Making your own candles is so much fun and a great project to do with any big kiddos in your life! Last year we loved making homemade bath bombs together for our holiday gifts—they were great for teachers, friends, party hosts, the mail carrier, you name it. This year, we thought we'd switch it up with high-quality candles made from all-natural beeswax and holiday-scented essential oils from our sponsor Plant Therapy.
Before we dive in though, I have to tell you why I despise conventional scented candles. Don't get me wrong, I love burning candles—it's hard to beat that ambiance this time of year—and it's certainly nice to add a pleasant aroma to the room while enjoying one. BUT, breathing in those synthetic fragrances—not to mention the paraffin wax they're usually made with—can be toxic! Some even say it's as bad for you as second-hand smoke or the fumes from your car.
According to the Environmental Protection Agency, along with researchers at the University of Michigan and South Carolina State, certain types of candles have been found to discharge the dangerous chemicals benzene and ketones, both known cancer-causing agents.
Synthetic and artificial ingredients are the #1 additive I try to avoid in my food and, naturally (pun intended, LOL), this extends to other products in my life. So, rather than emit questionable fumes into my home while burning candles, we thought we'd make (and share) our own DIY natural candles with beeswax and essential oils!
Thankfully, not wanting artificial fragrances in our candles doesn't mean we have to go the unscented route. Essential oils have been around for centuries and we thought the fun holiday scents from our sponsor Plant Therapy would be perfect for this project.
This Cozy for Christmas Holiday Blend Set would be perfect for making some holiday-themed candles!
Essential oils are concentrated, volatile, aromatic liquids obtained from the fruits, seeds, flowers, bark, stems, roots, leaves or other parts of plants. Plant Therapy offers only 100% pure essential oils and is one of the few companies who offer USDA Certified Organic options. All of their oils go through multiple rounds of testing and are always free from additives, adulterants, and dilutions to uphold the highest quality. While you can certainly find many essential oil options out there, know that they are not all made the same. Finding a quality product is essential, which is why Plant Therapy has been a longtime partner of ours!
As a bonus, new customers can take 10% off of their first order when you use our code 100DAYS10. A great time to try Plant Therapy!
I highly recommend you read this full list of SAFETY TIPS before getting started. Melting wax for candles is really simple to do, but it's never a bad idea to take extra precautions. Also, make sure you understand why using your gas stove (or expensive pots) isn't such a great idea for this project!
Thread each wick through a wick sustainer tab (twist it around or tie a knot where it comes out at the bottom), place in the bottom of a jar, and temporarily hold in place with a clothespin or by wrapping it around a pencil that lays across the top of the jar. Repeat for all six jars and set aside.
Heat the beeswax in a candle-making pitcher on a double boiler over medium heat (electric stove recommended, see above) until completely melted, 10 to 15 minutes.
Use a wooden skewer to stir in your essential oil of choice. Carefully pour almost all the wax into the jars (leaving some behind in the pitcher) and adjust the placement of the wicks if necessary. As the wax begins to solidify, embed any organic items near the top (if desired).
Once the wax completely hardens it may sink around the wick. Simply reheat remaining wax and fill in the gap (adding additional embed items if desired). I think it looks better if you fill beyond the gap, all the way to the edges, for one smooth surface. Let cool till it hardens, trim wick, and it's ready to gift or use!
The number of candles this recipe will make is approximate. It will depend on the size of your containers.
I love how cute my 6th grader finished these off for everyone on her list! :) And a big thanks to my talented niece for writing all the pretty cards for us.
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I had no idea about candles giving off bad fumes! Scary! Are Soy candles any better? Or are there any commercial kinds that are okay?
Soy can be better, but often it's not pure.
How many drops of essential oil did you add? Obviously would adjust if I'm making a different number of candles but just looking for a ballpark. Thanks!
If you'd rather measure out in drops it's about 150.
Can you please tell me what's in the Spiced Apple Cider candle. I would love to make it, but would love to know what exactly you put in yours!
That is a great idea with the cinnamon sticks. Do you know what type of oils did she use to make is the "spiced apple"?
Devon, it was the Spiced Cider scent from Plant Therapy Essential Oils.
How would you feel about doing a how to video of yourself making the candles? I think seeing it done would be festive and fun and give me more confidence that I can do this. I would love watching the extra ideas you throw out like you do when you make lunches.
Sheila, this is a wonderful idea. Thank you for the suggestion! We'll see what we can do for the future.
Hi! I just want to clarify…do you put the tablespoon of essential oil in the large pitcher or in the individual candle jars? I'm thinking the pitcher, correct? So one tablesooon of essential oil makes 6 candles? Or is it a tablespoon in each candle jar? if you want to use a different scent do you just do another batch? I'm just kind of confused how you made different scents in one batch. I'm sorry…I am not very good with crafts but really want to give this one a try. Thank you so much!


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West Launches Two New Elastomer Product Innovations at CPhI Worldwide
Advanced Elastomer Formulation and AccelTRA® Line Extension Components Expand Company's Drug Containment and Delivery Portfolio; West Marks First Anniversary of Integrated Solutions Program
EXTON, Pa., Nov. 5, 2019 /PRNewswire/ -- (Booth #111F62)—West Pharmaceutical Services, Inc. (NYSE: WST), a global leader in innovative solutions for injectable drug administration, today announced two innovative product offerings in the elastomer space at the 2019 CPhI Worldwide conference in Frankfurt, Germany. West introduced its advanced elastomer, the new 4040/40 formulation, created with customer insight to deliver enhanced performance and reliability, while helping to mitigate risk for customers. The Company also launched a line extension of its AccelTRA® component program, AccelTRA Select, which features new configurations of stoppers and plungers in a high-performing, next-generation 4031/45 elastomer formula to offer generics customers optimized quality, speed and simplicity.
"These new elastomer product offerings reflect West's deep commitment to innovation based on customer insights. Designed with the customers' challenges in mind, we aim to simplify their journey with drug packaging and delivery solutions and help bring much-needed injectable medicines to patients more quickly and efficiently," said Karen Flynn, Senior Vice President & Chief Commercial Officer, West. "CPhI also marks our first full year offering the Integrated Solutions program, our comprehensive approach to working by our customers' side to help reduce risk and regulatory complexity. Together with these new product offerings, West supports customers as they navigate the journey from early development to commercialization."
West thought leaders will offer interactive product demonstrations and presentations on the 4040/40 formulation and AccelTRA line extension components each day of the CPhI conference, November 5-7, at Booth #111F62 located in the InnoPack zone of the Messe Frankfurt venue. Company scientific and industry experts will also be on hand to share additional highlights from West's high-value product and service portfolio, including the Integrated Solutions program.
About the Advanced Elastomer: 4040/40
West's advanced elastomer was created with customer insight to power the future, to enhance performance and help with risk mitigation. In the 4040/40 formulation, two LyoTec® stopper designs are available—13mm and 20mm, with a versatile universal design that delivers high functionality and reliability. It was developed through a Quality-by-Design (QbD) approach to material selection and component analysis along with an unparalleled level of scientific ingredient knowledge that combined has resulted in a reduction of extractables. The formulation features Westar® Select quality and low particulate levels, with optimal design, drug compatibility and quality to protect drug stability, drive robust performance and minimize fill-finish rejects.
About the AccelTRA® Line Extension
The AccelTRA® component program offers delivery times and a single next-generation formulation that helps customers stay competitive and move product to market quickly. The newly introduced AccelTRA Select elastomer components include AccelTRA 13mm and 20mm serum and lyo stoppers in multiple configurations, along with a 1-3mL uncoated plunger. The AccelTRA Select line extension leverages the Westar® Select wash process to provide additional high-quality options for generic drug manufacturers. The AccelTRA program will continue to expand in 2020.
About West Integrated Solutions Program
West's Integrated Solutions program brings together decades of primary packaging, device, analytical, regulatory and contract manufacturing expertise in a single-source, comprehensive approach to drug containment and delivery system development. Available in defined and customized packages, the offering combines West's suite of drug packaging and delivery products with the Company's proven service offerings to meet the unique needs of the drug product and its delivery system at any stage of development—across all injectable formats. Integrated Solutions helps customers manage the regulatory landscape while helping to reduce development and supply risk, accelerate path to market, minimize total cost of ownership and improve the patient experience.
For more information on West's high-quality packaging technologies and drug delivery solutions, please visit us online at www.westpharma.com.
Trademarks and registered trademarks are the property of West Pharmaceutical Services, Inc., in the United States and other jurisdictions, unless noted otherwise.
Certain forward-looking statements are included in this press release. They use words such as "will," "deliver," "mitigate," "new," "offer," "aim," "reduce," "future," "drive," "minimize," and other similar terminology. These statements reflect management's current expectations regarding future events and operating performance and speak only as of the date of this release. There is no certainty that actual results will be achieved in-line with current expectations or that the new advanced elastomer formulation or that the new AccelTRA® elastomer components described in this release will achieve any particular result. Similarly, there is no certainty that the services offered in our Integrated Solutions program will achieve any particular result. These forward-looking statements involve a number of risks and uncertainties. The following are some of the factors that could cause our actual results to differ materially from those expressed in or underlying our forward-looking statements: customer decisions to move forward with our new product and service offerings, dependence on third-party suppliers and partners and the ability to meet development milestones with key customers. These important factors are not all inclusive. For a description of certain additional factors that could cause West's future results to differ from those expressed in any such forward-looking statements, see Item 1A, entitled "Risk Factors," in West's Annual Report on Form 10-K for the year ended December 31, 2018. Except as required by law or regulation, West undertakes no obligation to publicly update any forward-looking statements, whether as a result of new information, future events, or otherwise.
West Pharmaceutical Services, Inc. is a leading manufacturer of packaging components and delivery systems for injectable drugs and healthcare products. Working by the side of its customers from concept to patient, West creates products that promote the efficiency, reliability and safety of the world's pharmaceutical drug supply. West is headquartered in Exton, Pennsylvania, and supports its customers from locations in North and South America, Europe, Asia and Australia. West's 2018 net sales of $1.7 billion reflect the daily use of approximately 112 million of its components and devices, which are designed to improve the delivery of healthcare to patients around the world. For more information, visit www.westpharma.com.
View original content to download multimedia:http://www.prnewswire.com/news-releases/west-launches-two-new-elastomer-product-innovations-at-cphi-worldwide-300951099.html
SOURCE West Pharmaceutical Services, Inc.
Emily Denney, Global Communications, +1-610-594-3035, Emily.Denney@westpharma.com; Catriona Kennedy, Global Communications, Europe, + 35-35-131-2448, Catriona.Kennedy@westpharma.com

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: How can I hide a $_GET variable to be more secured in PHP? So far all my sites use mostly $_GET's to get the data for a page.
Ex:
editad.php?posting_id=131

editaccount.php?user_id=2

-->is there a way to hide or be more secured about what the user can see? I don't want them to be just able to say type "editad.php?posting_id=40" in the URL. I know I can use POSTS, but is there a way for GETs or not?
-->I pass along data through a GET, then validating that data by checking if the user's id is equal to the page's user's id. If they are equal, it would allow the user to edit that page, if not, it would only show that page.  I also make sure a number is a number, a string a string, etc.
Is there any other way to make it more secure?

A: there's nothing wrong with passing query parameters like that in _GET.  _POST is no more secure.
If a user is able to edit ad 30, but not ad 31, your code needs to enforce those rules.

A: No, you can not do this with $_GET. To obtain security through obscurity*, you can use the $_POST variable, but $_POST is also insecure (and can be modified by the user). You should always validate incoming data, regardless whether you use $_GET or $_POST, and ensure that the user is permitted to access the data.
*This will only be obscure to laymen. It will be immediately transparent to any interested programmer/hacker.

A: The only way to secure data from eavesdroppers is to use POST over https://.
However, there is no way to secure from the the user, since the user can modify for GET and POST data easily.

A: Talking about security, you may consider using either of the following :

*

*Use session to pass the variables

*Add a salt+hash key in the url to be passed.

sender :
$hashedKey = sha1( $salt + 'posting_id=131' );
editad.php?posting_id=131&$key=$hashedKey;

receiver :
$params = getUrlParams();
$hashedKey = sha1( $salt + params );

if ( $_POST['$key'] == $hashedKey )
   continue;
else
    displayError();

A: You answered your own question*, you use POST.

*

*However, I'm not sure what you mean by "more secured". It's a web page, you can look at the source and see what key/value pairs are being posted to the form.

A: If you want to hide the parameters from the user, you could always serialize your data and pass an encrypted string in the query. POST doesn't improve security and shouldn't be used if you are not sending data to the server.
Note that depending on your application, even encryption is not enough. For example, if you are passing a security token, it's easy enough to steal even if you can't look at the contents and you would need to use https as well as a few other things. But that's an entirely different can of worms.

A: Maybe you could use session-state to keep track of this information instead. PHP has inbuilt functions which will manage the session state for you.
Users can't see this as the session information is stored on the server only.
Then you can basically access and store information using the $_SESSION array.
Here are some websites I just found in google about session state:

*

*http://www.w3schools.com/php/php_sessions.asp

*http://userweb.cs.utexas.edu/~mitra/csFall2005/cs329/lectures/php.html

A: In this age of Firefox and Firebug it's not that easy to hide what values are being passed from page to page, especially if it's with the URL...
Any "interested parties" can use the developer tools that come bundled with the browsers to pry and look how the page actually works....
The only solution, as many others suggested above is to encrypt the part that shows the user's identification with some ingenuity so that only the developers know how it works....
Example : Why pass it as 'user_id'....? Try passing it as 'cxv=32'... Additionally you can encrypt the actual id with some algorithm and then decrypt it back in the next page.. This may stop any attempted modification of the URL... at least, it can make it hard...!!
Just use your imagination...! ;)

A: One thing that people haven't mentioned yet is the use of the PHP extension Suhosin here. You can fix a number of known security holes in PHP's superglobals by installing Suhosin, and additionally, control the maximum array length/depth/size for each of $_GET, $_POST etc. It also provides transparent encryption of session data. Excerpt from the standard suhosin.ini configuration file:

The encryption key used consists
   of [a] user defined string (which can be altered by a script via ini_set())
   and optionally the User-Agent, the Document-Root and 0-4 Octects [sic] of the
   REMOTE_ADDR.

Suhosin should still be used with $_SESSION over HTTPS, as there's no feasible way to protect against loss of information without using encryption in the transport layer. And you should salt your session ID with something similar to Suhosin's method for encrypting the session data itself (using something semi-unique to the user, and maybe the time or date too).

A: One way to be a little more secure is to use a random session id instead of a clear text user id. Once a user logs in, create something like 41b96964c35747e19019d2d0f2efb0d1 and use this for the session to identify a user. This way another user cannot just guess the next id.

A: What I usually do is urldecode it (just to get the raw value) and then run this function
function safedata($original) {
 return stripslashes(strip_tags(htmlspecialchars(trim($original))));
}

Works like a charm. Additionally, you can add mysql_real_escape_string() to the function if you're already connected to a database.

A: use nextpage.php?uid=base64_encode($id);
and on nextpage.php use
$user_id=base64_decode($_GET[uid]);

redpajama_set_name: RedPajamaStackExchange


If you are an enthusiastic gambler that now wants to indulge in online betting then you must know about betting ban in your country so that you can play without risk. Most nations around the world and their states have oyunkuram305.com often debated on as well as approved several resolutions imposing, revoking or upholding bans enforced upon gambling, particularly online betting, which in turn could ensure that your money as well as your earnings remain secure within your online account.
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In case you are thinking of moving your passion regarding gambling to online sites then you definitely must remember to remain on the right side of gambling laws and regulations within your nation before you decide to move your mouse towards gambling websites. It is very important to understand if your country has enforced a betting ban on some or even just about all types of online gambling as your money and your freedom should remain protected when you happily wager on various online games and sports activities inside the virtual world.


text:
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Search for "south asian canadians"
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FILTER BY CONTENT TYPEArticles (2266)Authors (0)Timelines (33)Collections (3)Education Guides (0)Quizzes (0)Primary Sources (0)Videos (0)Podcasts (0)
Toronto Shunned over SARS Fears
This article was originally published in Maclean's magazine on May 5, 2003. Partner content is not updated.
Alberta Clipper
An Alberta Clipper is a type of low-pressure weather system that forms in Alberta or nearby, on the eastern side of the Rocky Mountains. It is a fast-moving storm, hence the name "clipper," which refers to 19th-century ships known for their speed. Depending on the province where the system approaches the Canada-United States border, sometimes it is called a Saskatchewan Screamer, Manitoba Mauler or Ontario Scary-o. It may also be called a Canadian Clipper or simply a Clipper. Such storms mostly occur in December and January but are common in the fall and spring, too. They form about 5–20 times per season.
Canada Development Corporation
Canada Development Corporation, headquartered in Toronto, developed and maintained Canadian-controlled and -managed companies in the private sector. Created in 1971 through a special Act of Parliament, the CDC helped to widen the investment opportunities open to Canadians.
Zouaves
Between February 1868 and September 1870, 7 contingents totalling 507 Canadians enrolled in the papal army (whose soldiers were known as Papal Zouaves) to help defend Rome from the Italian troops who wanted to bring about Italian unification.
Breaches of Personal Privacy Are Growing
JENNIFER STODDART IS A DEDICATED public servant who has spent years - first working for the province of Quebec, and since 2003 as the federal privacy commissioner - trying to protect Canadians' personal information from prying governments and greedy businesses.
Economic Nationalism
Economic nationalism, in Canada, is a movement aimed at achieving greater control by Canadians of their own economy. In recent years it arose in response to the high degree of foreign (especially American) control of the Canadian economy.
The old-age pension is a government initiative to help Canadians avoid poverty in retirement. It has changed from a strictly anti-poverty measure, that often humiliated the elderly, into an accepted, mainstream aspect of post-work life.
Working Class History: Québec
Most adult Canadians earn their living in the form of wages and salaries and are therefore associated with the definition of "working class." In Québec, working people and unions have played an essential role in the province's development.
The Heritage Minutes collection is a bilingual series of history-focused public service announcements. Each 60-second short film depicts a significant person, event or story in Canadian history. They are produced by Historica Canada, the not-for-profit organization that also publishes this encyclopedia. First released in 1991, the Heritage Minutes have been shown on television, in cinemas and online. They have become a recognizable part of Canadian culture. The collection currently includes 99 episodes.
Rebellion in Upper Canada
The 1837 rebellion in Upper Canada was a less violent, more limited affair than the uprising earlier that year in Lower Canada. However, its leaders, including William Lyon Mackenzie, were equally serious in their demands. They wanted democratic reform and an end to the rule of a privileged oligarchy. The rebellion itself failed, but its very failure helped pave the way for moderate and careful political change in British North America. This included the union of Upper and Lower Canada into the Province of Canada and the eventual introduction of responsible government.
Quebec Act, 1774
The Quebec Act received royal assent on 22 June 1774. It revoked the Royal Proclamation of 1763, which had aimed to assimilate the French-Canadian population under English rule. The Quebec Act was put into effect on 1 May 1775. It was passed to gain the loyalty of the French-speaking majority of the Province of Quebec. Based on recommendations from Governors James Murray and Guy Carleton, the Act guaranteed the freedom of worship and restored French property rights. However, the Act had dire consequences for Britain's North American empire. Considered one of the five "Intolerable Acts" by the Thirteen American Colonies, the Quebec Act was one of the direct causes of the American Revolutionary War (1775–83). It was followed by the Constitutional Act in 1791.
This is the full-length entry about the Quebec Act of 1774. For a plain language summary, please see The Quebec Act, 1774 (Plain-Language Summary).
History of the Armed Forces in Canada
The armed forces are the land, naval and air forces commanded by the federal government for the purpose of defending Canada's security, protecting its citizens, and promoting its strategic interests at home or abroad. The armed forces have evolved since colonial times from small, local militia units to the modern professional military forces of today.
In the 18th century, British and American ships cruised the Atlantic seaboard. In the 19th century, Canadians entered the field, establishing a whaling station in Newfoundland, and taking whales as part of a deep-sea fishery operation from Gaspé.
Orthodox Church, also commonly known as the Eastern, Greek or Byzantine Church, a family of Christian churches historically found in eastern Europe, the Near East, Africa and Asia (see CHRISTIANITY).
Canadians' Personal Debt at Historic Level
RUSSELL KENT learned earlier than most about the allure and the pitfalls of credit - he was 14 when his father gave him his first credit card.
Ypres: Inexperienced Canadians Hold the Line
Oystercatcher is a name given to 11 species of large shorebirds of the family Haematopodidae.
A regiment is a body of troops composed of squadrons, batteries or companies; it is often divided into battalions for military operations. A single-battalion regiment ranges in size from 300 to 1,000.
High Cost of Healing
Despite how it may seem some days as the public tunes into the debate over health-care funding, governments in Canada have not turned off the tap. Canadians spent an estimated $76.6 billion on health care in 1997, up from $75.
V-chip Technology
Tim Collings is one of those techies who uses the word "neat" as often as some Canadians use "eh." A soft-spoken engineering instructor at Simon Fraser University in Burnaby, B.C., the 34-year-old Collings clearly gets excited by gadgetry.


No need to make a ecard online with any skills, just write name and get name ecards. This free birthday cards facility for you to celebrate friends and family birthday in a special and unique way. Write family name or your friends name on amazing Happy Birthday Cards to make their birthday more sweet and special. This is the top editor for personalized free birthday cards and greetings ecards with name. Wish birthday to your family and friends with their names to spread happiness and love. They will love it.
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Morgan Stanley holding off on BlackBerry upgrade due to fear of company's future | BlackBerry Blast!
BlackBerry sales are taking a huge hit as customer fears over the company's future affect their purchasing decisions. Retail customers and companies alike are nervous about BlackBerry's future prospects. According to Bloomberg, Morgan Stanley is holding off on upgrading its stable of BlackBerry devices because they fear the company may not be around.
Morgan Stanley would normally have a firm timeline for an upgrade by now, more than five months after the new phones were introduced, said one of the people, who asked not to be identified because the bank�s deliberations are private. The bank has chosen instead to keep using earlier models such as BlackBerry 7 devices, introduced in 2011, because it wants assurance of support for BlackBerry 10 now that the smartphone maker is considering strategic changes, the people said.
BlackBerry 10 has not been a hit so far, and the company is bleeding big time. BlackBerry's board is still considering its options and it looks like they will either break up the company or go private.


Give hot cross buns a delicious makeover with this easy mini doughnut recipe. Make a lightly spiced dough, pipe with almond crosse, fry, and dust with sugar – it's that easy! These sweet Easter treats are guaranteed to impress. Don't forget to screenshot the handy ingredients list at the bottom of the page before you go shopping.
Pour 80ml warm water into a jug, stir in ½ x 7g sachet fast-action dried yeast and set aside for 5 mins until frothy.
Tip: When the yeast froths it is alive and active and is releasing the gas needed to make the dough rise, meaning it is ready to be added to your mixture.
Sift 250g strong bread flour, 25g caster sugar, ½ tsp salt and ¼ tsp each of ground nutmeg, mixed spice and ground cinnamon into a large bowl and, using your fingertips, rub 50g chilled cubed butter until it resembles breadcrumbs. Stir in 1 lightly beaten large egg and the yeast mix and bring together with a wooden spoon.
Tip: Using cold cubed butter and keeping handling to a minimum makes blending easier and quicker.
Lightly dust a clean surface with flour and knead for 10 mins. To knead, fold the dough, then use the heel of your hand to gently press it down and away from you. Fold the dough in half and turn 45 degrees. Repeat until the dough is smooth on the outside and springs back when you press it. Put the dough in a lightly greased bowl; cover loosely with oiled clingfilm. Leave to prove in a warm place for 1-2 hrs or until doubled in size.
Knock the air out of the dough by kneading for 2 mins on a floured surface. Divide the dough into 20 equal pieces, then shape into smooth balls by rolling them on the surface with the palm of your hand. Divide the dough balls between 2 lightly greased baking trays, leaving 3cm between each for them to expand as they prove. Cover loosely with oiled clingfilm; leave to prove in a warm place for 1-2 hrs or until doubled in size.
Tip: Only dust your hands and the work surface with the smallest amount of flour necessary to stop the dough from sticking – otherwise it could dry out.
When ready to cook, mix together 20g plain flour, 2-3 drops of almond extract to taste and 20ml water, then spoon into a piping bag fitted with a 0.5cm plain nozzle. Pipe crosses over each dough ball.
Tip: A piping nozzle will make your crosses neater and more uniform, but if you don't have one in the correct size, simply snip a small hole off the end of a disposable piping bag.
Pour 1ltr sunflower oil into a large, deep saucepan; use a kitchen thermometer to heat the oil to 160°C. If you don't have a thermometer, drop a cube of bread into the oil – it should take 30 secs to turn golden. Working in batches, use a slotted spoon to lower dough balls into the hot oil. Fry for 1-2 mins each side until golden brown. Transfer to sheets of kitchen paper with the slotted spoon and leave to cool for 5-10 mins. Repeat with the remaining dough balls. Roll gently in the remaining sugar while they are still warm.
Tip: Keep checking the oil temperature is at 160°C to cook evenly. Alternatively, bake the doughnuts in a medium oven on a greased tray for 8-10 mins until golden, then roll in the sugar.
Serve the doughnuts warm, with cream, if you like. Stir almond extract into whipped cream and serve alongside the doughnuts to dip.
Follow the recipe until you knock the air out of the dough in step 4. Instead of dividing into balls, re-cover with greased clingfilm and chill in the fridge overnight. The following day, divide into 20 pieces and roll into balls as in step 4. Leave to prove for 4 hrs or until doubled in size, and continue to follow the recipe from step 5.
Doughnuts are best enjoyed on the day they are made, but you can make up to 1 day ahead and store in an airtight container at room temperature. Revive by popping in the oven at 160°C for 5 mins, or in batches in the microwave for 15 secs. To freeze, place in an airtight container or wrap in foil. Defrost, uncovered, for 30 mins-1 hr.
We've made a handy shopping list, so you can get everything you need to make these hot cross bun doughnuts. Don't forget to screenshot before you go shopping!


text:
Das Stadio Pio XII ist ein Fußballstadion in Albano Laziale, südlich der italienischen Hauptstadt Rom. Es wurde nach Papst Pius XII. (1876–1958) benannt. Derzeit bietet das Stadion auf seiner unüberdachten Haupttribüne etwa 1500 Zuschauern Platz.

Nutzung
Die Anlage wird hauptsächlich für Fußball genutzt. Der unterklassige Fußballverein ASD Albalonga (Associazione Sportiva Dilettante Albalonga) aus der Eccellenza Lazio/A nutzt die Sportstätte für seine Spiele. Es dient neben dem Stadio Petriana auch als Spielstätte der Fußballauswahl der Vatikanstadt.

Weblinks
 albalongacalcio.it: Stadion auf der Webseite des ASD Albalonga (italienisch)
 stadiumdatabase.com: Daten zum Stadion (englisch)

Albano Laziale
Fußballstadion im Latium
Fußballstadion in Europa
Fußball (Vatikanstadt)

redpajama_set_name: RedPajamaWikipedia


text:
Le Grand Prix Colli Rovescalesi (en italien : Gran Premio Colli Rovescalesi) est une course cycliste italienne qui se déroule au mois d'août à Rovescala, en Lombardie. Créé en 1948, il est organisé par l'ASD Rovescalese.

Cette épreuve fait partie du calendrier national de la Fédération cycliste italienne. Elle est ouverte aux coureurs espoirs (moins de 23 ans) et élites.

Histoire

Les éditions 2020 et 2021 sont annulées en raison du contexte sanitaire lié à la pandémie de Covid-19.

Palmarès

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| 1948
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| 1949
|  Raffaele Cattaneo
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| 1950
|  Fernando Brandolini
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| 1951
|  A. Zucca
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| 1952
|  Bruno Lodigiani
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| 1953
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| 1954
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| 1955
|  Gianni Alini
|  Luigi Rapaccioli
|  Bruno Lodigiani
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| 1956
|  Giovanni Metra
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| 1957
|  Graziano Pertusi
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| 1958
|  Benito Trioli
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| 1959
|  A. Braghi
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| 1960
|  Luigi Baretta
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| 1961
|  Adriano Durante
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| 1962
|  Clay Santini
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| 1963
|  Ambrogio Portalupi
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| 1964
|  B. Stangalini
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| 1965
|  Tommaso Giroli
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| align=center colspan=4| Pas de course
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| 1967
|  Felice Salina
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| 1968
|  L. Barbieri
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| 1969
|  Paolo Zini
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| 1970
|  Giovanni Varini
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| 1971
|  Antonio Ottaviano
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| 1972
|  Antonio Tavola
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| 1973
|  Vincenzo Vanoni
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| align=center colspan=4| Pas de course
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| 1975
|  Walter Tabai
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| 1976
|  Mario Gualdi
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| 1977
|  Bruno Leali
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| 1978
|  Luigi Gritti
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| align=center colspan=4| Pas de course
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| 1980
|  Benedetto Patellaro
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| 1981
|  Tullio Cortinovis
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| 1982
|  Maurizio Viotto
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| 1983
|  Fiorenzo Bressan
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| 1984
|  C. Antonelli
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| 1985
|  R. Elli
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| 1986
|  Stefano Tomasini
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| 1987
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| 1988
|  Gianluca Tarocco
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| 1989
|  Learco Filippini
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| 1990
|  Davide Perona
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| 1991
|  Dino Rinaldi
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| 1992
|  Luca Prada
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| 1993
|  R. Bergognini
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| 1994
|  Gianluca Tonetti
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| 1995
|  Stefano Faustini
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| 1996
|  Paul Bertino
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| 1997
|  Andrea Tonti
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| 1998
|  Claudio Lucchini
|  Antonio Rizzi
|  Andrea Tonti
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| 1999
|  Marius Sabaliauskas
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| 2000
|  Luca Solari
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| 2001
|  Marco Marzano
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| 2002
|  Luca Solari
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| 2003
|  Giancarlo Ginestri
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| 2004
|  Mirko Allegrini
|  Moisés Aldape
|  Drąsutis Stundžia
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| 2005
|  Miguel Ángel Rubiano
|  Michael Schär
|  Denis Shkarpeta
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| align=center colspan=4| Pas de course
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| 2007
|  Aristide Ratti
|  Marco Cattaneo
|  Andriy Buchko
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| 2008
|  Egor Silin
|  Sacha Modolo
|  Maurizio Anzalone
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| 2009
|  Alberto Contoli
|  Sacha Modolo
|  Diego Ulissi
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| 2010
|  Stefano Agostini
|  Federico Rocchetti
|  Daniele Aldegheri
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| 2011
|  Marco Canola
|  Luigi Miletta
|  Sonny Colbrelli
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| 2012
|  Oleksandr Polivoda
|  Ilya Gorodnichev
|  Matteo Mammini
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| 2013
|  Andrea Zordan
|  Niccolò Bonifazio
|  Paolo Colonna
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| 2014
|  Mirko Trosino
|  Mirco Maestri
|  Simone Andreetta
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| 2015
|  Pierpaolo Ficara
|  Simone Velasco
|  Matteo Pozzoli
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| 2016
|  Paolo Totò
|  Andrea Vendrame
|  Umberto Orsini
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| 2017
|  Andrea Garosio
|  Matteo Moschetti
|  Andrea Toniatti
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| 2018
|  Andrea Cacciotti
|  Jalel Duranti
|  Samuele Zoccarato
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| 2019
|  Julian Mertens
|  Filippo Fiorelli
|  Emanuele Barison
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| align=center colspan=4| annulé
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| 2022
|  Nicolò Buratti
|  Sergio Meris
|  Francesco Busatto
|}

Notes et références

Liens externes

Compétition cycliste en Italie
Compétition fondée en 1948
Cyclisme en Lombardie
Province de Pavie


text:
Judicial Dissent under Externalities and Incomplete Information
Romaniuc, Rustam
Abstract: The issue of the stability and change of legal rules occupies a central place in the discussions of alternative ways of organizing justice and the provision of legal rules. There nonetheless remains a theoretical aspect that has never been raised in the literature on judicial decision making and legal change. Judges that are not bound by precedent and can change the law directly by overruling previous decisions have to make a particular decision about the direction the new precedent will take. We show that under incomplete information about judges' eagerness to choose according to their ideal points, there are two candidates for the particular legal rule that is to become the new precedent: (i) judge's private optimum; and (ii) some other legal rule that can differ from (i) and corresponds to the empirical and normative expectations of a large subset of judges within the judicial population. The individual judge that has decided not to stick to the precedent faces therefore a trade-off, he has to choose among alternative legal rules that yield alternative levels of public and private satisfaction of preferences.
JEL classification: D79, K00, K40
Keywords: Judicial decision-making, reputation, legal change, evolution of judge-made law


text:
\section{Introduction}
Recent years have witnessed a rapid growth in the study of heat engines operating at the nanoscale.  More generally, this area of research is increasingly progressing towards a multitude of energy efficient nano-technologies \cite{gemmerlnp2009,hanggirmp2009,sekimotolnp2010,gelbwasser2015,pekolanaturephysics2015}. On the experimental front, there have been several realizations of mesoscopic heat engines that employ a wide range of working fluids, albeit  operating almost exclusively in the classical domain. Typical examples include piezoelectric materials \cite{SteenekenVanBeek2011}, colloidal systems \cite{BlickeBechinger2012} and even a single atom \cite{RossnagelSinger2015}, to name but a few.

On the other hand, our theoretical understanding of quantum thermodynamics has undergone considerable development that has enhanced our ability to manipulate and control thermal devices at the nanoscale. For example, with the use of tailored driving protocols in various strategies collectively termed shortcuts to adiabaticity,  we are equipped to generate adiabatic or adiabatic-like dynamics in systems that are driven within a finite amount of time \cite{DemirplackRice2008, Berry2009, DengGong2013, PalmeroMuga2013, TorronteguiMuga2013, Jarzynski2013, DeffnerDelCampo2014, DelCampoPaternostro2014, DelCampo2013, AcconciaDeffner2015, DelCampoZurek2012, CampbellFazio2014, RohringerTrupke2015}. However their practical usefulness is  conditional upon the relative timescales of the cycle and the nature of the driving fields \cite{ZhengPoletti2015a}. More recently, studies of many-body working fluids in thermodynamic cycles are providing guiding principles that can enhance the performance of quantum heat engines. For instance, quantum statistics has been shown to significantly influence the work distribution of Hamiltonian processes \cite{YiTalkner2012, GongQuan2014}. In particular, the interplay between quantum statistics and other properties of the working fluid such as the trap geometry \cite{ZhengPoletti2015b} and/or many-body interactions \cite{JaramilloDelCampo2015} can result in augmenting the performance of a heat engine operating in the quantum regime. See \cite{gelbwasser2015,Kosloff2013, VinjanampathyAnders2015, KosloffLevy2014, GooldSkrzypczyk2015} for recent reviews on quantum thermodynamics and heat engines.

Furthermore, our understanding of heat engines at the nanoscale  has benefited from salient advances in statistical physics, namely the area of  fluctuation theorems \cite{hanggiNP2015,CampisiTalkner2011,CampisiTalkner2011err,Jarzynski1997,Crooks1999}. Among the various fundamental relations, we mention in particular the Jarzynski equality that has been validated experimentally in the classical regime, e.g. see Refs.~\cite{hanggiNP2015,CampisiTalkner2011,douarcheepl2005}. Although presenting a formidable challenge for experiment, the Jarzynski equality has also been verified also in the quantum regime \cite{batalhaoprl2014,AnKim2015}. These fluctuation relations allow us to explore various peculiarities in the thermodynamic behavior of non-equilibrium heat engines \cite{CampisiFazio2015a, CampisiFazio2015b}. Such peculiarities may arise from (but are not limited to) squeezed or non-thermal baths \cite{AbahLutz2012, AbahLutz2014, AlickiGelbwaserKilmovsky2015, Leggioantezza2016, MehtaPolkovnikov2013}, irreversibility \cite{JiangSegal2015,RezekKosloff2006}, finite-time effects of the driving \cite{GevaKosloff1992, FeldmannKosloff2000}, and more recently from the time-asymmetry used in the driving protocol \cite{GingrichGeissler2014,PalJayannavar2016}. Moreover, cycles that contain sudden changes in the Hamiltonian parameters have also been investigated \cite{FeldmannKosloff2003, FeldmannKosloff2012, FeldmannKosloff2015, UzdinKosloff2014}, thereby accounting for the role of noise in the cycles' performance as well \cite{FeldmannKosloff2006, AlecceZambrini2015}.

\begin{figure}
\includegraphics[width=0.9\columnwidth]{fig1.pdf}
\caption{(color online) (a)  {{\bf Schematics of a quantum Otto Cycle of total time duration} \boldmath${\tau=\tau_u+\tau_b}$}. Mean energy $ \langle E\rangle$ versus a time-dependent manipulation of the trap frequency  $\omega(t)$: $1 \to 2$. Compression: Unitary (subscript $u$) time evolution using a linearly increasing $\omega^2(t)$ during  the  time span $r_u \tau_u$. $2 \to 3$: Iso-parametric coupling to the hot bath (subscript $b$) at effective temperature $1/\beta_3$ during time $r_b\tau_b$. $3 \to 4$: Expansion: Unitary time evolution with linearly decreasing $\omega^2(t)$ during time interval $(1-r_u)\tau_u$. $4\to 1$: Iso-parametric coupling to the cold bath at effective temperature $1/\beta_1$ in remaining time span $(1-r_b)\tau_b$. Projective energy measurements $\Pi\left(\hat{\rho}(t_i)\right) $ are executed at the end of each stroke. (b) {\bf Time Dependence of Cycle Parameters.} The square of the angular frequency variation $\omega^2(t)$, depicted by the blue continuous line, increases linearly between $t_{1}$ and $t_{2}=t_{1}+r_u\tau_u$ while the bath coupling parameters $\lambda^{\pm}$, given by the red dot-dashed line ($\lambda^+$) and the green dashed line ($\lambda^-$), respectively, are held at vanishing values (zero system-bath coupling). Subsequently, after an instantaneous energy measurement and until time $t_{3}=t_{2}+r_b\tau_b$, both $\lambda^{\pm}$ are abruptly adjusted to  values which yield the hot effective temperature, $1/\beta_3$, while $\omega^2(t)$ is held fixed. After yet another energy measurement and till time $t_{4}=t_{3}+(1-r_u)\tau_u$, the angular frequency $\omega^2(t)$ is linearly reduced while the bath-coupling strengths $\lambda^{\pm}$ are again switched to zero. In the last stroke between $t_{4}$ and $t_{1}+\tau$ the angular frequency is held fixed while the $\lambda^{\pm}$ are turned to their new respective values corresponding to a lower effective temperature, $1/\beta_1$. Projective energy measurements are represented by vertical black dotted lines. Note that the ratio $\lambda^+/\lambda^-$ is different in the strokes indicating different effective temperatures in the two baths.}

\label{fig:1}
\end{figure}
\noindent

In this study, we further develop the understanding of non-equilibrium heat engines that operate during an overall time span $\tau$ upon employing strokes that are individually performed in finite time. In our analysis of the cycle, we introduce an explicit projective energy measurement which is performed before and after each stroke of the cycle, so as to determine the work via the two-time energy measurements protocol \cite{TalknerHanggi2007}. We then explore the non-equilibrium behavior by exploring the conditions for optimal work output and efficiency of the cycle and find characteristic discontinuities as a function of the system parameters.

In section (\ref{sec:model}) we describe the Otto cycle setup and detail the relevant parameters and figure of merits of the quantum engine. The Otto cycle is composed of four strokes: two unitary strokes, of total time $\tau_u$, intercalated by two strokes in which the system is weakly coupled to baths, for a total time $\tau_b$. Hence the total duration of the cycle is $\tau=\tau_u+\tau_b$. We consider a single ion in a harmonic trap as the the working substance of the system, while each bath consists of two lasers weakly coupled to the system, which raise and lower the occupation number of the quantum harmonic oscillator at different rates.  The overall effect of this weak system-bath interaction is such that after sufficient time has elapsed, the system becomes a thermal-like state at an effective temperature determined by a ratio involving the raising and lowering occupation number rates.

In section (\ref{sec:unitary}) we first analyze the limiting case of the ideal bath couplings where the system relaxes to final states that are effectively thermal-like at the end of the two dissipative strokes.

In the following section (\ref{sec:dissipative}) we generalize our study to the case of an engine cycle in which the dissipative strokes are not coupled for long enough times to bring the system to a thermal-like state. Lastly,  we summarize our main findings and  present our conclusions in section (\ref{sec:conclusions}).

\section{Model}\label{sec:model}

We study as an idealized model for a quantum Otto cycle a one dimensional harmonic oscillator whose trapping frequency can be controlled in time and which is {\it weakly} coupled to external baths \cite{Alicki1979}, see Fig.~(\ref{fig:1}). We focus on a particular experimental realization made with a single ion in a Paul trap which can be  cooled and heated via side-band cooling by the use of two simultaneously acting lasers \cite{sidebandcooling}. The evolution of the density operator $\hat{\rho}(t)$ of the system to the external baths can thus be described by a master equation in (Markovian) Lindblad form \cite{GoriniSudarshan1976,Lindblad1976},
\begin{align}
 \frac{d\hat{\rho}}{dt} = -\frac{{\rm i}}{\hbar}\left[\hat{H}(t),\hat{\rho}\right] + \mathcal{D}(\hat{\rho},t) \;.
 \label{eq:master}
\end{align}
The time-dependent system Hamiltonian is explicitly given by
\begin{equation}
\hat{H}(t)=\left(\hat{n}+\frac{1}{2}\right)\hbar\omega(t)\label{eq:Ham}
\end{equation}
Here, $\hat{n}=\hat{a}^{\dagger}\hat{a}$ is the number operator and $\hat{a}$ ($\hat{a}^{\dagger}$) is the lowering (raising) operator, while $\omega(t)$ denotes the time-dependent frequency of the trap. The dissipator $\mathcal{D}(\rho,t)$ in (\ref{eq:master}) is given by \cite{CiracPhillips1992}:
\begin{multline}
\mathcal{D}(\hat{\rho},t)  = \lambda^+(t) \left(2\hat{a}^{\dagger}\hat{\rho}\hat{a} - \left\{\hat{a}\hat{a}^{\dagger},\hat{\rho} \right\}\right)
\\ + \lambda^-(t) \left(2\hat{a}\hat{\rho}\hat{a}^{\dagger} - \left\{\hat{a}^{\dagger}\hat{a},\hat{\rho} \right\} \right) \;,
\label{eq:dissipator}
\end{multline}
where $\lambda^+$ and $\lambda^-$ denote the raising and lowering occupation rates respectively. Note that as a consequence of the protocol used for $\omega^2(t)$ (see Fig.~\ref{fig:1}), the system Hamiltonian does not change in time  during the dissipative parts of the cycle when the external baths are acting on the system. Given a fixed trapping frequency $\omega$, the dissipator tends to drive the system towards the diagonal quantum state that assumes the form
\begin{equation}
\hat{\rho}=\sum_n\rho_{nn} |n\rangle \langle n|=\sum_n\frac{e^{-(n+1/2)\beta\hbar\omega}}{Z(\beta,\omega)} |n\rangle \langle n| \;,
\end{equation}
where $\rho_{nn}$ denotes the normalized occupation probability in state  $|n\rangle$, being the eigenstate of the Hamiltonian (\ref{eq:Ham}) and the effective inverse temperature $\beta$ of the steady state is such that $\lambda^+/\lambda^-=e^{-\beta\hbar\omega}$. $Z(\beta,\omega)$ is the partition function of a 1D harmonic oscillator at inverse temperature $\beta$ and trapping frequency $\omega$, and is given by
\begin{equation}
Z(\beta,\omega)=\frac{{e^{-\beta\hbar\omega/2}}}{1-e^{-\beta\hbar\omega}}.
\end{equation}
The relative strengths of $\lambda^+$ and $\lambda^-$ determine the effective temperature for the system, provided that the steady state is reached. We would like to emphasize that although the baths considered can prepare a single ion in a thermal-like state, they do not constitute actual thermal baths. Instead, they impose a certain distribution of occupation of the energy levels that is independent of the energy difference between the levels. Given the non-thermal property of the baths we prefer to refer more precisely to the specific steady state of the (time independent) master equation as `thermal-like' and to $\beta$ as an `effective' inverse temperature.\\

Next we consider the operation of the quanutm Otto engine in greater detail, see Fig.~\ref{fig:1}. The cycle consists of two {\it unitary} strokes, each followed by a corresponding dissipative stroke in which the system is weakly coupled to the environment while the system parameters are held fixed (iso-parametric processes) \cite{ZhengPoletti2014, ZhengPoletti2015b}. We stress that the dissipative coupling is based on the weak coupling assumption, where the raising and lowering rates are much smaller than the internal electronic levels of the ion. In complete analogy to the classical Otto cycle, no heat is thus being exchanged during the unitary strokes $1 \to 2$ and $3 \to 4$, while no work is done during the iso-parametric processes $2 \to 3$ and from $4 \to 1$ of the cycle (see below for a more detailed explanation).

The evaluation of quantum work fluctuations \cite{TalknerHanggi2007,Talknerpre2008,HanggiTalkner2016}  requires nonselective, projective energy measurements on the {\it total} combined system  composed of the system, the baths and the mutual system-bath interactions \cite{HanggiTalkner2016,Watanabepre2014}. The determination of work in a stroke operation thus mandates (nonselective) energy measurements to be applied before and after each stroke of the Otto cycle.

Typically this presents a formidable  challenge, both for theory and even more so for experiments. This difficult task persists {\it even} in the case in which the coupling among the baths and the system of interest is weak \cite{Campisi2009}. Namely, with all energetic contributions of the system-bath interactions being neglected, the work fluctuations for the system  are still composed of both the changes in the internal energy of the system and, in general, finite energy exchanges with the baths.

Both these contributions are typically non-vanishing. However, the difficult task becomes feasible if for instance, the average heat exchange is vanishing, yielding an average work exchange $\langle W \rangle$ that is equal to the change of the energy of the system $\langle\Delta E\rangle$, i.e.  $\langle W \rangle = \langle \Delta E\rangle$ \cite{footnote}. Likewise, when the work on the total system is vanishing, it implies that the change of the energy of the system alone is determined solely by the typically quite intricate heat exchange $Q$ among the  baths and the system, i.e. $\langle \Delta E \rangle = \langle Q \rangle$. In this case the projective measurement of the (nonselective)  bare system energy alone is sufficient \cite{footnote}. It thus demands that the quantum state given by the corresponding reduced density operator must be calculated. This in turn allows the overall average exchanges of either work or heat to be evaluated. \\

We next introduce a nonselective energy postmeasurement following each stroke of the cycle. This can be formalized by writing down  the corresponding (postmeasurement) density operators explicitly. The average energies are obtained in terms of projective energy measurements of the corresponding quantum state of the Otto engine. By introducing the projection operator $\Pi_n(t)=|n(t)\rangle\langle n(t)|$, where $|n(t)\rangle$ is the instantaneous $n$-th energy eigenstate of the corresponding time-frozen system Hamiltonian at time $t$, the effect of the postmeasurement on the state at time $t$ is then given by a nonselective quantum state, and the reduced density operator $\hat{\rho}(t^+)$ that reads
\begin{equation}
\hat{\rho}(t^+)=\Me\big(\hat{\rho}(t)\big) = \sum_n \Pi_n(t) \hat{\rho}(t) \Pi_n(t)\;.  \label{eq:measure}
\end{equation}
Since we are primarily interested in studying time-asymmetric protocols, we consider cycles in which a total  time span $\tau_u$ is spent on the unitary strokes and a total time $\tau_b$ on the dissipative strokes. We further parametrize the distribution of the time intervals within the unitary and dissipative strokes to allow for asymmetry in the driving protocol. For instance the time spent on the compression stroke $1 \to 2$, is given by $t_2-t_1=r_u\tau_u$ where $r_u$ is a real number between $0$ and $1$, while the time spent on the expansion stroke, $3 \to 4$, is given by $t_4-t_3=(1-r_u)\tau_u$. Similarly, for the dissipative strokes, coupling to the hot bath $2 \to 3$ is performed in time $t_3-t_2=r_b\tau_b$ and to the cold bath $4 \to 1$, in time $t_1+\tau-t_4=(1-r_b)\tau_b$.

For the unitary strokes of the cycle, we consider a protocol in which $\omega^2(t)$ varies linearly between $\omega_1$ and $\omega_2$, such that  $\omega^2(t)=\omega_1^2 + (\omega_2^2-\omega_1^2)(t-t_{1})/r_u\tau_u$
for the compression stroke and
$\omega^2(t) = \omega_2^2 + (\omega_1^2-\omega_2^2)(t-t_{3})/[(1-r_u)\tau_u]$
for the expansion stroke. Here we have used $t_{1}$ and $t_{3}$ respectively for the times at which the system is at stages $1$ and $3$ of the cycle. A plot of the time dependence of $\omega^2(t)$ is given in Fig.~\ref{fig:1}(b) (continuous blue line).

On the dissipative end of things, the coupling to the hot bath is turned on instantaneously at time $t_{2}^+$ from zero to the values $\lambda^\pm_{3}$ and back to zero at time $t_{3}$. Similarly, on the cold end, the bath couplings are again instantaneously switched from zero to  $\lambda^\pm_{1}$ for the time between $t_{4}^+$ and $t_{1}+\tau$. A depiction of the change of $\lambda^{\pm}$ is given in Fig.~\ref{fig:1}(b), where the green-dashed line represents $\lambda^-$ and the dot-dashed red line depicts $\lambda^+$. Note that $\lambda^- > \lambda^+$ and that their ratio is different in the two dissipative strokes, indicating that the system is driven towards  different Gibbs-like states.

In the following we use the notation $S_{a\to b}(\hat{\rho})$ for the map corresponding to the stroke from $a$ to $b$ acting on the state $\hat{\rho}$. Explicitly, considering a postmeasurement density operator $\hat{\rho}(t^+_1)$ for the system, just after an energy measurement, the various strokes are given by
\begin{align}
\hat{\rho}(t^+_2)&=S_{1\to 2}\left(\hat{\rho}(t^+_1)\right) \nonumber \\
&= M_{t_2}\Big(K_{t_1,t_2}\hat{\rho}(t^+_1)\Big) \label{eq:rho12}
\end{align}
where $K_{t,t'}(\hat{\rho}(t))=\hat{U}_{t,t'}\hat{\rho}(t)\hat{U}^{\dagger}_{t,t'}$ with $\hat{U}_{t,t'}=\mathcal{T}\exp\left( -{\rm i} \int_t^{t'} \hat{H}(s)ds  \right)$ and $\mathcal{T}$ denotes time ordering.
It then follows that
\begin{align}
\hat{\rho}(t^+_3)&=S_{2\to 3}\left(\hat{\rho}(t^+_2)\right) \nonumber \\
&= M_{t_3}(\Lambda_{t_2,t_3,\omega_2,\lambda^\pm_3}\hat{\rho}(t^+_2))  \label{eq:rho23}
\end{align}
where $\Lambda_{t_2,t_3,\omega_2,\lambda^\pm_3}$ is a non-unitary map that evolves a density operator $\hat{\rho} (t)$ from $t^+_2$ to $t_3$ using the dissipative Lindblad master equation (\ref{eq:master}-\ref{eq:dissipator}) with $\omega(t)=\omega_2$ and $\lambda^\pm(t)=\lambda^{\pm}_3$, where the parameters are time independent.
The cycle closes upon applying the last two strokes; i.e.,
\begin{align}
\hat{\rho}(t^+_4)&=S_{3\to 4}\left( \hat{\rho}(t^+_3) \right) \nonumber \\
& = M_{t_4}(K_{t_3,t_4}\hat{\rho}(t^+_3))  \label{eq:rho34}
\end{align}
and back to the initial steady state, a fixed point of the cycle composed of four strokes, i.e.,
\begin{align}
\hat{\rho}(t^+_1+\tau)= \hat{\rho}(t^+_1)&= S_{4\to 1}\left( \hat{\rho}(t^+_4) \right) \nonumber\\
&= M_{t_1}(\Lambda_{t_4,t_1+\tau,\omega_1,\lambda^\pm_1}\hat{\rho}(t^+_4))  \label{eq:rho41}
\end{align}

The steady state of the map is thus used to characterize the cycle given by the combination of the four strokes, which in our case is unique, and is equivalent to the diagonal fixed point, obeying
\begin{align}
\hat{\rho}(t^+_1)= S_{4\to 1}\!\Bigg(\!S_{3\to 4}\!\bigg(\!S_{2\to 3}\!\Big(\!S_{1\to 2}\!\big(\hat{\rho}(t^+_1)\!\big)\!\!\Big)\!\!\bigg)\!\!\Bigg).  \label{eq:fixedpoint}
\end{align}

Because the compression and expansion strokes are unitary the system is isolated from the baths; i.e., no heat  can be  exchanged. In presence of vanishing heat the mean work output determines the average work via the sole  difference of average energies of the system. This implies that the average work for the compression and expansion strokes are defined by the average of the two projectively measured energies of the isolated system \cite{TalknerHanggi2007,HanggiTalkner2016}; i.e.,
\begin{align}
\langle W_{1\to 2} \rangle &= \langle E_{2} \rangle - \langle E_{1 }\rangle \;, \label{eq:W12}
\\ \langle W_{3 \to 4} \rangle &= \langle E_{4} \rangle - \langle E_{3 }\rangle \;, \label{eq:W34}
\end{align}
where the average energies are
\begin{align}
\langle E_i \rangle = {\rm tr}\left( \hat{H}(t_i)\hat{\rho}(t_i)  \right). \label{eq:energy}
\end{align}
Clearly the average energy can also be computed using the post measurement density operator giving $\langle E_i \rangle  = {\rm tr}\left( \hat{H}(t_i)\hat{\rho}(t^+_i) \right)$.

Keeping in mind that the baths are  weakly coupled to the system, heat exchange with any bath is solely given by the negative of the corresponding bath energy changes. Moreover, during the strokes $2\to 3$ and $4\to 1$ the system Hamiltonian does not change; put differently, {\it no} work is applied on the {\it total} system composed of system and baths including the weak mutual interactions (energy conservation). Therefore, the average work applied to the system  with the control parameter for ${\hat H}$ held constant is vanishing as well \cite{CampisiTalkner2011,Campisi2009}. The balance of energies exchanged thus implies that average heat exchange follows from a corresponding change in bare system energy alone, assuming here that the system Hamiltonian is not dressed by its interaction with the environment \cite{couplingprl}. The average system energies are  evaluated from the corresponding quantum state reached at the corresponding times $ \{t_i\}$. These mean values follow from the set of projective measurements of the system Hamiltonian by use of the corresponding reduced density operator for the system at time ${\hat{\rho}(t_i)}$.

Accordingly, we  hence find that the average values of heat exchanged are determined by
\begin{align}
\langle Q_{2 \to 3} \rangle &=  \langle E_{3} \rangle - \langle E_{2 }\rangle \label{eq:heat23} \;, \\
\langle Q_{4 \to 1} \rangle &=  \langle E_{1} \rangle - \langle E_{4 }\rangle \;. \label{eq:heat23}
\end{align}
The net work of the cycle is thus given by
\begin{align}
\langle W \rangle =\langle W_{1\to 2} \rangle + \langle W_{3\to 4} \rangle \label{eq:network}
\end{align}

The efficiency of this cycle can be appropriately defined as the ratio involving the net average work output $\langle W \rangle$ divided by the net heat transferred from the hot bath into the system, $Q_{ 2\to 3}$. Note that here we adopt a negative sign convention for the net work, because we are primarily interested in a thermodynamic engine which does work on a load. The efficiency $\eta$ for this quantum Otto cycle is thus given by
\begin{align}
\eta &=-\frac{\langle W \rangle}{\langle Q_{2 \to 3} \rangle} \;. \label{eq:efficiency}
\end{align}

\section{Optimal time distribution between unitary strokes} \label{sec:unitary}

Next, we numerically investigate different scenarios in which the operations are performed in finite-time. For details of our numerical analysis, we refer the readers to Appendix A. We begin by first considering the cases in which the time spans of the processes $2 \to 3$ and $4 \to 1$ (i.e. $r_b\tau_b$ and $(1-r_b )\tau_b$) are both sufficiently long, such that we can safely assume that the quantum states $1$ and $3$, after the respective dissipative strokes, are given by a thermal-like quantum state; i.e.,
\begin{equation}
\hat{\rho}_{i}=\sum_n{\frac{e^{-(n+1/2)\beta_{i} \hbar\omega_i}}{Z(\beta_i,\omega_j)} |n\rangle\langle n|}
\end{equation}
where $i=1,3$, $\omega_3=\omega_2$. Upon combining Eqs.~(\ref{eq:rho12}), (\ref{eq:rho34}) and (\ref{eq:W12}-\ref{eq:energy}), it is possible to compute $\langle W_{1\to 2}\rangle$ and $\langle W_{3\to 4}\rangle$. Note  \cite{DeffnerLutz2008, RezekKosloff2009} for analytical expressions of the mean work for various forms of $\omega(t)$.

\begin{figure}
\includegraphics[width=\columnwidth]{fig2.pdf}
 \caption{(color online) {\bf Optimal distribution of times between strokes.} Optimal values of the unitary parameter (a) $r^{*}_{u,_W}$ and (b) $r^*_{u,\eta}$ that optimize respectively, the work extracted $\langle W \rangle/\hbar \omega_1 $ and efficiency $\eta$ versus $\tau_u$. (c) The optimal work, $\langle W\rangle^*$, corresponding to the values of $r^*_{u,_W}$ in (a) as a function of $\tau_u$. (d) Maximal efficiency $\eta^*$ corresponding to the values of $r^*_{u,b}$ in (b) a function of $\tau_u$. Hamiltonian and bath parameters are $\omega_2=2\omega_1, \beta_{1}\hbar\omega_1=0.5, \beta_{3}\hbar\omega_1=0.1$ for all cycles. The insets in (c,d) are close-ups of the respective quantities at $\omega_1\tau_u \approx 6.8$, where $r^*_{u,_W}$ changes discontinuously while $r^*_{u,\eta}$ changes smoothly. We note that the derivative of the optimal work $\langle W \rangle^*$ changes abruptly while that of the maximum efficiency $\eta^*$ is smooth. The vertical dashed black lines indicate the position of the jumps of $r^*_{u,_W}$ and $r^*_{u,\eta}$.
}
\label{fig:2}
\end{figure}

\begin{figure}
\includegraphics[width=\columnwidth]{fig3.pdf}
\caption{(color online) {\bf Work transfer of a single compression and expansion process.} (a) $\langle W_{1\to 2} \rangle / \hbar\omega_1$ and (b) $\langle W_{3 \to 4} \rangle / \hbar\omega_1$  as a function of $r_u$ for the compression arm of an Otto cycle that operates between $\omega_1$ and $\omega_2=2\omega_1$ with $\tau_u\omega_1=2$ (continuous blue line), $\tau_u\omega_1=4$ (dash-dotted red), $\tau_u\omega_1=6$ (dashed green). Inverse temperatures of the bath are held at $\beta_{ 1}\hbar\omega_1=0.5$ and $\beta_{3 }\hbar\omega_1=0.1$ respectively for the compression and for the expansion processes. }
\label{fig:3}
\end{figure}

We next search for the optimal distribution of the total time spent on the unitary processes $\tau_u$ between the two strokes, which is parametrized by $r_u$. For instance, for $r_u=0$ the stroke from $1 \to 2$ constitutes an abrupt quench while a total of time $\tau_u$ is spent in the stroke $3 \to 4$. For larger values of $r_u$ the time spent in the stroke from $1 \to 2$ increases while the one from $3 \to 4$ decreases until $r_u=1$, i.e.,  when this last stroke becomes an abrupt quench. The ratio $r_u$ for which the net work is optimum is referred to as  $r^*_{u,_W}$ and we denote the maximum work as $\langle W \rangle^*$, given by
\begin{align}
-\langle W\rangle^* = \max_{r_u}\left(-\langle W\rangle\right) \label{eq:maxwork}
\end{align}
(we remind the reader that the net work for an engine is negative). We depict with Fig. \ref{fig:2}(a) the value of $r^*_{u,_W}$ as a function of the total time spent on the unitary strokes $\tau_u$. We observe that at some critical values of $\tau_u$, discontinuities in the ratio $r^*_{u,_W}$ occur. At the occurrence of these jumps, also the derivative of the net work output changes abruptly, see Fig.~\ref{fig:2}(c) and its inset.

A similar result emerges when $r_u$ is chosen so as to maximize the efficiency, denoted here as $r^*_{u,\eta}$, see Fig.~\ref{fig:2}(b). The corresponding optimal efficiency is denoted as $\eta^*$ and it is
\begin{align}
\eta^* = \max_{r_u}\left(\eta\right). \label{eq:maxeffi}
\end{align}
The maximum efficiency $\eta^*$ as a function of $\tau_u$ is shown in Fig.~\ref{fig:2}(d). In Fig.~\ref{fig:2}(b) we observe that the abrupt jumps are also present in the values of $r^*_{u,\eta}$, although they occur at different values of $\tau_u$ from the jumps in $r^*_{u,W}$. Moreover, in certain regions of $\tau_u$ an abrupt jump of $r^*_{u,_W}$ can occur while a continuous variation of $r^*_{u,\eta}$ occurs, as is the case for $\omega_1\tau_u\approx 6.8$, see the insets of Fig.~\ref{fig:2}(c,d). Hence, given a total time $\tau_u$ for the unitary strokes, the optimal distribution of times between the strokes $1\to 2$, e.g. $r_u\tau_u$, and $3 \to 4$, e.g. $(1-r_u)\tau_u$, depends on the quantity being optimized for; For instance either the net output work or the efficiency. Also note that values of our numerically evaluated optimal efficiency are always below that of the Carnot bound $\eta_C=1-\frac{\beta_3}{\beta_1}=0.8$ as they should be.

The nonlinear behavior in the optimal ratio $r^*_{u,_W}$ and $r^*_{u,\eta}$ can be understood by analyzing the work output from a single compression $\langle W_{1\to 2} \rangle$, or expansion process $\langle W_{3 \to 4} \rangle$. As can be seen from Fig.~\ref{fig:3} (see also \cite{AcconciaDeffner2015}), the work transferred in a single unitary stroke becomes a non monotonic function of the ratio $r_u$ when the value of $\tau_u$ becomes sufficiently large. This behavior is ultimately responsible for the phenomenon we observe. In fact, finding the optimal time spans between the strokes stems from matching the optimal work output from two non-monotonic functions of time under the constraint of a given total time spent on the two unitary strokes. In Fig.~\ref{fig:3} we observe that the number of oscillations present in the work output as a function of $r_u$ increases with the  duration of total time spent on the two unitaries $\tau_u$

In Fig.~\ref{fig:4}, the value of average work (left) and efficiency (right) as a function of the ratio $r_u$ are shown for different values of $\tau_u$. Since the work in each stroke is a non-monotonic function of the time spent, the net work, which is the sum of work in the two unitary strokes becomes an oscillating function.
For larger $\tau_u$-values  the number of local minima or maxima of the net work output, or of the efficiency, increases as the total time in the unitary strokes increases. The emergence of a new global extremum can occur either via the increase in magnitude of a local extremum, such that it becomes the global one, or when the global extremum turns unstable and in turn yields two extrema, with one of the two becoming the new global extremum. The former route is reminiscent of the behavior of the free energy as a function of the order parameter as temperature changes in an ordinary first order phase transition, while the latter mimics the behavior of a second order phase transition.

\begin{figure}
\includegraphics[width=\columnwidth]{fig4.pdf}
 \caption{(color online) {\bf Oscillations of the net work and efficiency.} (Left panels) Mean work extracted and (Right panels) efficiency of cycles as a function of $r_u$ for cycles with the parameters set at $\omega_2=2\omega_1, \beta_{1}\hbar\omega_1=0.5, \beta_{3}\hbar\omega_1=0.1$. Increasing number of oscillations in both net work and efficiency with the unitary timescale $\tau_u$ results in discontinuities in $r_{u,_W}^{*}$ and $r^*_{u,\eta}$.} \label{fig:4}
\end{figure}

\begin{figure}
\includegraphics[width=\columnwidth]{fig5.pdf}
 \caption{(color online) {\bf Cycle Performance at short bath coupling timescales.} (a) Average net work $\langle W \rangle$, (b) average heat from the hot bath $\langle Q_{2 \to 3} \rangle$ and (c) efficiency $ \eta $ of Otto cycles where $\omega_1\tau_u=\omega_1\tau_b/10=5$ as a function of $r_u$ and $r_b$. Regions that are shaded white are domains in which the cycle is non physical as it is not doing work but instead receiving it. Plot (d-f) show the horizontal cuts highlighted by white lines in figures (a-c). In particular, in (d-f) the blue continuous line corresponds to $r_b=0.25$, the red dashed line to $r_b=0.5$, and the black dot-dashed line to $r_b=0.75$. We use $\lambda^-_{1,3}=\omega_1/10$, $\lambda^+_3=\lambda^-_3/e$ and $\lambda^+_1=\lambda^-_1/e^{10}$ which corresponds to $\beta_{1}\hbar\omega_1=10$ and $\beta_{3}\hbar\omega_1=0.5$.  } \label{fig:5}
\end{figure}

\section{Optimal time distribution within unitary and dissipative strokes} \label{sec:dissipative}

In the previous section, the state at the beginning of the compression and expansion strokes, $1$ and $3$ respectively, were assumed to be effectively thermal-like (because enough operation time was spent on the two dissipative strokes $2 \to 3$ and $4 \to 1$). We now consider the case in which the time spans of the dissipative strokes, $r_b\tau_b$ and $(1-r_b)\tau_b$, are too short for thermalization to occur such that the quantum states in $1$ and $3$ are no longer thermal-like. Under such circumstances, as detailed with Eq. (\ref{eq:fixedpoint}), $\hat{\rho}(t_i^+)$ is the (unique) fixed point of the four strokes which connects the quantum state $1$ back to itself.

Since after each energy measurement the density operator is diagonal in the basis of instantaneous energy eigenstates, computing $\hat{\rho}(t_1^+)$ amounts to finding the eigenvector associated to the eigenvalue $1$ of the corresponding Markovian map in Eq. (\ref{eq:fixedpoint}). In particular, we would like to stress that the numerical evolution of Eq. (\ref{eq:master}) in the strokes $2 \to 3$ and $4 \to 1$ is particularly simple because after the measurements in $2$ and $4$ the density operator is diagonal in the instantaneous eigenbasis of $\hat{H}(t_i^+)$. Moreover, our  specific choice of dissipator $\mathcal{D}$, given by Eq.(\ref{eq:dissipator}), preserves the diagonal form when acting on a diagonal density operator. This implies that the density operator, in the strokes $2\to 3$ and $4 \to 1$ commutes with the Hamiltonian and hence its evolution only depends on the part involving the dissipation.

In order to stay in the weak coupling regime throughout the evolution, we ensure  that the ratio $\lambda^{\pm}_i / \omega_1$ is always much lesser than $1$. However, given the stylized setup of our system, keeping the products $\lambda_3^{\pm}r_b\tau_b$ and $\lambda_1^{\pm}(1-r_b)\tau_b$ fixed while varying $\lambda_i^{\pm}$, $r_b$ and $\tau_b$ individually, results in the same $\hat{\rho}(t_i^{+})$ obtained and hence leads to the same net work output and efficiency for the cycle \cite{validity}.

In Fig.~\ref{fig:5} we depict the color coded intensity  for net average work $\langle W\rangle$, average heat input $\langle Q_{2 \to 3}\rangle$ and the efficiency $\eta$ [cf. in Fig.~\ref{fig:5}, panels $(a)$, $(b)$ and $(c)$]. We choose $\tau_u=\tau_b/10=5/\omega_1$ because this is a long enough time to obtain two extrema in the cycle work output when the total time is distributed across the strokes (there would be only one maximum for shorter timescales). It should also be noted that in Fig.~\ref{fig:5} some regions are colored in white. These  regions correspond to cases (similarly to \cite{FeldmannKosloff2003, FeldmannKosloff2012, FeldmannKosloff2015}) for which the finite-time operation of the cycle  does not yield an overall  negative net work output. Notably, these regions occur when any one of the dissipative or unitary strokes is performed in too short a time. In Fig.~\ref{fig:5} we observe a quantitative change of the mean work output, heat and efficiency due to the finite time spent on the dissipative strokes, but do not find any qualitative changes.
This is highlighted in Fig.~\ref{fig:5}(d-f) by the horizontal cuts of the intensity maps in Fig.~\ref{fig:5}(a-c) for three different values of $r_b$.

\section{Conclusions}\label{sec:conclusions}

With this work we investigated the efficiency, net work output and input heat for a quantum Otto engine operated in a finite time. The cycle we consider is composed of two unitary strokes connected by two dissipative strokes. During the total time $\tau=\tau_u + \tau_b$ of the cycle operation, a typically asymmetric portion is spent on the two unitary strokes of total duration $\tau_u $ and the remaining time span $\tau_b$ on the two dissipative strokes. We numerically evaluated the optimal distribution of time spans within the unitary and dissipative strokes while optimizing either the net work output or the efficiency. The distribution of times is parametrized by $r_u$ and $r_b$ such that the time in the stroke $1 \to 2$ is $r_u\tau_u$ and $2 \to 3$ is $r_b\tau_b$. In Sec.~\ref{sec:unitary} we elaborated on the case in which the time spent in the dissipative strokes is long enough such that the baths effectively thermalize the system at the end of the stroke.

We observed that optimizing for the work output results in discontinuous jumps in $r^*_u$ across values of $\tau_u$. Likewise, optimizing for the efficiency results in a similar jump behavior, albeit in a different location along $\tau_u$. This feature stems from a non-monotonic dependence of work output on the time spent in each unitary  stroke. This phenomenon  is  present as well when the baths do not fully thermalize the system as shown in Sec.~\ref{sec:dissipative}.

We would like to note that the engine cycle considered includes energy measurements at the end of each stroke. Because in quantum mechanics each measurement affects the system via a back action, and since energy measurements are necessary to obtain the net energy balance for work output and heat exchange, it is essential to detail these measurements after each individual stroke of the cycle. We also stress that in any of these strokes we encounter non-equilibrium scenarios as the energy balance is {\it not} between corresponding thermal equilibrium states. Put differently, all our energy balance relations are manifestly non-equilibrium  relations that cannot be labelled `thermodynamic first law' relations.  The latter involves knowing the difference between two internal energy state functions.

In contrast to the the quasi-static and reversible Otto cycle in thermal equilibrium such features of abrupt jumps are absent. Therefore, it would be of interest to see if the features as depicted in our set of figures, are indeed present in an experiment of a quantum Otto cycle.

The study of finite-time quantum engine cycles is necessary for the implementation of such systems.
As exemplified by this work, the dynamics involved in finite time quantum engine cycles is rich and should be studied thoroughly.   \\

{\bf Acknowledgments} D.P. acknowledges support from Singapore MOE Academic Research Fund Tier-2 project (Project No. MOE2014-T2-2-119, with WBS No. R-144-000-350-112) and fundings from SUTD-MIT IDC (Project No. IDG21500104). Y.Z. is supported by NTU SUG M4081346. D.P. also acknowledges fruitful discussions with F. Binder, S. Fazio, J. Goold, K. Modi, S. Vinjanampathy.

\setcounter{equation}{0}
\renewcommand{\theequation}{A.\arabic{equation}}
\setcounter{figure}{0}
\renewcommand{\thefigure}{A.\arabic{figure}}

\begin{appendix}

\section{Numerical computations}

After each stroke, inclusive of the energy measurement, the density operator $\hat{\rho}$ is diagonal in the instantaneous energy eigenbasis and can thus be written as
\begin{align}
\hat{\rho}(t_i^+) = \sum_n \rd_n(t_i^+) \Pi_n(t).
\end{align}
where $\rd_n$ is the $n$-th element of the diagonal density operator. For a unitary stroke from $t_i^+$ to $t_{i+1}^+$ we get, using Eq.(\ref{eq:rho12}) or (\ref{eq:rho34})
\begin{align}
\rd_n(t_{i+1}^+) = \sum_m {{P}}^{n,m}_{t_i,t_{i+1}}\;\rd_m(t_i^+)
\end{align}
where
\begin{align}
{{P}}^{n,m}_{t_i,t_{i+1}} = |\langle n(t_{i+1})|\hat{U}_{t_i,t_{i+1}}|m(t_i)\rangle|^2.
\end{align}
The dissipative evolution for $t\in [t_i^+,\;t_k^+)$, due to Eqs.(\ref{eq:master}-\ref{eq:dissipator}) is instead given simply by
\begin{align}
\frac{d\rd_n(t)}{dt} = 2& \left\{ n \lambda_{k}^+  \rd_{n-1}(t) + (n+1) \lambda_{k}^-  \rd_{n+1}(t)   \right.\nonumber\\
&-\left.\left[   (n+1)\lambda_k^+ +n\lambda_k^-       \right]\rd_n(t)\right\}
\end{align}
where $i=2$ or $4$ and $k=\left[(i+1)\mod(4)\right]$. This simple form of time evolution is due to the fact that the density operator $\hat{\rho}$ is diagonal in the instantaneous energy eigenbasis at all instances of the dissipative strokes and hence it commutes with $\hat{H}$. In our implementation we have kept $n=50$ eigenstates of the harmonic oscillator, which is sufficient for the effective temperatures and dynamics involved.

In our numerical simulations, we have rewritten Eq.~(\ref{eq:master}-\ref{eq:dissipator}) in terms of dimensionless parameters. Explicitly, by dividing Eq.~(\ref{eq:master}) by $\omega_1$, we obtain
\begin{align}
 \frac{d\hat{\rho}}{d\tilde{t}} = -{\rm i}\left[\tilde{H}(\tilde{t}),\hat{\rho}\right] + \tilde{\mathcal{D}}(\hat{\rho},\tilde{t}) \;.
\end{align}
where $\tilde{t}=\omega_1 t$,
\begin{align}
\tilde{H}=\hat{H}/\hbar\omega_1 = (\hat{n}+1/2)\tilde{\omega},
\end{align}
and
\begin{multline}
\mathcal{D}(\hat{\rho},\tilde{t})  = \tilde{\lambda}^+(\tilde{t}) \left(2\hat{a}^{\dagger}\hat{\rho}\hat{a} - \left\{\hat{a}\hat{a}^{\dagger},\hat{\rho} \right\}\right)
\\ + \tilde{\lambda}^-(\tilde{t}) \left(2\hat{a}\hat{\rho}\hat{a}^{\dagger} - \left\{\hat{a}^{\dagger}\hat{a},\hat{\rho} \right\} \right) \;, \nonumber
\label{eq:dissipator_rescaled}
\end{multline}
where $\tilde{\omega}=\omega/\omega_1$ and $\tilde{\lambda}^{\pm}=\lambda^{\pm}/\omega_1$. As a consequence the inverse temperature $\beta$ can be written in dimensionless form $\tilde{\beta}=\beta\hbar\omega_1$ because
\begin{align}
\beta\hbar\omega=\left(\beta\hbar\omega_1\right)\left(\omega/\omega_1\right)=\tilde{\beta}\tilde{\omega}.
\end{align}

\end{appendix}

redpajama_set_name: RedPajamaArXiv


This paper was originally published as: Hannay, P. (2011). Kindle forensics: acquisition and analysis. Paper presented at the 2011 ADFSL Conference on Digital Forensics, Security and Law. Richmond, Virginia, USA. Original conference proceeding available here.


text:
After Several Weeks of Competition, European Leagues Ready for Break
The EuroLeague and EuroCup, which have completed five and four weeks of competition, respectively, are now on a nearly three-week break for the Nov. 7-15 international window for women's basketball. Competition will resume on Nov. 23 (EuroCup) and 24 (EuroLeague). During the break in European league games, the FIBA AmeriCup 3x3 Championship will be held in Miami, as well as EuroBasket qualifying games.
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American Athletes Tops Among EuroLeague Scorers
Kayla McBride, scoring at a clip of 21.0 ppg. through five games, is leading all EuroLeague regular season scorers. Ranked tied for second are Kennedy Burke and Natasha Howard with 20.0 ppg. Take a look at where other Americans rank among the top 30 EuroLeague scorers.
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Seven Punch Ticket to EuroCup Playoffs
The EuroCup, which capped its fourth week of games, features 48 teams split into 12 regular season groupings. Each team plays a home and away game against each team in its group, and a total of 32 teams eventually will advance to the first round of playoffs.
As of the conclusion of this week's games, seven teams secured playoff spots, with 25 more slots up for grabs. The seven teams assured of advancement include 2021 SuperCup champions Valencia, BC Polkowice, Tango Bourges, Roche Vendee, Tarbes GB, CBK Mersin Yenisehir amd BC Nadezhda. Four of those teams feature top U.S. talent, in Tiffany Hayes (Mersin), Kristen Mann (Bourges), Stephanie Mavunga (Polkowice) and Kaleena Mosqueda-Lewis (Roche Vendee).
EuroCup Highlights
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2021-22 EuroLeague Regular Season Standings & Week 5 Games
Group A W-L Group B W-L
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UMMC Ekaterinburg 82, KSC Kzekszard 67
Led by 17 points and 10 boards from Jonquel Jones and 16 points from Allie Quigley, UMMC Ekaterinburg (5-0) stands as the only undefeated team in EuroLeague action after defeating winless KSC Szekszard (0-5) 82-67 in Hungary.
Sopron Basket 79, Dynamo Kursk 72
Playing on its home court, Sopron Basket (4-1) moved into the lead in Group B with a 79-72 win over Dynamo Kursk (3-2). Sopron was paced to victory with a 23-point performance from Gabby Williams and Shay Peddy added 19 points, while Natasha Howard notched 21 points and Arike Ogunbowale scored 18 in the loss, which put Kursk in a three-way tie for second place in the group standings.
ZVVZ USK Prague 80, Perfumerias Avenida 55
ZVVZ USK Prague (3-2) dominated previously unbeaten Perfumerias Avenida (4-1) 80-55 to move into a three-way tie for third place in Group A. Trailing 39-33 at the end of the first half, the Czech club outscored Avenida 41-22 in the second half for the 25-point victory. Spain's Maria Conde scored a game-high 21 points, while 2021 USA 3x3 AmeriCup Team member Brionna Jones added 15 points, six rebounds and three steals for the Czech club. Katie Lou Samuelson topped the scoring for Avenida, contributing 13 points in the loss.
MBA Moscow 62, Umana Reyer 61
MBA Moscow (2-3) edged Umana Reyer (1-4) 62-61 to pick up a critical victory and keep its playoff hopes alive. The game, in which neither team owned a double-digit lead, saw nine lead changes and was close throughout. MBA Moscow, which lists only Russians on its roster, was led by Elena Kirillova and Zhosselina Maiga, who scored 15 points apiece. Serbian Yvonne Anderson scored 12 points as Umana's high scorer.
Beretta Famila Schio 64, Fenerbahce Safiport 60
Despite receiving a game-high 27 points from Kayla McBride, Fenerbahce Safiport (2-3) dropped its game against Beretta Famila Schio (2-3) 64-60. France's Sandrine Gruda scored 17 points, had eight rebounds and four assists to help lead Schio to its second win of the season.
BLMA 63, TTT Riga 54
BLMA (3-2) never trailed and picked up a big win this week, 63-54 over TTT Riga (2-3) to remain among the top four teams in Group A. Playing in France on its home court, BLMA was paced to victory by Haley Peters, who tallied 15 points, 11 rebounds, three assists and three steals; and Jasmine Thomas chipped in 11 points and seven rebounds in Riga's loss.
Basket Landes 79, VBW Arka Gdynia 70
Paced by 23 points, seven rebounds and four assists from Sophie Cunningham, Basket Landes (3-2) remained among the top teams of Group B with a 79-70 win over VBW Arka Gdynia (1-4). Ireland's Alice Kunek finished as Gdynia's leader with 19 points and Croatia's Ana-Marija Begic added 18.
Galatasaray 69, Spar Girona 55
Owning a 27-17 lead at the end of the first quarter, Galatasaray (3-2) continued to cruise to a 69-55 win over Spar Girona (2-3) in Spain. Gala had three players close out with 17 points, including Turkey's Pelin Bilgic, Serbian Tina Krajisnik and Riquna Williams. Rebekah Gardner, 15 points, and Kennedy Burke, 13 points, were the Spanish squad's top two scorers.
Natasha Howard
Katie Lou Samuelson
Jessica Shepard
Arike Ogunbowale
Speakers Announced for Nov. 6 USA Basketball Minneapolis Coach Academy
USA 3x3 Men's and Women's AmeriCup Teams Set to Open Florida Training Camp
Women's National Team's unifying message in 2023
Ian Kayanja
Ahead of what promises to be a busy 2023, the word on Briana Weiss' mind is joy.
Celebrated National Team Star Maya Moore Retires
Chros McDougall, Red Line Editorial
Moore helped lead the U.S. to two Olympic gold medals and two World Cup titles.
FIBA World Cup for Women
Wilson Named Female Athlete of the Year
USA Basketball Annual Awards
Shawn Smith, Red Line Editorial
Wilson helped the USA Women's National Team to its fourth consecutive World Cup gold earlier this year.
Women's National Team Named USA Basketball's National Team of the Year
The American women won their sixth FIBA World Cup in seven years earlier this year.
USA Basketball Statement on Brittney Griner
Brittney Griner has shown bravery and resolve over the last nearly 300 days. USA Basketball is relieved that she is on her way home and will happily reunite with her wife, family and friends.
Tweets from https://twitter.com/usabasketball/lists/usa-basketball-accounts
@usabasketball With a busy 2023 on deck, the goal is more gold & more joy. Those are irreplaceable memories for the 🇺🇸 Women's National Team program.21 Hours ago