signed up for our SEMINAR PROGRAM (which is $1,575) you will be assessed the Facility Fee. This fee includes invitations to the group's private cocktail parties (approximately nine) plus access to our exclusive viewing area during the solar eclipse.
Once you book with Insight Cruises, you are allotted 35 emails and/or phone calls (each phone call is counted as two emails). Included in this count — as one each — are: each phone call to Insight Cruises; each email you send to us; our reply to your email; plus each email we send out and/or receive to research and answer your questions that are not answered or addressed on our webpages.
$79. Shift mental gears and start your trip by joining us at Pre-cruise Cocktail Party! Take this opportunity to meet your fellow eclipse/cruise participants. The reception will be held in our hotel the night before departure. Premium beer, wines, and light hors d'oeuvres will be served.
The optional Conference Fee ($1,575) includes over 24 hours of programming plus nine parties. Traveling companions who do not want to participate in our Conference will be assessed our Facility Fee ($200 pp) which includes invitations to the group's private cocktail parties plus access to our exclusive viewing area during the solar eclipse.
NOTE — The items listed in this paragraph are not included in the table of cabin prices at the top of this page. Except for the $15 (approx.) per person, per day cruiseline gratuities (assessed by Holland America during the cruise), all of these charges are bundled into the price quoted under BOOK / PRICE NOW: Port charges, government taxes, and fees (estimated to be $380); Non-refundable Booking Service Fee ($150); tour leader gratuities ($150). The following items and services are not included in any of our pricing and can be purchased onboard: the spa; casino action; Holland America shore excursions; dining in the two private restaurants (about $25 pp); internet access; and any expenses of a personal nature are extra. Airfare is not included.
A Passport (valid through July 1, 2021) is required. Non-U.S. citizens residing in the United States will need valid Alien Registration (green) cards as well. All others must have valid passports and any required visas when boarding the vessel. All travel documents such as passports, visas, proof of citizenship, etc., that are required for embarkation, disembarkation at the ports of call, and re-entry into the United States are the responsibility of the passenger. Non-U.S. citizens are asked to check with government agencies, embassies or consulates to determine documentary requirements.
Once your itinerary is set, we charge $150 per person to purchase the tickets — if you would like us to do that. But because you now know the exact flights, dates, itineraries, and costs you can easily purchase the tickets yourself, if you wish, thus saving this $150 fee.
Smoking is not allowed in your cabin or inside the ship. There is a smoking area, outside, on the Lido deck, all the way aft.
The Sky & Telescope Eclipse December 2020 cruise is managed by Insight Cruises, hired as an independent contractor. Insight Cruises acts only as an agent for the respective suppliers by making arrangements for transportation, accommodations, and other services. Neither Sky & Telescope nor Insight Cruises shall be held liable for personal injury, death, property damage or accident, delay, or irregularity arising out of any act or omission of these suppliers. Sky & Telescope and Insight Cruises reserve the right, without penalty, to make changes in the published itinerary whenever, in their judgment, conditions warrant, or if they deem it necessary for the comfort, convenience, or safety of our participants.
Sky & Telescope and Insight Cruises reserve the right, without penalty, to decline to accept any person as a participant. Insight Cruises reserves the right to require any participant to withdraw, at the participant's own expense, from the event at any time, when such action is determined by Insight Cruises' staff to be in the best interests of the health, safety, or general welfare of the group or the individual participant; Insight Cruises will then refund the recoverable portion of the total amount paid that corresponds to the cost of unused services and/or accommodations, if applicable. Sky & Telescope and Insight Cruises accept no liability for the purchase of non-refundable airline tickets to the cruise departure city and return. Baggage and personal effects are at all times the sole responsibility of the participant.
Dates, schedules, and program details, although provided in good faith based on information available at the time of publication of the flyer(s) or the website, are subject to change and revision. Neither Insight Cruises or Insight Cruises' partners, co-producers, sponsors, or agents accept liability for cancellation penalties or change fees related to domestic or international airline tickets purchased independently in conjunction with Insight Cruises' events.
The undersigned has read carefully the Responsibility Statement and Liability Disclaimer set forth above, the schedule of activities for this event, as well as the terms and conditions of application and participation as set forth in the event brochure and/or these webpages, and recognizes and accepts any risk associated with the event and the conditions, including the refund policy, set forth above. The undersigned further acknowledges that there are many risks and uncertainties inherent in any travel, including but not limited to the hazards of various modes of transportation, forces of nature, force majeure, acts or omissions of foreign governments, terrorism, civil unrest, war or insurrection, theft, illness, disease, strikes, and damage to person or property due to the negligent acts or omissions of event staff or others. In consideration of, and as part payment for, the right to participate in the event, the undersigned, on behalf of himself, his dependents, heirs, executors, administrators and assigns, agrees to release Sky & Telescope and Insight Cruises and its officers, employees and agents, from liability for personal injury, death, property damage or loss suffered by any person in connection with this event, even if caused by the negligence (but not the reckless, willful, or fraudulent conduct) of event staff or other related persons or entities. In addition, by registering for this event, the applicant certifies that he or she is mentally and physically capable of full participation in this event.


The Central Connecticut State University Police Department has a six-officer bike squad that was established in the summer of 1993. The bike patrol operates 12 months out of the year, 24 hours a day and is capable of riding in almost all weather conditions. The officers are certified police cyclist's through the (IPMBA) International Police Mountain Bike Association.
The bike patrol has proved to be beneficial to the campus community and to the police officers. An approach to policing associated with Community Oriented Policing, the bike patrol has been very well received by students because of the added police visibility an approachability of a bike officer. At the same time, officers enjoy the opportunity to interact with students, faculty and staff in a positive way. Would-be criminals are not especially fond of bike patrols because of the mobility and unpredictability of such patrols.
Patrolling on a bike gives the officer a great deal of mobility and enables the officer to quickly and efficiently patrol and respond to areas of campus that are inaccessible to patrol vehicles but too large for traditional foot patrols. These are traits that do no endear bike patrol officers to would-be criminals. The bike officers are able to respond quickly to many service calls, arrive unnoticed at times, and increase the likelihood of capturing a suspect.
The bicycle patrol will not replace the traditional police vehicle but the program has benefited the University community by returning the police officer to the "beat".
The CCSU bike patrol employs Raleigh 24-speed mountain bikes. Six police officers are qualified to ride and up to two units per shift are in operation.
Bicycles are specially designed for police work. The frames, brakes and gears have been expressly designed for high performance riding. Both bikes are equipped with high-tech lighting systems that provide excellent illumination while on patrol at night. Equipment bag with side pouches are also attached to provide carrying room for equipment.
Bike officers are issued long and short riding pants, jacket with winter liner, and polo shirts along with appropriate safety gear. All uniform items are equipped with proper patches, emblems, insignias and reflective trim.
The bike patrol units operate year round, around the clock -- taking into consideration weather conditions and staffing needs.
All officers selected for this patrol should be in excellent health and physical condition and be able to pass a physical and/or physical fitness test. Once selected, officers must achieve perfection in balancing, skid control, stair descent, hill and curb management, road safety and self defense techniques in a week-long course taught by a certified instructor. All officers who complete the course are certified Police Cyclists through the International Police Mountain Bike Association.


text:
balita.ph – Online Filipino News
Sports/Entertainment
Health/LifeStyle
Lead Photo
Development goals seen to help end poverty in Eastern Visayas
TACLOBAN CITY, Oct. 5 –- The government is stepping up awareness drive on Sustainable Development Goals (SDGs) in Eastern Visayas as part of the month-long National Statistics Month (NSM) celebration this October.
"Sustainable Development: Making Statistics Count" is the theme of this year's NSM celebration, which focuses on the critical role of statistics in monitoring the country's progress on achieving SDGs.
"Sustainable Development Goals or the 2030 agenda is a plan for action for people, the planet and prosperity," said Philippine Statistics Authority (PSA) Regional Director Wilma Perante.
SDG will play a key role in the target setting. It aims to end poverty, to protect the planet, and for the people to enjoy peace and prosperity, according to the PSA official.
As member of the United Nations, the country will join other countries in adopting the 2030 Agenda for Sustainable Development, which includes a set of 17 SDGs to end poverty, fight inequality and injustice, and tackle climate change by 2030.
National Economic and Development Authority regional project monitoring and evaluation division chief Evangeline Paransaid the theme is very timely for the region because Eastern Visayas has been ranked as 2nd poorest region in the country.
"The SDGs will be the guide to resolve issues concerning the development in Eastern Visayas," Paran said.
Poverty incidence in Eastern Visayas has worsened between 2012 to 2015, making the region as the country's second poorest, based on the latest Family Income and Expenditure Survey result, the PSA reported.
Poverty level inched up to 47.3 percent during the first half of 2015 from 45.4 percent three years earlier. The region moved one notch up and dislodged Soccsksargen as the second poorest region in the country.
The Autonomous Region in Muslim Mindanao remained the poorest area in the country with a poverty incidence of 59 percent.
The month-long celebration, spearheaded by the PSA, aims to promote, enhance and instill the awareness and appreciation of the public on the importance and value of statistics.
Joining the celebration are different government agencies, state universities, and the private sector.
According to PSA's website, the National Statistics Month (NSM) was first observed in 1990 pursuant to Presidential Proclamation No. 647 signed by then President Corazon Aquino on Sept. 20, 1990, declaring the month of October of every year as the NSM.
The NSM celebration aims to promote, enhance and instill awareness and appreciation of the importance and value of statistics to the different sectors of society; and to elicit the cooperation and support of the general public in upgrading the quality and standards of statistics in the country. (PNA) JMC/SQM/Dara Pearl Dacuyan (OJT)
/EGR
Filed Under: Provincial
Tagged: Eastern Visayas, NSM, PSA, SDG
SSS charges 3% penalty on overdue contributions
Kakawate leaves as pesticide, bio-organic fertilizer
Investment on ready-to-lay hens
Oct. 10, 1977 Patikul massacre recalled (Feature)
DOH releases new 5-in-1 vaccine for babies in Western Visayas
Myanmar targets 7-M tourist arrivals in 2020
Pampanga to open up livelihood opportunities to boost tourism industry, says official
More Fun in the PHL campaign has failed to attract more tourists, says study
Expect influx of Israeli tourists in PHL
Government allocates PHP410-M to relocate about 2,000 Intramuros settlers
US $1 = PHP 46.9500
2013 Campaign Trail
Bayanihan News Filipino news and around the world about people, events and the environment.
Home · About · Privacy · Copyright · Contact
Copyright © 1994-2016 balita-dot-ph
Another quality website by Celso Barriga


text:
Berkeleyside
Berkeley, CA's independent news site
Free for all, funded by readers
The Oaklandside
COVID: The numbers ● Vaccines ● Get tested | MARINA: Special project | WE'RE HIRING: Climate/transportation reporter ● Photographer
Master craftsman, Zen priest Paul Discoe puts his touch on new Berkeley Art Museum
Dec. 242015, 10 a.m. Nov. 62019
Paul Discoe and his associate review plans. Photo: Josephine Wu
By Kathleen Maclay / Berkeley News
When the Berkeley Art Museum and Pacific Film Archive reopens at its new downtown location on Jan. 31, the University of California, Berkeley, visual arts center will feature wooden furnishings revived from a previous life by a local master craftsman, ordained Zen Buddhist priest and designer of Buddhist temples.
"I like trees of all kinds. I like to grow them, trim them, chop them and make wonderful new things with them," says Paul Discoe, an artisan and student of Japanese culture. Before his meditative work at BAMPFA, he designed the famed Zen centers in Tassajara and Green Gulch, California, as well as temples and even a temple-inspired home for tech mogul and Oracle chief Larry Ellison.
The trunks of salvaged trees are stacked up on Paul Discoe's collection yard in Oakland. Photo: Josephine Wu
Now Discoe is applying the finishing touches on seating for BAMPFA's airy new amphitheater, its store shelving and a reception desk, all made out of woods collected from campus and community locations – and bringing a bit more Zen to Berkeley in the process.
The website for his Oakland-based shop, Joinery Structures, notes the eco-friendly business is based around "material, mindfulness and balance."
"I like turning things that people think of as waste into something beautiful. It's very rewarding," says Discoe, who began his relationship with trees as the age of 6 when he asked for a woodworking set for Christmas.
With a Jan. 31 opening date for the new BAMPFA, Paul Discoe and his team put the finishing touches on new furnishings made from salvaged wood. Photo: Josephine Wu
The trees include several Canary Island pine trees salvaged from BAMPFA's construction at the Center and Oxford streets location prior to construction there, and black acacia, which Discoe described as a cross between rosewood and mahogany.
Discoe says he was surprised when he began to work with the long-needle pine. Initially, he saw them a not-too-impressive, invasive species that is "soft, fluffy, namby-pamby and show-offy." But once the trees arrived at his West Oakland facility and he looked inside, he found them to be "strong ,with a lot to say aesthetically."
Discoe says he believes all trees have value and stories to tell, alive or dead.
A close-up of new seating at BAMPFA. Photo: BAMPFA
In Zen Architecture: The Building Process as Practice (2008), Discoe and Alexandra Quinn describe the "crooked cucumber" approach to construction, in which the late Shunryu Suzuki Roshi of the San Francisco Zen Center would pick the odd-looking or misshapen vegetables at a farmers market because if he didn't, no one would. Discoe's use of salvaged wood from the urban forest follows the same principle.
Discoe has teamed with Berkeley on projects involving reclaimed wood for more than 20 years. He also designed the Obata Gate, a Japanese mountain-style gate that stands by the entrance to theJapanese Pool at the UC Botanical Garden.
He also is a longtime acquaintance of BAMPFA director Lawrence Rinder, who asked Discoe to share some ideas for the new museum. Also, Discoe's wife, philanthropist Ann Hatch, is a former member of the museum's board and an integral part of BAMPFA's fundraising efforts around its move to the downtown Berkeley arts district.
An overhead view of installation work at the new BAMPFA. Photo: BAMPFA
"We are thrilled to have such an important contribution to our new building from Bay Area legend Paul Discoe," said Rinder, "Paul is a magician with wood and his work will bring a feeling of elegance and warmth to our pubic gathering areas."
Discoe says he started conversations with the new museum's architect of record, EHDD of San Francisco, over a year ago. Finally, the process is nearing a close with the opening soon of the new BAMPFA, an 83,000-square-foot facility designed by the acclaimed New York-based architectural firm Diller Scofidio + Renfro.
BAMPFA's opening exhibit, "Architecture of Life," curated by Rinder, will fill all the new building's gallery spaces with more than 250 artworks, architectural drawings and models, and scientific illustrations reflecting on life experience and dating back more than 2,000 years. Very Zen.
This story was first published by UC Berkeley's Berkeley News, on Dec. 15, 2015. Reprinted with permission. BAMPFA opens on Jan. 31. Visit the new BAMPFA website for more information.
New museum gets ready to open in the heart of Berkeley (11.19.15)
Berkeley Art Museum's iconic building closes after 44 years (12.24.14)
Gallery: Fans celebrate Berkeley Art Museum milestone (07.21.14)
Salvaged trees to be used in Berkeley's new art museum (05.22.14)
On the cusp: Berkeley Art Museum/Pacific Film Archive (05.01.13)
Before new Berkeley art museum can rise, a demolition (04.08.13)
Art museum chief: New space good for Town & Gown (02.13.13)
Work begins on new Berkeley Art Museum, top open in 2016 (02.12.13)
Palpable possibilities: Berkeley Art Museum's home awaits (01.25.12)
New Berkeley Art Museum mixes old with eye-catching new (09.16.11)
Follow Berkeleyside on Twitter and on Facebook where we often break news. Email us at tips@berkeleyside.com. Would you like the latest Berkeley news sent to your email inbox once a day? Click here to subscribe to Berkeleyside's free Daily Briefing.
Can you help us make a difference?
The reporters and editors at Berkeleyside are dedicated to covering our city and providing you with the information you need to be an informed citizen. If you value what you get from Berkeleyside, please join us with a tax-deductible donation so we can continue doing the local reporting that matters to you.
Will you chip in to Berkeleyside today?
Yes, I'll chip in!
More at Berkeleyside
BAMPFABerkeley Art Museum rebuildDowntown BerkeleyUC Berkeley
Most-read in Arts
Wonder Woman's Black twin, Nubia, inspired Cal professor's book on superhero comics
Denny Abrams, creator of Fourth Street, has a jazzy second life
Strong ticket sales, empty seats for Berkeley venues during omicron
Is 'Bad Luck Banging and Loony Porn' the most enlightening film of the year?
In new biography of Nobel Prize winner Jennifer Doudna, science is a 'competitive sport'
Outdoor dining guide
Nosh features
Subscribe to Nosh
Donate to Berkeleyside and support independent local journalism.
© Cityside. All Rights Reserved.


Mad Hatter Amusements Inflatable Rentals SC - Bounce House Rentals in SC.
Welcome to Mad Hatter Amusements, your local family-owned supplier of rental inflatables, rides, concessions, carnival games, and fun since 1991. Whether you're looking for dunk tanks in SC or bounce house inflatables in NC, we are your one stop shop for guaranteed entertainment. Welcome to the party!
Mad Hatter Amusements has a proud, family-owned history that dates backs to 1991. We offer over 100 unique and quality attractions to take your next party or event to the next level. More importantly, we put you first and strive to deliver the highest standard of service possible.
At Mad Hatter we're all passionate about amusement, but that doesn't mean we're easily amused. That's why all of our inflatables and games are fully insured, inspected, and kid-approved. We pride ourselves in delivering the best in entertainment, and your party is no exception. While we specialize in inflatable rentals SC and NC, we also offer a full range of other games and entertainment sure to please the whole crowd.
•	Tropical-themed slip and slide.
This is just a small selection of what we have to offer. Please contact us to learn more, as our mission is to deliver the fun that will bring your vision and party to life.
At Mad Hatter if it's not fun, we're not interested. All of our inflatables and amusements have been tried, tested, and are sure to bring the excitement. We make the process easy with fully insured products, convenient delivery, and friendly service. We treat every event as if it were our own, and pride ourselves on over 20 years of customer satisfaction.


text:
by Harlow Giles Unger
Nonfiction / Biography & Autobiography / Presidents & Heads Of State
He fought for Washington, served with Lincoln, witnessed Bunker Hill, and sounded the clarion against slavery on the eve of the Civil War. He negotiated an end to the War of 1812, engineered the annexation of Florida, and won the Supreme Court decision that freed the African captives of The Amistad. He served his nation as minister to six countries, secretary of state, senator, congressman, and president.
John Quincy Adams was all of these things and more. In this masterful biography, award winning author Harlow Giles Unger reveals Quincy Adams as a towering figure in the nation's formative years and one of the most courageous figures in American history, which is why he ranked first in John F. Kennedy's Pulitzer Prize-winning Profiles in Courage.
A magisterial biography and a sweeping panorama of American history from the Washington to Lincoln eras, Unger's John Quincy Adams follows one of America's most important yet least-known figures.


text:
Journal of Agricultural and Food Chemistry es una revista científica revisada por pares publicada desde 1953 por la American Chemical Society. La frecuencia de publicación es bimensual y publica artículos de investigación originales en el campo de la agricultura, química aplicada y la ciencia y tecnología de los alimentos.

De acuerdo con Journal Citation Reports, el factor de impacto de esta revista fue 2,912 en 2014. Actualmente el editor de esta publicación es James N. Seiber, de la Universidad de California en Davis, en EE. UU.

Journal of Agricultural and Food Chemistry está indexada actualmente en las bases de datos Chemical Abstracts Service (CAS), Scopus, ProQuest, PubMed, CABI, Ovid, Web of Science, y SwetsWise.

Referencias

Revistas publicadas por la American Chemical Society
Revistas científicas quincenales
Publicaciones fundadas en 1950
Revistas de química
Revistas científicas de Estados Unidos

redpajama_set_name: RedPajamaWikipedia


CHELMSFORD -- The Board of Selectmen will have a female majority for the first time in the town's history.
Incumbent Pat Wojtas was reelected to a fifth term with 1,580 votes and political newcomer Virginia Crocker Timmins was elected in her first run for office, pulling in the most votes at 2,030, according to unofficial results. Glenn Kohl came in last with 1,270 votes.
Overall turnout in the election was 12 percent.


Egee throws are woven with the finest baby alpaca fibers giving this throw an amazingly lush feel. An excellent accent for any bedroom or living room space.
Available in four colors: Eau, Marine, Pierre, Pollen.
Finished Size: 51 in. x 67 in.


You'll find much to love about this three-bedroom Hyannis home, a cozy, family-friendly escape with a screened-in porch, a spacious backyard with a firepit and a deck, and easy access to some of the most beloved beaches on Cape Cod!
This home sits one mile north of the famed Kennedy compound in Hyannis Port, where guests can create their very own idyllic Cape Cod vacation. Spend your days riding bikes, taking hikes, and wading in the cool waters of Craigville Beach, Kalmus Beach, and Veterans Park Beach (each of which is three miles away).
Come home from the beach each afternoon to toss your bathing suits in the private washer/dryer, fix a few cocktails and cold drinks in the full kitchen (with a dishwasher), and play cards with your loved ones outside on the screened porch. Use the free WiFi to look up a new recipe, tell stories and roast marshmallows around the firepit, and find a cable movie to watch in the warmth of the wood-burning fireplace.
Discover the beauty of Cape Cod living - book today! We are available 24 hours a day, seven days a week. Contact us with any questions and for complete, real-time pricing information (Vacasa listing #15239).
Additional availability info: Minimum night stays might be higher for select holiday weeks. This is a Saturday to Saturday vacation rental.


Music could affect your sleep. You'd be amazed at the things they've discovered about sleep learning. When you're asleep, your thoughts are open to whatever is playing. When you go to sleep, you ought to adopt enjoyable thoughts to assist you producing pleasurable dreams. There have been times when I've gone to bed pressured regarding something during my waking life only to dream about it all night long so I believe when it's soft tranquil music you get relaxed and you will certainly dream of more pleasant things yet If you drop off to sleep with a horror movie on you might have bad dreams. Your subconscious grabs that there is a degree of fact in there somewhere. Music could have a wonderful impact on dreams.


(ESRD) in a time when renal replacement treatments were in their first steps.
results, and strong organ transplant programs were generalized everywhere throughout the world.
transplants, 3927 lung transplants, 2362 pancreas transplants, and 227 small bowels.
clinical condition, and quality of life of healthy organ transplant recipients.
ESRD patients may survive with steady dialysis and diabetic patients with insulin treatment.
and respiratory failures as per the Nephrology journal.


Thumbtack headquarters HQ office address, customer service phone number, toll free helpline number, customer support number, email id and website is given with the Thumbtack contact office address, telephone number, fax number, TTY toll free phone number, Thumbtack complaints, reviews, ratings, social links, official support link, etc.
Thumbtack headquarters HQ and customer support team is available to provide best service for their customers during office timings of Thumbtack, and the customers can call one of these contact numbers to get help from Thumbtack listed below. If Thumbtack phone numbers are unavailable, so kindly connect to Thumbtack headquarters HQ by using following contact information of Thumbtack including office addresses, email ids and telephones.
The contact details of Thumbtack headquarters HQ are sharing below. Thumbtack customer support department provides help and support to the customers during the working / after hours through Thumbtack emails, phones and online. If you want help and general support concerning Thumbtack products, kindly call Thumbtack customer service representatives and call centre to receive a prompt resolution related issue you might have.
The complete office contact information of Thumbtack headquarters HQ is given above with Thumbtack mailing office address, Thumbtack postal office address, Thumbtack payment office address, Thumbtack customer service office address and official website. Many people are looking for customer service helpline number of Thumbtack, toll free number of Thumbtack, customer support email id of Thumbtack, corporate headquarters address of Thumbtack, mailing address of Thumbtack, postal / payment address of Thumbtack. The all-important contact details of Thumbtack are listed above.


most importantly, I realised that I did my best writing in Scrivener. I wrote my undergraduate dissertation in Scrivener, and I was able to publish it in an A-ranked peer-reviewed journal. The main thing I notice going back and reading that article is that my progression of thought and argument was clear. Scrivener doesn't make it easy to write, but it does make it easy to organise the ideas in a long piece of writing.
one aspect of this is its outlining tool. For my masters writing, I used a separate outliner. A specialised tool is always easier and better, but the problem is that the writing and the outline are never in sync with each other, because as I write my idea of the outline changes. Scrivener's builtin outliner is very good, not as good as a specialised tool but still excellent — and because the outliner, synopsis, and notes tools are attached to the sections in the document hierarchy, they never get divorced from the actual thesis.
version 3 of Scrivener introduces excellent support for Markdown and other markup-based formats, by allowing the conversion of its styles to markup. This is a game-changer for my use (processing via Pandoc).
The real test will come in a few weeks when I submit my first major piece of work for assessment.
Six companies have been fined so far this year.
But even if we can agree on this, who gets to speak for the poor?
The situation with BHS highlights a couple of the ethical challenges around pension funds.


It is indeed a surprising turn of events when Malaysia entered the big business of golf courses and delivered its own brand of highly feasible, highly attractive golf courses in Kuala Lumpur. So, get on with an experience of the Asian brand of golf culture in this listing of golf courses in Kuala Lumpur.
Since its opening in 1986, Saujana Golf & Country Club has hosted several distinguished events: three events of Kosaido Malaysian Ladies Open, two separate events Eisenhower Trophy and the Espirito Santo Trophy for the 2002 World Amateur Golf Team Championships. It was also the venue for the $910,000 Carlsberg Malaysia Open Golf Championship of 2001.
It is because Saujana Golf & Country Club possesses two spectacular golf courses The Palm and the Bunga Raya that it got so much accolade by golf critics, including the Asian Golf Monthly 2005 The Best Championship Course in Asia for Palm Course and the 69th spot on the Top 100 Best Courses outside the USA for the Bunga Raya Course by Golf Digest 2005 Survey.
Undulating terrain and fresh greenery provides plenty of aesthetics for the Bukit Jambul Golf & Country Resort, but yet no one can ignore the challenges that are subtlety expressed by the scenic beauty of the place. It even has fruit trees that can be enjoyed by the golfers, an interesting bonus that only adds to its deserving ranking among the best golf courses in Kuala Lumpur. Even the opening hole can be rightfully bear the index rating of one.
Golf courses are also nature walks, benefiting mind and body. While most golf course do take you to nature, Bukit Unggul Country Club takes you one step closer still. Because this course is one fine example of how a golf course can be carve out of nature's bosom without really changing anything. The effect? Challenges in their most natural and accepted setting. Waterfalls, natural elevated greens, copses of trees, just naturally perfect.
The Glenmarie Golf & Country Club's approach for the TPC at Sawgrass the "Island Green" or the 17th hole may be more accepted than TPC's but that's not what made the Glenmarie spectacular. A water course, the Glenmarie features plenty of water hazards and water carries remeinscient to the 17th hole. Glenmarie is also vast, plus coupled with those water traps it can definitely pose real challenges even to veteran golfers.
Identity Logo Design – How Important is it For Your Business?


numero UNO: our friends and neighbours Francesca and Paolo finally received the itinerary for their trip to China to become parents, on the 22nd of February they will at last be able to hold their 1 yr old daughter Lè Chen in their arms.!!! Just wait until they tell her about all the crazy people anxiously awaiting her back here at Incocco, she may decide to remain in Guixi !!!!
And in the new arrival theme, YES the first chicks have hatched!!!! Spring must be on its way. At this moment (6pm) we are up to 15 and still lots more pipped and peeping!! Little LeChen is going to love them!
Ok and about yesterday, the first group hike in the almost spring weather, water everywhere on the trails. It was a great group hike with the usual people (8) and dogs (4) but for fun Frà decided to add in Sophia the donkey and Sole the goat. Just so you see what silliness we can get up to on Sundays!
Mi sembrano 3 magnifiche asienelle!
Ci vediamo al tuo ritorno. Mega Party a Incocco per dare il benvenuto alla tua piccola!!!
Very fantastic place! All beautiful. Grazie molte per la splendida giornata ed accoglienza.


(a) Registration and Ordering. Before using certain parts of any Site or ordering products, you must complete an online registration form. During registration, you will be prompted to provide to us certain personal information, including but not limited to your name, shipping and billing address(es), phone number, email address, and credit card number. If you have elected to use the Bill Me Later? payment method, you will have to provide the last four (4) digits of your social security number and your birth date. We use this information solely to facilitate the Bill Me Later? transaction and will not store or keep this information in our files. In addition, we may also ask you for your country of residence and/or your organization's country of operation, so we can comply with applicable laws and regulations, and for your gender. These kinds of personal information are used for billing purposes, to fulfill your orders, to communicate with you about your order and the Sites, and for internal marketing purposes. If we encounter a problem when processing your order, your personal information may be used to contact you.


text:
\section{Introduction}
\vspace{1cm}

Boundary conformal field theory (BCFT) is simply the study of conformal
field theory (CFT) in domains with a boundary. It gains its significance
because, in some ways, it is mathematically simpler: the
algebraic and geometric structures of CFT appear in a more straightforward
manner; and because it has important applications: in string theory in
the physics of open strings and D-branes, and in condensed matter physics in
boundary critical behavior and quantum impurity models.

In this article, however, I describe the basic ideas from the point of
view of quantum field theory, without regard to particular applications nor
to any deeper mathematical formulations.

\section{Review of CFT}
\subsection{Stress tensor and Ward identities}
Two-dimensional CFTs are massless, local, relativistic
renormalized quantum field theories.
Usually they are considered in imaginary time, i.e. on two-dimensional manifolds
with euclidean signature. In this article the metric is also taken to be
euclidean, although the formulation of CFTs on general Riemann surfaces is
also of great interest, especially for string theory. For the time being
the domain is the entire complex plane.

Heuristically the correlation functions of such a field
theory may be thought of
as being given by the euclidean path integral, that is, as
expectation values of products of
local densities with respect to a Gibbs  measure
$Z^{-1}\,e^{-S_E(\{\psi\})}[d\psi]$, where the $\{\psi(x)\}$
are some set
of fundamental local fields, $S_E$ is the euclidean action, and the
normalization factor $Z$ is the partition function. Of course, such an
object is not in general well-defined, and this picture
should be seen only as a guide to formulating the basic principles of CFT
which can then be developed into a mathematically consistent theory.

In two dimensions, it is useful to use so-called complex coordinates
$z=x^1+ix^2$, $\bar z=x^1-ix^2$.
In CFT there are
local densities $\phi_j(z,\bar z)$, called primary fields,
whose correlation functions transform
covariantly under conformal mappings $z\to z'=f(z)$:
\begin{equation}
\label{cov}
\langle\phi_1(z_1,\bar z_1)\phi_2(z_2,\bar z_2)\ldots\rangle
=\prod_if'(z_j)^{h_j}{\overline f'(z_j)}^{\bar h_j}
\langle\phi_1(z'_1,\bar z'_1)\phi_2(z'_2,\bar z'_2)\ldots\rangle\,,
\end{equation}
where $(h_j,\bar h_j)$ (usually real numbers, not complex conjugates of each
other) are called the \em conformal weights \em of $\phi_j$.
These local fields can in general be normalized so that their two-point
functions have the form
\begin{equation}
\langle\phi_j(z_j,\bar z_j)\phi_k(z_k,\bar z_k)\rangle=
\delta_{jk}/(z_j-z_k)^{2h_j}(\bar z_j-\bar z_k)^{2\bar h_j}\,.
\end{equation}
They satisfy an algebra known as the operator product expansion (OPE)
\begin{equation}
\label{OPE}
\phi_i(z_1,\bar z_1)\cdot\phi_j(z_2,\bar z_2)
=\sum_kc_{ijk}(z_1-z_2)^{-h_i-h_j+h_k}(\bar z_1-\bar z_2)^{-\bar h_i-\bar h_j
+\bar h_k}\phi_k(z_1,\bar z_1)+\cdots\,,
\end{equation}
which is supposed to be valid when inserted into higher-order
correlation functions in the limit when $|z_1-z_2|$ is much less than the
separations of all the other points. The ellipses denote the contributions
of other non-primary scaling
fields to be described below. The structure constants
$c_{ijk}$, along with the conformal weights, characterize the particular CFT.

An essential role is played by the energy-momentum tensor,
or, in euclidean field
theory language, the stress tensor $T^{\mu\nu}$. Heuristically, it is
defined as the response of the partition function to a local change in the
metric:
\begin{equation}
T^{\mu\nu}(x)=-(2\pi)\,\delta\ln Z/\delta g_{\mu\nu}(x)
\end{equation}
(the factor of $2\pi$ is included so that similar factors disappear in later
equations).

The symmetry of the theory
under translations and rotations implies that $T^{\mu\nu}$ is conserved,
$\partial_\mu T^{\mu\nu}=0$, and symmetric. Scale invariance implies that it
is also traceless $\Theta\equiv T^{\mu}_{\mu}=0$. It should be noted that
the vanishing of the trace of the stress tensor for a scale invariant
classical field theory
does not usually survive when quantum corrections are taken into account:
indeed $\Theta\propto\beta(g)$, the renormalization group (RG) beta-function.
A quantum field theory is thus only a CFT when this vanishes, that is at an
RG fixed point.

In complex coordinates the components
$T_{z\bar z}=T_{\bar z z}=4\Theta$ vanish, while the conservation equations
read
\begin{equation}
\partial_{\bar z}T_{zz}=\partial_zT_{\bar z\bar z}=0\,.
\end{equation}
Thus correlators of $T(z)\equiv T_{zz}$ are locally analytic (in fact,
globally
meromorphic) functions of $z$, while those of $\overline T(\bar z)\equiv
T_{\bar z\bar z}$ are anti-analytic. It is this property of analyticity which
makes CFT tractable in two dimensions.

Since an infinitesimal conformal transformation $z\to z+\alpha(z)$ induces
a change in the metric, its effect on a correlation function of primary
fields, given by (\ref{cov}),
may also be expressed through an appropriate integral
involving an insertion of the stress tensor. This leads to the \em conformal
Ward identity:\em
\begin{equation}
\label{WI}
\int_C\langle T(z)\prod_j\phi_j(z_j,\bar z_j)\rangle\,\alpha(z)dz
=\sum_j\left(h_j\alpha'(z_j)+\alpha(z_j)(\partial/\partial z_j)\right)
\langle\prod_j\phi_j(z_j,\bar z_j)\rangle\,,
\end{equation}
where $C$ is a contour encircling all the points $\{z_j\}$. (A similar equation
hold for the insertion of $\overline T$.) Using Cauchy's theorem, this
determines the first few terms in the
OPE of $T$ with any primary density:
\begin{equation}
\label{Tphi}
T(z)\cdot\phi_j(z_j,\bar z_j)={h_j\over(z-z_j)^2}\phi(z_j,\bar z_j)
+{1\over z-z_j}\partial_{z_j}\phi(z_j,\bar z_j)+O(1)\,.
\end{equation}
The other, regular, terms in the OPE generate new scaling fields, which are
not in general primary, called descendants.
One way of defining a density to be primary is by the
condition that the most singular term in its OPE with $T$ is a double pole.

The OPE of $T$ with itself has the form
\begin{equation}
\label{TT}
T(z)\cdot T(z_1)={c/2\over(z-z_1)^4}+{2\over(z-z_1)^2}T(z_1)+\cdots\,.
\end{equation}
The first term is present because $\langle T(z)T(z_1)\rangle$ is non-vanishing,
and must take the form shown, with $c$ being some number (which cannot be
scaled to unity, since the normalization of $T$ is fixed by its definition)
which is a property of the CFT. It is known as the \em conformal anomaly number
\em or the \em central charge\em. This term implies that $T$ is not itself
primary. In fact under a finite conformal transformation $z\to z'=f(z)$
\begin{equation}
\label{Trans}
T(z)\to f'(z)^2T(z')+\ffrac c{12}\{z',z\}\,,
\end{equation}
where $\{z',z\}=\big(f'''f'-\frac32{f''}^2\big)/{f'}^2$ is the
Schwartzian derivative.

\subsection{Virasoro algebra}
As with any quantum field theory, the local fields can be realized as
linear operators acting on a Hilbert space. In ordinary QFT, it is customary
to quantize on a constant time hypersurface. The generator of infinitesimal
time translations is the hamiltonian $\hat H$, which itself is independent
of which time slice is chosen, because of time translational symmetry.
It is also given by the integral over the hypersurface of the time-time
component of the stress tensor. In CFT, because of scale invariance, one
may instead quantize on fixed circle of a given radius. The analog of the
hamiltonian is the dilatation operator $\hat D$,
which generates scale transformations.
Unlike $\hat H$, the spectrum of $\hat D$ is usually discrete, even in an
infinite system.
It may also be expressed as an integral over the radial component of the
stress tensor
\begin{equation}
\hat D={1\over 2\pi}\int_0^{2\pi}r\,\hat T_{rr}\,rd\theta
={1\over 2\pi i}\int_Cz\,\hat T(z)dz-{1\over 2\pi i}\int_C\bar z\,
\hat{\overline T}(\bar z)d\bar z
\equiv \hat L_0+\hat{\overline L}_0\,,
\end{equation}
where, because of analyticity,
$C$ can be any contour encircling the origin.
This suggests that one define other operators
\begin{equation}
\hat L_n\equiv{1\over 2\pi}\int_Cz^{n+1}\hat T(z)dz\,,
\end{equation}
and similarly the $\hat{\overline L}_n$. From the OPE (\ref{TT}) then
follows the Virasoro algebra $\cal V$
\begin{equation}
[\hat L_n,\hat L_m]=(n-m)\hat L_{n+m}+\frac c{12}n(n^2-1)\delta_{n+m,0}\,,
\end{equation}
with an isomorphic algebra $\overline{\cal V}$ generated by the
$\hat{\overline L}_n$.

In radial quantization there is a vacuum state $|0\rangle$. Acting on this
with the operator corresponding to a scaling field gives a
state $|\phi_j\rangle\equiv\hat\phi_j(0,0)|0\rangle$ which is an eigenstate
of $\hat D$: in fact
\begin{equation}
\hat L_0|\phi_j\rangle=h_j|\phi_j\rangle\,,\qquad
\hat{\overline L}_0|\phi_j\rangle=\bar h_j|\phi_j\rangle\,.
\end{equation}
From the OPE (\ref{Tphi}) one sees that $|L_n\phi_j\rangle
\propto \hat L_n|\phi_j\rangle$, and, if $\phi_j$ is primary,
$\hat L_n|\phi_j\rangle=0$ for all $n\geq1$.

The states corresponding to a given primary field,
and those generated by acting on these with all the $\hat L_n$
with $n<0$
an arbitrary number of times, form a highest weight representation
of $\cal V$.
However, this is not necessarily irreducible. There may be
\em null vectors\em, which are linear combinations of states at a given
level which are themselves annihilated by all the $\hat L_n$ with $n>0$.
They exist whenever $h$ takes a value from the Kac table:
\begin{equation}
\label{Kac}
h=h_{r,s}={\big(r(m+1)-sm\big)^2-1\over 4m(m+1)}\,,
\end{equation}
with the central charge parametrized as $c=1-6/\big(m(m+1)\big)$, and
$r$, $s$ are non-negative integers. These null states should be projected out,
giving an irreducible representation ${\cal V}_h$.

The full Hilbert space of the CFT is then
\begin{equation}
\label{decomp}
{\cal H}=\bigoplus_{h,\bar h}\,n_{h,\bar h}\,{\cal V}_h
\otimes{\overline{\cal V}}_{\bar h}\,,
\end{equation}
where the non-negative integers $n_{h,\bar h}$ specify how many distinct
primary fields of weights $(h,\bar h)$ there are in the CFT.

The consistency of the OPE (\ref{OPE}) with the existence of null vectors
leads to the fusion algebra of the CFT. This applies separately to the
holomorphic and antiholomorphic sectors, and determines how many copies
of ${\cal V}_c$ occur in the fusion of ${\cal V}_a$ and ${\cal V}_b$:
\begin{equation}
{\cal V}_a\odot{\cal V}_b = \sum_c N^c_{ab}{\cal V}_c\,,
\end{equation}
where the $N^c_{ab}$ are non-negative integers.

A particularly important subset of all CFTs consists of the
\em minimal models\em. These have rational central charge
$c=1-6(p-q)^2/pq$, in which case the fusion algebra closes with a finite
number of possible values $1\leq r\leq q$, $1\leq s\leq p$ in the Kac
formula (\ref{Kac}). For these models, the fusion algebra
takes the form
\begin{equation}
{\cal V}_{r_1,s_1}\odot{\cal V}_{r_2,s_2}=
{\sum_{r=|r_1-r_2|}^{r_1+r_2-1}}'
{\sum_{s=|s_1-s_2|}^{s_1+s_2-1}}'{\cal V}_{r,s}\,,
\end{equation}
where the prime on the sums indicates that they are to be restricted
to the allowed intervals of $r$ and $s$.

There is an important theorem
which states that the only \em unitary \em
CFTs with $c<1$ are the minimal models with $p/q=(m+1)/m$, where
$m$ is an integer $\geq3$.

\subsection{Modular Invariance}
The fusion algebra limits which values of $(h,\bar h)$ might appear in
a consistent CFT, but not which ones actually occur, i.e. the values of the
$n_{h,\bar h}$. This is answered by the requirement of modular invariance
on the torus.
First consider the theory on an infinitely long cylinder,
of unit circumference. This is related to the (punctured) plane by the
conformal mapping $z\to(1/2\pi)\ln z\equiv t+ix$. The result is
a QFT on the circle $0\leq x<1$, in imaginary time $t$. The generator
of infinitesimal time translations is related to that for dilatations in the
plane:
\begin{equation}
\label{H}
\hat H=2\pi\hat D-\frac{\pi c}6=2\pi\big(\hat L_0+\hat{\overline L}_0\big)
-\frac{\pi c}6\,,
\end{equation}
where the last term comes from the Schwartzian derivative in (\ref{Trans}).
Similarly, the generator of translations in $x$, the total momentum operator,
is $\hat P=2\pi\big(\hat L_0-\hat{\overline L}_0\big)$.

A general torus is, up to a scale transformation, a parallelogram with
vertices $(0,1,\tau,1+\tau)$ in the complex plane, with the opposite edges
identified. We can make this by taking a cylinder of unit circumference
and length ${\rm Im},\tau$, twisting the ends by a relative amount
${\rm Re}\,\tau$,
and sewing them together. This means that the partition function of the CFT
on the torus can be written as
\begin{equation}
Z(\tau,\bar\tau)={\rm Tr}\,e^{-({\rm Im}\,\tau)\hat H+i({\rm Im}\,\tau)\hat P}
={\rm Tr}\,q^{\hat L_0-c/24}\,
{\bar q}^{\hat{\overline L}_0-c/24}\,,
\end{equation}
 using the above expressions for $\hat H$ and $\hat P$ and
introducing $q\equiv e^{2\pi i\tau}$.

Through the decomposition (\ref{decomp}) of $\cal H$,
the trace sum can be written as
\begin{equation}
\label{char}
Z(\tau,\bar\tau)=\sum_{h,\bar h}n_{h,\bar h}\,\chi_h(q)\,\chi_{\bar h}(q)\,,
\end{equation}
where
\begin{equation}
\chi_h(q)\equiv{\rm Tr}_{{\cal V}_h}\,q^{\hat L_0-c/24}
=\sum_Nd_h(N)\,q^{h-(c/24)+N}
\end{equation}
is the character of the representation of highest weight $h$, which counts
the degeneracy $d_h(N)$ at level $N$. It is purely an algebraic property
of the Virasoro algebra, and its explicit form is known in many cases.

All of this would be less interesting were it not for the observation
that the parametrization of the torus through $\tau$ is not unique. In fact
the transformations $S:\tau\to-1/\tau$ and $T:\tau\to\tau+1$ give the same
torus (see Fig.~\ref{figtorus}).
\begin{figure}
\centering
\includegraphics[width=8cm]{tori.eps}
\caption{\label{figtorus}\small
Two equivalent parametrizations of the same torus.}
\end{figure}
Together, these operations generate the modular group
SL$(2,{\bf Z})$, and the partition function $Z(\tau,\bar\tau)$ should be
invariant under them. $T$-invariance
is simply implemented by requiring that $h-\bar h$ is an integer, but the
$S$-invariance of the right hand side of (\ref{char}) places highly nontrivial
constraints on the $n_{h,\bar h}$. That this can be satisfied at all relies
on the remarkable property of the characters that they transform linearly
under $S$:
\begin{equation}
\label{mod}
\chi_h(e^{-2\pi i/\tau})=\sum_{h'}S^{h'}_h\chi_{h'}(e^{2\pi i\tau})\,.
\end{equation}
This follows from applying the Poisson sum formula to the explicit
expressions for the characters, which are related to Jacobi theta-functions.
In many cases (for example, the minimal models) this representation is
finite-dimensional, and the matrix $\bf S$ is symmetric and orthogonal.
This means that
one can immediately obtain a modular invariant partition function by
forming the diagonal sum
\begin{equation}
Z=\sum_h\chi_h(q)\chi_h(\bar q)\,,
\end{equation}
so that $n_{h,\bar h}=\delta_{h\bar h}$.
However, because of various symmetries of the characters, other modular
invariants are possible: for the minimal models (and some others) these
have been classified. Because of an analogy of the results with the
classification of semisimple Lie algebras, the diagonal invariants are
called the A-series.

\section{Boundary CFT}
In any field theory in a domain with a boundary, one needs to consider how
to impose a set of consistent boundary conditions. Since CFT is formulated
independently of a particular set of fundamental fields and a lagrangian,
this must be done in a more general manner. A natural requirement is
that the off-diagonal component $T_{\parallel\perp}$ of the stress tensor
parallel/perpendicular to the boundary should vanish. This is called
the conformal boundary condition. If the boundary is
parallel to the time axis, it implies that there is no momentum flow across
the boundary. Moreover, it can be argued that, under the RG, any uniform
boundary condition will flow into a conformally invariant one. For a given
bulk CFT, however, there may be many possible distinct such boundary
conditions, and it is one task of BCFT  to classify these.

To begin with, take the domain to be the upper half plane, so that the
boundary is the real axis. The conformal boundary condition then implies
that $T(z)=\overline T(\bar z)$ when $z$ is on the real axis. This has the
immediate consequence that correlators of $\overline T$ are those of $T$,
analytically continued into the lower half plane. The conformal Ward identity,
\em c.f. \em (\ref{Tphi}), now reads
\begin{eqnarray}
\langle T(z)\prod_j\phi_j(z_j,\bar z_j)\rangle
&=&\sum_j\left({h_j\over(z-z_j)^2}+{1\over z-z_j}\partial_{z_j}\right.
\nonumber\\
&&\qquad
\left.+{\bar h_j\over (\bar z-\bar z_j)^2}+{1\over\bar z-\bar z_j}\partial_{\bar z_j}
\right)\langle\prod_j\phi_j(z_j,\bar z_j)\rangle\,.
\label{BWI}
\end{eqnarray}

In radial quantization, in order that the Hilbert spaces defined on different
hypersurfaces be equivalent, one must choose semicircles centered on some
point on the boundary, conventionally the origin. The dilatation operator
is now
\begin{equation}
\hat D={1\over 2\pi i}\int_Sz\,\hat T(z)dz-{1\over 2\pi i}\int_S\bar z\,
\hat{\overline T}(\bar z)d\bar z\,,
\end{equation}
where $S$ is a semicircle. Using the conformal boundary condition,
this can also be written as
\begin{equation}
\label{DL}
\hat D=\hat L_0={1\over 2\pi i}\int_Cz\,\hat T(z)dz\,,
\end{equation}
where $C$ is a complete circle around the origin. As before, one may similarly
define the $\hat L_n$, and they satisfy a Virasoro algebra.

Note that there is now only one Virasoro algebra. This is related to the
fact that conformal mappings which preserve the real axis correspond to
real analytic functions. The eigenstates of $\hat L_0$ correspond to
\em boundary operators \em $\hat \phi_j(0)$ acting on the
vacuum state $|0\rangle$. It is well-known that in a renormalizable QFT
operators at the boundary require a different renormalization  from those
in the bulk, and this will in general lead to a different set of conformal
weights. It is one of the tasks of BCFT to determine these, for a given
allowed boundary condition.

However, there is one feature unique to boundary CFT in two dimensions.
Radial quantization also makes sense, leading to the same form (\ref{DL})
for the dilation operator, if the boundary conditions on the negative
and positive real axes are different. As far as the structure of BCFT goes,
correlation functions with this mixed boundary condition behave as though
a local scaling field were inserted at the origin. This has led to
the term `boundary condition changing (bcc) operator', but it must be stressed
that these are not local operators in the conventional sense.

\section{The annulus partition function}
Just as consideration of the partition function on the torus illuminates
the bulk operator content $n_{h,\bar h}$, it turns out that consistency
on the annulus helps classify both the allowed boundary conditions, and
the boundary operator content. To this end, consider a CFT in an annulus formed
of a rectangle of unit width and height $\delta$, with the top and bottom
edges identified (see Fig.~\ref{figannulus}).
\begin{figure}
\centering
\includegraphics[width=5cm]{annulus.eps}
\caption{\label{figannulus}\small The annulus, with boundary conditions
$a$ and $b$ on either boundary.}
\end{figure}
The boundary conditions on the left and right edges, labelled by $a,b,\ldots$,
may be different. The partition function
with boundary conditions $a$ and $b$ on either edge is denoted by
$Z_{ab}(\delta)$.

One way to compute this is by first considering the CFT on an infinitely
long strip of unit width. This is conformally related to the upper half plane
(with an insertion of boundary condition changing operators at $0$ and
$\infty$ if $a\not=b$)
by the mapping $z\to(1/\pi)\ln z$. The generator of infinitesimal translations
along the strip is
\begin{equation}
\hat H_{ab}=\pi\hat D-\pi c/24=\pi\hat L_0-\pi c/24\,.
\end{equation}
Thus for the annulus
\begin{equation}
Z_{ab}(\delta)={\rm Tr}\, e^{-\delta\,\hat H_{ab}}
={\rm Tr}\,q^{\hat L_0-\pi c/24}\,,
\end{equation}
with $q\equiv e^{-\pi\delta}$. As before, this can be decomposed into
characters
\begin{equation}
\label{Zab}
Z_{ab}(\delta)=\sum_hn^{ab}_h\,\chi_h(q)\,,
\end{equation}
but note that now the expression is linear. The non-negative integers
$n_{ab}^h$ give the operator content with the boundary conditions
$(ab)$: the lowest value of $h$ with $n_{ab}^h>0$
gives the conformal weight of the bcc
operator, and the others give conformal weights of the other allowed
primary fields which may also sit at this point.

On the other hand, the annulus partition function may be viewed, up to
an overall rescaling, as the
path integral for a CFT on a circle of unit circumference, being
propagated for (imaginary) time $\delta^{-1}$. From this point of view,
the partition function is no longer a trace, but rather the matrix element
of $e^{-\hat H/\delta}$ between \em boundary states\em:
\begin{equation}
\label{Zab2}
Z_{ab}(\delta)=\langle a|e^{-\hat H/\delta}|b\rangle\,.
\end{equation}
Note that $\hat H$ is the same hamiltonian that appears in (\ref{H}),
and the boundary states lie in $\cal H$, (\ref{decomp}).

How are these boundary states to be characterized? Using the transformation
law (\ref{Trans}) the conformal boundary condition applied to the circle
implies that $L_n=\overline L_{-n}$. This means that any boundary state
$|B\rangle$ lies in the subspace satisfying
\begin{equation}
\label{LL}
\hat L_n|B\rangle=\hat{\overline L}_{-n}|B\rangle\,.
\end{equation}
Moreover, because of the decomposition (\ref{decomp}) of $\cal H$,
$|B\rangle$ is also some linear superposition of states
from ${\cal V}_h\otimes\overline{\cal V}_{\bar h}$.
This condition can therefore be applied
in each subspace.
Taking $n=0$ in (\ref{LL}) constrains $\bar h=h$.
For simplicity, consider only the diagonal CFTs
with $n_{h,\bar h}=\delta_{h,\bar h}$. It can then be shown
that the solution of (\ref{LL}) is unique and
has the following form. The subspace
at level $N$ of ${\cal V}_h$ has dimension $d_h(N)$. Denote an orthonormal
basis by $|h,N;j\rangle$, with $1\leq j\leq d_h(N)$, and the same basis
for $\overline{\cal V}_h$ by $\overline{|h,N;j\rangle}$. The solution
to (\ref{LL}) in this subspace is then
\begin{equation}
|h\rangle\rangle\equiv\sum_{N=0}^\infty\sum_{j=1}^{d_h(N)}
|h,N;j\rangle\otimes\overline{|h,N;j\rangle}\,.
\end{equation}
These are called Ishibashi states. Matrix elements of the translation
operator along the cylinder between them are simple:
\begin{eqnarray}
&&\langle\langle h'|e^{-\hat H/\delta}|h\rangle\rangle\\
&&=\sum_{N'=0}^\infty\sum_{j'=1}^{d_{h'}(N')}
\sum_{N=0}^\infty\sum_{j=1}^{d_h(N)}
\langle h',N';j'|\otimes\overline{\langle h',N';j'|}
e^{-(2\pi/\delta)(\hat L_0+\hat{\overline L}_0-c/12)}\nonumber\\
&&\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad
|h,N;j\rangle\otimes\overline{|h,N;j\rangle}\\
&&=\delta_{h'h}
\sum_{N=0}^\infty\sum_{j=1}^{d_h(N)}e^{-(4\pi/\delta)\big(h+N-(c/24)\big)}
=\delta_{h'h}\,\chi_h(e^{-4\pi/\delta})\,.
\end{eqnarray}
Note that the characters which appear are related to those in
(\ref{Zab}) by the modular transformation $S$.

The physical boundary states satisfying
(\ref{Zab}), sometimes called the Cardy states,
are linear combinations of the Ishibashi states:
\begin{equation}
|a\rangle=\sum_h\langle\langle h|a\rangle\,|h\rangle\rangle\,.
\end{equation}
Equating the two different expressions (\ref{Zab},\ref{Zab2})
for $Z_{ab}$, and using the modular
transformation law (\ref{mod}) and the linear
independence of the characters gives the (equivalent) conditions:
\begin{eqnarray}
n^h_{ab}&=&\sum_{h'}S_{h'}^h\langle a|h'\rangle\rangle
\langle\langle h'|b\rangle\,;\label{C1}\\
\langle a|h'\rangle\rangle \langle\langle h'|b\rangle
&=&\sum_hS_h^{h'}n^h_{ab}\,.\label{C2}
\end{eqnarray}
These are called the Cardy conditions. The requirements that the
right hand side
of (\ref{C1}) should give a non-negative integer, and that the
right hand side of
(\ref{C2}) should factorize in $a$ and $b$, give highly nontrivial constraints
on the allowed boundary states and their operator content.

For the diagonal CFTs considered here (and for the nondiagonal minimal models)
a complete solution is possible.
It can be shown that the
elements $S^h_0$ of $\bf S$ are all non-negative,
so one may choose
$\langle\langle h|\tilde 0\rangle=\big(S_0^h\big)^{1/2}$. This defines a
boundary state
\begin{equation}
|\tilde 0\rangle\equiv\sum_h\big(S_0^h\big)^{1/2}|h\rangle\rangle\,,
\end{equation}
and a corresponding boundary condition
such that $n^h_{00}=\delta_{h0}$. Then, for each $h'\not=0$, one may define
a boundary state
\begin{equation}
\langle\langle h|\tilde{h'}\rangle\equiv S^h_{h'}/\big(S_0^{h}\big)^{1/2}\,.
\end{equation}
From (\ref{C1}), this gives $n^h_{h'0}=\delta_{h'h}$.
For each allowed $h'$ in the torus partition function, there is therefore
a boundary state $|\tilde{h'}\rangle$ satisfying the Cardy conditions.
However, there is a further requirement:
\begin{equation}
\label{verl} n^h_{h'h''}=\sum_\ell{S^h_\ell
S^\ell_{h'}S^\ell_{h''}\over S^\ell_0}
\end{equation}
should be a non-negative integer.
Remarkably, this combination of elements of $\bf S$ occurs in the
Verlinde formula,
which follows from considering consistency of the CFT
on the torus. This states that the right hand side of (\ref{verl})
is equal to the fusion algebra
coefficient $N^h_{h'h''}$. Since these are non-negative integers, the
consistency of the above ansatz for the boundary states is consistent.

We conclude that, at least for the diagonal models, there is a bijection
between the allowed primary fields in the bulk CFT and the allowed conformally
invariant boundary conditions. For the minimal models, with a finite number of
such primary fields, this correspondence has been followed through explicitly.

\subsubsection{Example}
The simplest example is the diagonal
$c=\frac12$ unitary CFT corresponding to $m=3$.
The allowed values of the conformal weights are $h=0,\frac12\frac1{16}$, and
\begin{equation}
{\bf S}=\pmatrix{\ffrac12&\ffrac12&\ffrac1{\sqrt2}\cr
                 \ffrac12&\ffrac12&-\ffrac1{\sqrt2}\cr
                 \ffrac1{\sqrt2}&-\ffrac1{\sqrt2}&0\cr}\,,
\end{equation}
from which one finds the allowed boundary states
\begin{eqnarray}
|\tilde0\rangle&=&\ffrac1{\sqrt2}|0\rangle\rangle
+\ffrac1{\sqrt2}|\ffrac12\rangle\rangle
+\ffrac1{2^{1/4}}|\ffrac1{16}\rangle\rangle\,;\\
|\tilde{\ffrac12}\rangle&=&\ffrac1{\sqrt2}|0\rangle\rangle
+\ffrac1{\sqrt2}|\ffrac12\rangle\rangle
-\ffrac1{2^{1/4}}|\ffrac1{16}\rangle\rangle\,;\\
|\tilde{\ffrac1{16}}\rangle&=&
|0\rangle\rangle-|\ffrac12\rangle\rangle\,.
\end{eqnarray}
The nontrivial part of the fusion algebra of this CFT is
\begin{eqnarray}
{\cal V}_{\frac1{16}}\odot{\cal V}_{\frac1{16}}&=&
{\cal V}_{0}+{\cal V}_{\frac12}\\
{\cal V}_{\frac1{16}}\odot{\cal V}_{\frac12}&=&
{\cal V}_{\frac1{16}}\\
{\cal V}_{\frac12}\odot{\cal V}_{\frac12}&=&
{\cal V}_{0}\,,\\
\end{eqnarray}
from which can be read off the
boundary operator content $n^h_{\tilde h}=1$
and $n^0_{\tilde{\frac1{16}}\tilde{\frac1{16}}}=
n^{\frac12}_{\tilde{\frac1{16}}\tilde{\frac1{16}}}=
n^{\frac12}_{\tilde{\frac1{16}}\tilde{\frac1{16}}}=
n^{\frac1{16}}_{\tilde{\frac12}\tilde{\frac1{16}}}=1$.

The $c=\frac12$ CFT is known to describe the continuum limit of the
critical Ising model, in which spins $s=\pm1$ are localized on the sites
of a regular lattice. The above boundary conditions may be interpreted as
the continuum limit of the lattice boundary conditions $s=1$, free and $s=-1$
respectively. Note there is a symmetry of the fusion rules which means that
one could equally well have inverted the ordering of this correspondence.

\section{Other topics}

\subsection{Boundary entropy}
The partition function on annulus of length $L$ and circumference $\beta$
can be thought of as the quantum statistical
mechanics partition function for a 1d QFT in an interval of length $L$, at
temperature $\beta^{-1}$. It is interesting to consider this in the
thermodynamic limit when $\delta=L/\beta$ is large. In that case, only the
ground state of $\hat H$ contributes in (\ref{Zab2}), giving
\begin{equation}
Z_{ab}(L,\beta)\sim \langle a|0\rangle\langle0|b\rangle\,e^{\pi cL/6\beta}\,,
\end{equation}
from which the free energy $F_{ab}=-\beta^{-1}\ln Z_{ab}$ and the entropy
${\cal S}_{ab}=$\\
$-\beta^2(\partial F_{ab}/\partial\beta)$ can be obtained.
The result is
\begin{equation}
{\cal S}_{ab}=(\pi c/3\beta)L+s_a+s_b+o(1)\,,
\end{equation}
where the first term is the usual extensive contribution. The other
two pieces $s_a\equiv\ln(\langle a|0\rangle)$ and
$s_b\equiv\ln(\langle b|0\rangle)$ may be identified as the \em boundary
entropy \em associated with the corresponding boundary states. A similar
definition may be made in massive QFTs. It has been shown that, analogously
to the statement of Zamoldochikov's $c$-theorem in the bulk,
the boundary entropy is a non-increasing function along
boundary RG flows, and is stationary only for conformal boundary states.

\subsection{Bulk-boundary OPE}
The boundary Ward identity (\ref{BWI}) has the implication that, from the
point of view of the dependence of its correlators on $z_j$ and $\bar z_j$,
a primary field $\phi_j(z_j,\bar z_j)$ may be thought of as the product of
two local fields which are holomorphic functions of $z_j$ and $\bar z_j$
respectively. These will satisfy OPEs as $|z_j-\bar z_j|\to0$, with the
appearance of primary fields on the
right hand side being governed by the fusion rules.
These fields are localized on the real axis: they are the boundary operators.
There is therefore a kind of bulk-boundary OPE:
\begin{equation}
\phi_j(z_j,\bar z_j)=\sum_kd_{jk}({\rm Im}\,z_j)^{-h_j-\bar h_j+h_k}
\phi^b_k({\rm Re}\,z_j)\,,
\end{equation}
where the sum on the right hand side
is in principle over all the boundary fields
consistent with the boundary condition, and the coefficients $d_{jk}$ are
analogous to the OPE coefficients in the bulk. As before, they are
non-vanishing only if allowed by the fusion algebra: a boundary field
of conformal weight $h_k$ is allowed only if $N^{h_k}_{h_j\bar h_j}>0$.

For example, in the $c=\frac12$ CFT, the bulk operator with $h=\bar h=
\frac1{16}$ goes over into the boundary operator with $h=0$, or that
with $h=\frac12$, depending on the boundary condition. The bulk operator
with $h=\bar h=\frac12$, however, can only go over into the identity
boundary operator with $h=0$ (or a descendent thereof.)

The fusion rules also apply to the boundary operators themselves. The
consistency of these with bulk-boundary and bulk-bulk fusion rules, as well
as the modular properties of partition functions,
was examined by Lewellen.

\subsection{Extended algebras}
CFTs may contain other conserved currents apart from the stress tensor,
which generate algebras (Kac-Moody, superconformal, W-algebras) which
extend the Virasoro algebra. In BCFT, in addition to the conformal
boundary condition, it is possible (but not necessary) to impose further
boundary conditions relating the holomorphic and antiholomorphic parts
of the other currents on the boundary.
It is believed that all rational CFTs can
be obtained from Kac-Moody algebras via the coset construction. The
classification of boundary conditions from this point of view is fruitful and
also important for applications, but is beyond the scope of this article.

\subsection{Stochastic Loewner evolution}
In recent years, there has emerged a deep connection between BCFT and
conformally invariant measures on curves in the plane which start at
a boundary of a domain. These arise
naturally in the continuum limit of certain statistical mechanics models.
The measure is constructed dynamically as the curve is extended,
using a sequence of random conformal mappings
called stochastic Loewner evolution (SLE). In CFT, the point where the
curve begins can be viewed as the insertion of a boundary operator. The
requirement that certain quantities should be conserved in mean under
the stochastic process is then equivalent to this operator having a
null state at level two. Many of the standard results of CFT correspond to
an equivalent property of SLE.

\subsection*{Acknowledgments}

This article was written while the author was a member of the Institute
for Advanced Study.
He thanks the School of Mathematics and the School of Natural Sciences
for their hospitality. The work was supported by the
Ellentuck Fund.

redpajama_set_name: RedPajamaArXiv