text:
Q: Paging in php mysql I'm trying to make a website with movies in it, everything is fine but i have just 1 little problem,when ever i make a website, i do all work in my local computer test it then I upload the  web, the code below is for paging with query it works fine in WAMP (locally).  But when I upload the paging code to my web server it says NOT EXIST.
it shows the else part,whats the problem?
<?php

$per_page = 35;
 $page = 1;
 if (isset($_GET['page']))
 {
  $page = intval($_GET['page']);
  if($page < 1) $page = 1;
}

 $start_from = ($page - 1) * $per_page;

$con= mysql_connect("localhost","sarya_asad","Thisisfor123");
 mysql_select_db('saryaal_com_movies',$con);

 $current_items = mysql_query( "SELECT * FROM `english` LIMIT $start_from, $per_page");
 if( mysql_num_rows($current_items) > 0)
 {
  while($item = mysql_fetch_assoc($current_items))
  {

  ?>

         <a href="english/english-preview.php?id=<?php echo$item['id']?>" ><?php echo $item['title'] ;?>
          <?php echo $item['year'] ;?>
          <?php echo $item['quality'] ;?>

    <?php
    }
 }
 else
 {
  echo 'this page does not exists';
 }

 $total_rows = mysql_query("SELECT COUNT(*) FROM `english`");
 $total_rows = mysql_fetch_row($total_rows);
 $total_rows = $total_rows[0];

 $total_pages = $total_rows / $per_page;
 $total_pages = ceil($total_pages); # 19/5 = 3.8 ~=~ 4

 for($i = 1; $i  <= $total_pages; ++$i)
 {
  echo "$i   ";
 }
 ?>

A: <?php if($Strkeyword=="" AND $StrLoc=="" AND $StrMinsal=="-1" AND $StrMaxsal=="-1" AND $StrMax_exp=="maximum" AND $Strcategory=="" AND $Strjobtype=="") {
 $sql=mysql_query("select * from job where AND status='Active'");
 }
$per_page = 5;
 $page = 1;
if (isset($_GET['page'])) {
$page = intval($_GET['page']);
 if($page < 1) $page = 1;
}
$start_from = ($page - 1) * $per_page;
 if($Strkeyword=="" AND $StrLoc=="" AND $StrMinsal=="-1" AND $StrMaxsal=="-1" AND $StrMax_exp=="maximum" AND $Strcategory=="" AND $Strjobtype=="")
{
$current_items=mysql_query("select * from job LIMIT $start_from, $per_page"); } $start_from, $per_page");
 if( mysql_num_rows($current_items)>0) { while($arr=mysql_fetch_array($current_items)) {
?>

<?php include("include/result.php") ?>// result u want to display
<?php
}
} else {
echo 'Data does not exists'; }
if($Strkeyword=="" AND $StrLoc=="" AND $StrMinsal=="-1" AND $StrMaxsal=="-1" AND $StrMax_exp=="maximum" AND $Strcategory=="" AND $Strjobtype=="") {
 $total_rows=mysql_query("select COUNT(*) from job where AND status='Active'");
 }
$total_rows = mysql_query("SELECT COUNT(*) FROM job");
 $total_rows = mysql_fetch_row($total_rows);
$total_rows = $total_rows[0];
$total_pages = $total_rows / $per_page;
 $total_pages = ceil($total_pages);
 # 19/5 = 3.8 ~=~ 4
echo "
";
 echo "Page : ";
 for($i = 1; $i <= $total_pages; $i++) {
 echo "[$i ]";
}
echo "
";
?>

A: change this
 $start_from = ($page - 1) * $per_page;

to
 $start_from = ($page) * $per_page;

A: you might want to use something like:
$per_page = 35;
$start_from = $page * $per_page - $per_page;

A: This is your problem:
$con= mysql_connect("localhost","sarya_asad","Thisisfor123");
    mysql_select_db('saryaal_com_movies',$con);

You need to change the host details. localhost is the local server on your machine.

A: Try this logic for pagination:
Your goal is to offset by the number of images you want to display on each page.
So let's say you want to display 6 movie thumbnails on a page... You'd have:
$videos_per_page = 6
$pageNumber = (isset($_GET['page']) ? ($_GET['page']) : 1);

And your offset would be:
$offset = $videos_per_page * $pageNumber

(6 videos * page 0... so you're offsetting 0 videos. That's good because you want to display the first 6 videos in your data structure on page 0).

So now that you have your offset value... You need to set your array pointer to the correct spot... Loop through your database rows storing your movies and move your pointer by your offset value... Store that in $videos_to_offset...
while ($videos_per_page < $offset && ($row = $Query_Result->fetch_assoc())) {
    $videos_to_offset++;
}

Now you can loop through your database rows, outputting your videos from wherever your offset array pointer left off:
    $video_counter = 0;
    while ($video_counter < $videos_per_page && ($row = $Query_Result->fetch_assoc())) {

        echo   $row['videopath'];
        $video_counter++;
}

Something like that.


text:
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Apartment PAC Austin
What is Apartment PAC Austin?
Apartment PAC Austin is the Austin Apartment Association's Political Action Committee —providing an opportunity for members interested in the welfare and future of the free enterprise rental housing market to support candidates for local and state offices who believe and have demonstrated their beliefs in our pro-housing point of view.
Contributed funds are directed to candidates who have been vetted by the Apartment PAC Austin Board of Trustees. PAC funds also may be used to support bond elections, ballot initiatives, and similar efforts that can help improve housing opportunities and the overall quality of life for Austin area residents.
For industry associations like the Austin Apartment Association, successful advocacy is a combination of presenting credible facts and information, building relationships with policymakers, and having a Political Action Committee (PAC) to fully participate in the legislative process; without all three working together our advocacy efforts will falter.
Invest in Apartment PAC Austin
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Contributions of $99 or more are invited to attend the annual Investors Reception.
Capitol View Penthouse $400+
Lady Bird Lake View $300-$350
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PAC Partner <$99
All contributions to Apartment PAC Austin are voluntary and all levels of contribution are welcome. Your PAC contribution can be divided into installments and paid out over several months.
Special Notes on PAC Donations
Texas law allows only personal donations and prohibits corporate contributions to PACs. PAC donations cannot be paid with corporate checks or corporate credit cards. Your AAA account cannot be billed. Personal, sole proprietor or partnership checks should be made payable to "AAA PAC," or you may use your personal, sole proprietor, or partnership credit card for PAC contributions. No corporate cards can be accepted. Texas law also requires political action committees to report the name, mailing address, occupation, and name of employer for each individual contribution. Contributions to AAA PAC are for political purposes and will be used as political contributions for candidates favorable to the rental housing industry. All contributions are voluntary. You may refuse to contribute without reprisal. Guidelines are merely suggestions; you may contribute more or less than the suggested amounts.
Have donation questions? Contact Emily Blair, CAE at emily@austinaptassoc.com or (512) 323-0990.
Apartment PAC Austin Makes A Difference
Helping elect candidates to office that understands the dynamics of housing and the real-life impacts that their policy decisions have is important to all members of the apartment industry:
The City of Austin routinely considers enacting a RENTAL REGISTRATION ORDINANCE with per unit annual fees and mandatory annual inspections. Due to our efforts, this has not yet come to pass, but if it were ever to pass it is estimated to cost the property owners in Austin over a $1,000,000 in fees annually! Many cities in Texas already have this type of ordinance in place and the fees are increased every year in the City's budgets- Dallas now has a $10 per unit annual fee but it started at $2 per unit!
The City of Austin TENANT RELOCATION ORDINANCE originally proposed to make property owners pay moving expenses and stipends to tenant affected by all type of property development and re-developmemt. This dangerous ordinance was narrowed but only after Apartment PAC Austin supported policy makers took the time to listen and understand our viewpoints. Had this ordinance gone forward the cost of property ownership would have soared affecting annual budgets and long-range property improvement plans.
Multifamily property owners can now take advantage of the property accessed clean energy district (PACE) financing that allow owners to install a myriad of energy and water efficiency improvements and pay for them through a monthly tax assessment. Because a PACE loan is considered a tax and not due upon sale, this innovative finance mechanism offers distinct advantages and provides instant monthly energy and water bill savings without a lengthy ROI period. This opportunity only came about because business-minded elected officials were elected that held a clear understanding of the rental housing industry and the economic impact such a program like PACE could have on multifamily property owners and service providers alike.
At the state level, legislation is often considered to require apartment leasing professionals to be LICENSED which carries annual fees and additional classroom hours for keeping the license current. Only our political involvement with legislators in all areas of Texas keeps licensing and registration for onsite personnel from being enacted.
Apartment PAC Austin FAQs
Apartment PAC Austin is the Austin Apartment Association's Political Action Committee —providing an opportunity for members interested in the welfare and future of the free enterprise rental housing market to support candidates for local and state offices who believe and have demonstrated their beliefs in our pro-housing point of view.
What is a Political Action Committee (PAC)?
A political action committee is the name given to a group organized to combine the contributions of many individuals and make contributions to support candidates for public office as well as to support bond elections, ballot initiatives and similar efforts that can help improve the quality of life for Austin area residents. Apartment PAC Austin is registered with the Texas Ethic Commission and follows their strict document filing and reporting rules as well as all rules established by local government entities.
What does the Apartment PAC (APARTMENT PAC AUSTIN) do?
Apartment PAC Austin accepts contributions from those involved in the rental housing industry and makes contributions to individuals running local and state office. Contributions are also used to support Texas statewide races such as those for governor, lieutenant governor and comptroller. PAC funds may also be used to support bond elections, ballot initiatives and similar efforts that can help improve housing opportunities and the overall the quality of life for Austin area residents.
Why do rental property owners and vendors need a PAC?
Elected officials affect the way you do business every day because local ordinances and state laws affecting nearly every facet of the rental housing industry are routinely discussed and debated at the local and state level. These laws involve your taxes, your contracts, your insurance protection, the roads you travel, the regulatory fees you pay and other related issues. In order to have a say in these issues, you have to be involved and your association must have the ability to make contributions to candidates who will listen to our viewpoint and understand the economics of rental housing.
Who decides where the Apartment PAC Austin money goes?
Apartment PAC Austin operates separately from the AAA Board of Directors and any other AAA committee. The Apartment PAC Austin is governed by a Board of Trustees consisting of the current AAA President, a PAC Chair appointed by the current President, AAA Past-Presidents in good standing, the Chair of the Products and Services Council, and AAA's current President-Elect.
It is the task of the Trustees to monitor, analyze, and review potential candidates, bond elections and related elections to determine their favorability towards the rental housing industry and potential benefits to the members of the AAA. Factors considered include a candidate's position on rental housing issues, existing support among members, and the candidate's ability to win. The Trustees are also tasked with urging AAA members to contribute to the PAC; to recommend ways of raising PAC funds and show support for and encourage participation in the Association-sponsored PAC fundraisers; to encourage all members to actively participate in the Texas Apartment Association PAC and the National Apartment Association PAC.
Apartment PAC Austin is registered with the Texas Ethic Commission and follows their strict document filing and reporting rules as well as all rules established by local government entities. Apartment PAC Austin represents our pro-housing interests at the state, county and local level, but is prohibited by law from donating to federal election campaigns.
Why should I contribute to the Apartment PAC Austin if I already make contributions to candidates of my choosing?
Apartment PAC Austin is able to pool the resources of the rental housing industry to have a greater impact than a single individual. Individual contributions are important, and AAA members are encouraged to continue making individual contributions, but the combined dollars of the PAC can have greater impact on more races. Plus, industry resources that are pooled can be directed to statewide candidates to maximize the prospects of having pro-rental housing candidates at all levels.
Please continue contributing to candidates of your choosing, but also please remember to contribute to Apartment PAC Austin because it gives industry members the opportunity to have an impact on the election of wide number of candidates who will shape the legislation that affects the multifamily rental housing industry.
If I contribute to the Apartment PAC Austin can I have a say in where the dollars go?
All contributors can make recommendations to the Board of Trustees on which candidates the contributor supports or opposes. Input from members is one of the criteria used to make decisions to support or oppose.
Are there limits on how much I can contribute?
There are no limits to how much an individual can contribute to the PAC. The only limitation is that corporate funds cannot be used as contributions to candidates for the Legislature and statewide offices in Texas. It is against the law for a political action committee to contribute corporate contributions to candidate.
Apartment PAC Austin must keep a record of the amount of each contribution received and the value and nature of any in-kind contribution, as well as the name and address of the individual or political committee making the contribution, and the date of the contribution.
Apartment PAC Austin investors that make a contribution of $99 or more will receive an invitation to the Apartment PAC Austin Investors Reception.
Why can't Apartment PAC Austin use my dues money?
Under federal law, the use of member dues to help elect candidates to federal office is strictly prohibited. Those who contribute, contribute voluntarily. Additionally, Apartment PAC Austin can only accept personal contributions and dues are often paid with corporate funds.
Can Apartment PAC Austin accept corporate checks?
No. It is against federal law for a political action committee to contribute corporate contributions to candidates. Corporate contributions can be given to the AAA's Better Government Fund (BGF).
The BGF is your industry's "war chest" and is is used to support the legal, lobbying and media firepower needed to fight anti-business/anti-rental housing initiatives that often surface when apartment construction or related land-use changes are debated in the public forum.
What if I am philosophically opposed to political action committees?
The legislative process is not like a going to Las Vegas where if you don't gamble you don't risk losing. If you sit out of the political process, you are guaranteed to lose. The legislative process is a full contact activity, and the ideas and perspectives of those who compete in the process are reflected in the laws that are enacted.
Operations cutbacks are an inevitable when owners are faced with the ever increasing costs of municipal fees, utility rates, onerous taxes and increasing regulations and inspections. Our PAC helps fight these increases. Through Apartment PAC Austin campaign contributions we broaden our reach and relationships with elected officials, and increase the opportunities to communicate our ideas and perspectives on the many issues that affect our industry debated and discuss in the political arena.
But I do not want my money to go to support a Democrat/Republican…
Apartment PAC Austin is nonpartisan in who it supports so long as they share our pro-housing point of view. The record, ideas, perspective and quality of each candidate determine who gets Apartment PAC Austin support and not party.
How can I learn more about Apartment PAC Austin?
Please call the Apartment PAC Austin Manager staff at (512) 323-0990 or email paul@austinaptassoc.com.
Have donation questions? Contact Emily Blair, CAE at emily@austinaptassoc.com or 512-323-0990.
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The 7th edition of Bucharest International Experimental Film Festival BIEFF, which will take place between March 28th and April 2nd, 2017 at the Cinema of the Peasant Museum and Cinema Elvire Popesco, invites to an exercise in empathy.
Most of BIEFF 2017's films confront us with the personal histories hidden beneath the often clickbait and sensationalist news we are assaulted by on a daily basis, news which create a general atmosphere of anxiety and rejection. Raising debate around the notion of "border" – physical versus psychological, geographical versus cultural and socio-political, stylistic versus conceptual – BIEFF 2017's selection proposes a denial of barriers – those between individuals, but also those of the cinematic language. The viewers are invited thus to internalize the tragedy of their fellow men and to see the world through the Other's eyes.
The selection, curated by Adina Pintilie in collaboration with Dan Angelescu, will present the Romanian premiere of some of the boldest short films of the past few years in their search for new forms of cinematic expression, with a special attention to works by significant contemporary visual artists, usually exhibited in museums and art galleries, rarely in cinemas.
Our recommendations from this year's programme below.
Also on our watch list: Over by Jörn Threlfall and 9 Days – From My Window in Aleppo by Floor van der Meulen, Thomas Vroege and Issa Touma.
Unique in Romania, BIEFF's educational partnerships with some of the major European film festivals and cultural institutions return this year.
In partnership with Arsenal – Institute for Film and Video Art Berlin and with the support of the Goethe-Institute, BIEFF will feature the most challenging works from the avantgarde section of the prestigious Berlin International Film Festival: Berlinale Forum Expanded.
BIEFF 2017 takes further the educational partnership with the International Film Festival Rotterdam, which shares an impressive sample of political activism in visual art.
One of our personal favorites, the dance cinema program, in partnership with Cinedans – Dance on Screen Festival Amsterdam.
BIEFF's long-term partnership with Cannes' Quinzaine des Réalisateurs brings again, with the support of the French Institute Bucharest, the Romanian premiere of one of the masters of the international avantgarde cinema.
The selection includes Timecode, by Juanjo Giménez (Palme d'Or for Short Film – Cannes Film Festival and Oscar nominee for Best Short Film).
Info, images and videos courtesy of BIEFF unless otherwise noted.
More info about the festival on their website, on Facebook, Instagram, YouTube. Keep up-to-date on their Facebook event.


Architecture is the single most resource-intensive industry known to man. In the construction of buildings and spaces, as well as in the configuration of lifestyles by said constructions, architecture is responsible for more than 50% of all energy and resource consumption in the modern world. Accordingly, architecture has incredible potential as a catalyst for bringing about a sustainable future.
Futureperfect presents a range of architects and commentators who see the role of architecture in sustainable living as an opportunity to deliver what the essential purpose of architecture has always been: to enable living well, privately and publicly.


The Screenwriters World Conference schedule is designed to help you hone your writing and pitching skills, and to put those skills into action in networking opportunities and events that directly connect you with the people who can help move your writing career forward. As Virgil said, "Fortune favors the bold"—so come to the conference ready to make your screenwriting dreams come true!
Jen Grisanti, Story/Career Consultant and Writing Instructor, Jen Grisanti Consultancy Inc.


Self Catering Ski Apartments are available for stays of 4 to 7 nights in the Winter.
Sleeps 4 in comfort, 4 nights 480€, 7 nights 840€.
This price is only available directly. Please click here to contact us.
Our apartments sleep 2-4 persons. each is around 40m² (approx 400 sq feet) and fully equipped for your holiday.
There is a separate bedroom so that if there are 4 persons everyone has some privacy.
The apartments allow enough space to relax and enjoy your holiday in Oz.
Our big, bright apartments all sleep at least 4 persons, some in two bedrooms, on full-size beds. These can be singles or doubles; its possible to sleep up to 6 persons, by arrangement.
Apartments either have a big shower or a bath and shower. There is plenty of hot water at all times.
All the apartments come supplied with bed linen and fluffy towels. A daily towel change is 1€ per item.
There is a washing machine and a dryer available so that you can do your washing for a small charge.
The kitchen has everything you need to cook meals; each has a fridge/freezer, an electric hob and some have a dishwasher and a full-size oven.
Pots, pans, kitchen knives, cutlery and glassware are all provided.
We provide Salt, Pepper, Olive Oil and Vegetable Oil along with washing up liquid, dishwasher tabs and other cleaning supplies.
End of stay cleaning is included in the price but we would appreciate if you left it tidy.
Each of the self catering apartments is fully equipped with everything you need for a self catering holiday.
However, you can still have an evening meal with us by telling us the day before.
We cater for most diets.
Breakfast is 9€, afternoon tea and cakes 9€ and the evening meal is 25€ for 3 courses.
Wine and beer are available when you take an evening meal with us.
You still get the benefit of being in the same building as us; we are always available to answer questions and help you have the best holiday you can.


text:
The Fight For America Has Only Just Begun
25 Mar, 2017 by	Susan Brown
For conservatives, the election of Donald Trump, while not ideal, represents the first chance in a long time to take the country back from the infestation of liberal ideology, and especially one world government globalism.
If the first two months of the Trump administration has taught us anything, it is that until liberalism is completely eradicated, it matters little who sits in the White House.Leftistshave succeeded ininfiltrating America like a locust plague, through our educationsystems, media, Hollywood,politics, churches, and the judiciary.
On one hand, we see activist judges at every turn opposing Trump's honest attempts to protect Americans. And on the other, we see unhinged liberalsand theiruncontrollable fits of rage, showing us what happens when a pro-America, pro-God, pro-U.S. Constitution president threatens to unseat their gods of globalism and secular humanism.
Liberals have gone bonkers but annoyingly, think they are normal. They see Russian boogeymenaround every corner with theoccasional Hitlerreference thrown in for good measure. Apparently, Ashley Judd believes Hitler is back, recently saying about Trump: "I didn't know devils could be resurrected, but I feel Hitler in these streets, a mustache traded for a toupee, Nazis renamed the Cabinet Electoral Conversion Therapy, the new gas chambers shaming the gay out of America…"
No editorializing necessary.
What's really crazyare the Nazi undertones coming from the left, as Anita Dittman, a born again Jewish woman who survived the Holocaust pointed out in an interview with WND.com. Dittman said, "When they say he [Trump] is another Hitler, they are crazy. If he was another Hitler, he'd be shooting people that riot and they wouldn't have the freedom to riot…"
Of course, many leftists are also Holocaust deniers, so sweet Ms. Dittman's personal experience with the real Hitler will have zero impact on those who deny the hell she, and millions like her experienced.
Leftism is the antithesis of the Biblical worldview and pretty much the opposite of how Americans across Main Street America think. Main Street Americans understand globalism is liberty's archenemy because a borderless America cannot protect traditions, religious beliefs, or American culture.
Main Street Americans watched former president Obama choose globalism over their safety when he ignored the rule of law concerning illegalimmigration. Now they notice the hypocrisy when the mainstream media, leftist judges and Democrats-at-large incessantly rail on Trump, yet ignored Obama's lawlessness.
It's one minute until midnight in America and we are standing at the crossroads between "Put Up" or "Shut Up."America as we know it is at risk, unless patriotic Americans join the fight betweenevil and good, wrong and right.
Taking back America won't be easy, but it is possibleif good people get involved by voting out globalists at the local, state and national levels and removing them from leadership positions in their churches. Parents should micromanage what their kids are taught in school and everyone can boycott news organizations that promote fake news. Think of all the money you could bank not going to movies starring Hollywood liberals who trash American values and all the time you'll save not watching television shows which seek to shove every abhorrent liberal idea down your throat.
Darkness calls and those who will must answer. As Welsh poet Dylan Thomas once wrote: "Do not go gentle into that good night…Rage, rage against the dying of the light."
©2017 Susan Stamper Brown Susan lives in Alaska and writes about culture, politics and current events. She is a regular contributor to Townhall, The Christian Post, Right Wing News and GOPUSA. Susan's nationally syndicated column is published in scores of newspapers and publications across the U.S. She writes about politics, culture and media and was selected as one of America's 50 Best Conservative writers for 2015 and 2016. Contact her by Facebook or at [email protected]
Democrats, Psychological Projection and Russia
More articles by Susan Brown


text:
Q: How to Get Array values in a Separate Variabales i am using ajax and get a response in json format but i have no idea how to separate each array format in a single variable
i am getting this
Response
final_string =     [{"stars":1,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":2,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":3,"q1":1,"q2":1,"q3":1,"q4":1,"q5":1,"q6":1,"q7":1,"q8":1,"q9":1,"q10":1,"q11":0},
    {"stars":4,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":5,"q1":17,"q2":17,"q3":17,"q4":17,"q5":17,"q6":17,"q7":17,"q8":17,"q9":17,"q10":17,"q11":17}  ]

    [ {"feedback":"Ambience"},
    {"feedback":"Efficiency of Service"},
    {"feedback":"Friendly and Attentive"},
    {"feedback":"Variety in Menu"},
    {"feedback":"Presentation of Food \u0026 Beverages"},
    {"feedback":"Quality and Taste of Beverages"},
    {"feedback":"Quality and Taste of Food"},
    {"feedback":"Anticipated your needs Prior to Asking"},
    {"feedback":"Value for Money"},
    {"feedback":"We made you feel like a Valued Guest"},
    {"feedback":"Would you Recommend us to Others"}  ]

i just want to make it like
variable1 =  [{"stars":1,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":2,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":3,"q1":1,"q2":1,"q3":1,"q4":1,"q5":1,"q6":1,"q7":1,"q8":1,"q9":1,"q10":1,"q11":0},
    {"stars":4,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":5,"q1":17,"q2":17,"q3":17,"q4":17,"q5":17,"q6":17,"q7":17,"q8":17,"q9":17,"q10":17,"q11":17}  ]

variable2 =  [ {"feedback":"Ambience"},
    {"feedback":"Efficiency of Service"},
    {"feedback":"Friendly and Attentive"},
    {"feedback":"Variety in Menu"},
    {"feedback":"Presentation of Food \u0026 Beverages"},
    {"feedback":"Quality and Taste of Beverages"},
    {"feedback":"Quality and Taste of Food"},
    {"feedback":"Anticipated your needs Prior to Asking"},
    {"feedback":"Value for Money"},
    {"feedback":"We made you feel like a Valued Guest"},
    {"feedback":"Would you Recommend us to Others"}  ]

Ajax
 $.ajax({
                type: "POST",
                url: "FeedBackGraph.aspx/getFeedBackdata",
                data: JSON.stringify(obj),
                contentType: "application/json; charset=utf-8",
                dataType: "json",
                success: function (Response) {
                    debugger;
                    console.log("Response",Response);
                    var d = Response.d; // Response
                    },
                error: function (result) {
                }
            });

i have no idea how to separate each in a variable using JavaScript/jquery?

A: Let's assume you fix your invalid JSON problem, then ES6 would allow for using a destructuring assignment:
const [variable1, variable2] = final_string

final_string = [
  [{
      "stars": 1,
      "q1": 0,
      "q2": 0,
      "q3": 0,
      "q4": 0,
      "q5": 0,
      "q6": 0,
      "q7": 0,
      "q8": 0,
      "q9": 0,
      "q10": 0,
      "q11": 0
    },
    {
      "stars": 2,
      "q1": 0,
      "q2": 0,
      "q3": 0,
      "q4": 0,
      "q5": 0,
      "q6": 0,
      "q7": 0,
      "q8": 0,
      "q9": 0,
      "q10": 0,
      "q11": 0
    },
    {
      "stars": 3,
      "q1": 1,
      "q2": 1,
      "q3": 1,
      "q4": 1,
      "q5": 1,
      "q6": 1,
      "q7": 1,
      "q8": 1,
      "q9": 1,
      "q10": 1,
      "q11": 0
    },
    {
      "stars": 4,
      "q1": 0,
      "q2": 0,
      "q3": 0,
      "q4": 0,
      "q5": 0,
      "q6": 0,
      "q7": 0,
      "q8": 0,
      "q9": 0,
      "q10": 0,
      "q11": 0
    },
    {
      "stars": 5,
      "q1": 17,
      "q2": 17,
      "q3": 17,
      "q4": 17,
      "q5": 17,
      "q6": 17,
      "q7": 17,
      "q8": 17,
      "q9": 17,
      "q10": 17,
      "q11": 17
    }
  ],

  [{
      "feedback": "Ambience"
    },
    {
      "feedback": "Efficiency of Service"
    },
    {
      "feedback": "Friendly and Attentive"
    },
    {
      "feedback": "Variety in Menu"
    },
    {
      "feedback": "Presentation of Food \u0026 Beverages"
    },
    {
      "feedback": "Quality and Taste of Beverages"
    },
    {
      "feedback": "Quality and Taste of Food"
    },
    {
      "feedback": "Anticipated your needs Prior to Asking"
    },
    {
      "feedback": "Value for Money"
    },
    {
      "feedback": "We made you feel like a Valued Guest"
    },
    {
      "feedback": "Would you Recommend us to Others"
    }
  ]
]

const [variable1, variable2] = final_string

console.log(variable1)
console.log(variable2)

A: probably you need this.
    var final_string =    [ [{"stars":1,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":2,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":3,"q1":1,"q2":1,"q3":1,"q4":1,"q5":1,"q6":1,"q7":1,"q8":1,"q9":1,"q10":1,"q11":0},
    {"stars":4,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":5,"q1":17,"q2":17,"q3":17,"q4":17,"q5":17,"q6":17,"q7":17,"q8":17,"q9":17,"q10":17,"q11":17}  ],

    [ {"feedback":"Ambience"},
    {"feedback":"Efficiency of Service"},
    {"feedback":"Friendly and Attentive"},
    {"feedback":"Variety in Menu"},
    {"feedback":"Presentation of Food \u0026 Beverages"},
    {"feedback":"Quality and Taste of Beverages"},
    {"feedback":"Quality and Taste of Food"},
    {"feedback":"Anticipated your needs Prior to Asking"},
    {"feedback":"Value for Money"},
    {"feedback":"We made you feel like a Valued Guest"},
    {"feedback":"Would you Recommend us to Others"}  ]]
var pp=Object.assign({}, final_string)
var z=Object.keys(pp)
var constVar="variable";
var newObj={};
for(var i=0;i<z.length;i++)
{
    var key=constVar+z[i];
    newObj[key]=pp[z[i]];
}

A: You are getting data correctly, but its not a valid json. The JSON should be like this,
[

  [put your star array here],
  [put your feedback array here]

]

so the final response code will be something like
[
  [{"stars":1,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":2,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":3,"q1":1,"q2":1,"q3":1,"q4":1,"q5":1,"q6":1,"q7":1,"q8":1,"q9":1,"q10":1,"q11":0},
    {"stars":4,"q1":0,"q2":0,"q3":0,"q4":0,"q5":0,"q6":0,"q7":0,"q8":0,"q9":0,"q10":0,"q11":0},
    {"stars":5,"q1":17,"q2":17,"q3":17,"q4":17,"q5":17,"q6":17, "q7":17,"q8":17,"q9":17, "q10":17,"q11":17}  ],

[ {"feedback":"Ambience"},
    {"feedback":"Efficiency of Service"},
    {"feedback":"Friendly and Attentive"},
    {"feedback":"Variety in Menu"},
    {"feedback":"Presentation of Food \u0026 Beverages"},
    {"feedback":"Quality and Taste of Beverages"},
    {"feedback":"Quality and Taste of Food"},
    {"feedback":"Anticipated your needs Prior to Asking"},
    {"feedback":"Value for Money"},
    {"feedback":"We made you feel like a Valued Guest"},
    {"feedback":"Would you Recommend us to Others"}  ]

]

You need to do the above in backend. Remove final_string = from response, you don't need that.
And in your success handler you can do something like this to get stars and feedback array.
var variable1 = Response[0];
var variable2 = Response[1];

A: you can use destruction of es6
const [variable1, variable2] = final_string

A: const data = final_string.match(/\[(\r\n|\r|\n|.)+?\]/g).map(s => JSON.parse(s))
const variable1 = data[0]
const variable2 = data[1]

This could be work, but not good.
const final_string_1 = "[[...],[...]]"
const final_string_2 = "[...], [...]"

This format maybe more good for parse.

redpajama_set_name: RedPajamaStackExchange


Add a drop of sophistication to your special occasion with a fun and interesting Wine Tasting in Manchester where you'll each get your hands on six glasses of wine!
Always reach for the same wine in the supermarket or at a restaurant? Want to branch out but not sure where to start? Worried you won't like what you've chosen? Now you can sit back and relax with Wine Tasting in Manchester where a range of wines are carefully selected for you to try from whites and reds to rosé and dessert wine, Yum! Head to Veeno the Italian Wine Café in Manchester for an enjoyable and authentic Wine Tasting session at Mermaid Quay, overlooking the beautiful bay. One of Veeno's friendly Baristas will teach you everything you've ever wanted to know about everyone's favourite tipple with an introduction to their winery and how their perfect plonk is made.
The barista will bring out each 70ml glass of wine one by one, sharing some fun facts with you and letting you know which flavour notes and aromas you should be looking out for. You'll each get a whopping six wines each including two reds, two white, a rosé and a dessert wine for those of you with a sweet tooth. To make a complete party package and to teach you even more, each glass of wine will be accompanied by some authentic Italian spuntini appetisers. These sharing nibbles will perfectly complement the drinks. You'll never struggle with which wine to order with your meal at a restaurant again after this! Whether you're choosing a birthday or hen party Wine Tasting in Manchester or just fancy doing a fun activity with friends, this one really spoils you! It even ends on a high with some seriously tempting tiramisu!
Want to the different between plonk and the good stuff or just fancy a evening out, sinking glasses of wine? Take a look through our listings for birthday and hen party Wine Tasting in Manchester now and find the perfect Wine Tasting workshop for your group.
Yes, the age restriction is 18+ in the UK, please bring your ID. Age restrictions for other European countries may vary, please check with the provider in advance.
Smart casual is the usual code of conduct. Please ask when you enquire if you can wear fancy dress.
Some venues can offer alternatives. Please check in advance with the provider.


text:
Microsoft blasts Sony's 'outdated' Home service
By Marc Chacksfield 2008-12-11T15:08:00.345Z Consoles
"It feels like 2005 tech in 2008," says Microsoft exec
PlayStation Home: outdated already?
The relevance of Sony's much-delayed PlayStation Home service has been put into question by Microsoft.
Discussing the service with gaming website Kotaku, Aaron Greenberg of Microsoft, spoke about Home and how it feels a tad outdated.
"What Home to me feels like is Second Life for hardcore gamers. It doesn't feel like it broadens the experience and invites people in," said Greenberg.
"When they unveiled it, it seemed innovative. I think what's happened is now here we are a couple of years later and we feel beyond that.
"It feels like 2005 tech in 2008. I'm not sure that's what people want."
Wrong to compete with Second Life
While remarks like this from Microsoft are to expected, considering the company is in direct rivalry with Sony for videogame console supremacy, the thoughts are echoed by that of EA founder Trip Hawkins who recently stated that: "I can't tell whether they're going more towards this mass market idea - the way I'm describing this 'omni-market' - or if they're being lured into essentially trying to compete with Warcraft or Second Life.
"My own personal opinion is: if Sony makes Home feel too much like a [World of] Warcraft environment, they're just never going to create the kind of audience size that you're going to see Nintendo and Microsoft create."
PlayStation Home went into Beta this week, so if you're a PS3 owner, log on and try it for yourself.
See more Consoles news


Who knew fish were such expert flippers? One species at least can flip a bank of genes on and off to cope with warmer water within just two generations.
The new finding raises hope that ocean ecosystems could deal with rising sea temperatures, and even lead to adaptations that help fish farmers.
Many fish species suffer extreme consequences when their water temperature is raised by just a couple of degrees.
Their circulatory system's ability to transport oxygen around the body can drop by half, meaning they cannot swim, grow or reproduce as effectively. This led to concerns that fish populations would shift their habitats or simply decline as the ocean warms this century.
Philip Munday from James Cook University in Townsville, Australia, and his colleagues showed in 2012 that one species of tropical fish affected by warmer waters – the spiny chromis damselfish – could completely adapt to 3 °C of warming over just two generations.
But how it happened remained a mystery until now.
To figure it out, Munday and his colleagues took wild fish and raised two new generations under tightly controlled conditions: some at the temperatures they naturally experience – averaging 23.2 °C to 28.5 °C – some at temperatures warmer than these averages by 1.5 °C or 3 °C.
They then measured their aerobic performance in the piscine equivalent of a treadmill – a cylindrical tank with a steady water current run through it. They also examined their full "transcriptome": all the RNA produced by each gene in the fishes' DNA, showing which genes were being used and which weren't.
Fifty-three key genes were switched on or off after two generations of acclimatisation. The fish were ramping up the use of genes involved in energy metabolism and some involved in immune and stress responses.
Munday says the results strongly suggest that epigenetic changes in fish are passed on and strengthened in each generation.
It's not evolution, because the experimental design ensured there was no selective breeding, but it's possible that this sort of phenotypic plasticity helps drive evolution, says Munday.
This adaptability is good news for fish and is likely to happen in many fish species, says Munday.
Munday says by figuring out the exact mechanisms behind the acclimatisation, those trade-offs can be understood and potentially even avoided by fish farmers.
"For example if you knew it was an energetic cost, you could supplement the feeding," he says.
John Pandolfi from the University of Queensland says the results may have implications beyond fish.


East Georgia Women's Center welcomes your questions, comments and concerns. To schedule and appointment or speak with a nurse please call us at (912) 871-4800. You can find many answers to your questions here on our website. You can also learn more about our office by visiting our Facebook, Twitter, and Blogger accounts.


text:
Dr. Wodarg: "I Think This Vaccination is Really the Pinnacle of the Crime"
Dr. Wolfgang Wodarg is a German physician, pulmonary specialist, and epidemiologist. He is also a former politician for the SPD (Socialist Party). He was an early and outspoken opponent of the draconian measures taken against the Wuhan Coronavirus, which has earned him the opprobrium of a number of people on the Left.
In the following video Dr. Wodarg (the white-haired gentleman with a goatee) discusses the latest COVID news, which concerns the establishment of what appear to be mass vaccination centers at airports and other large facilities.
Many thanks to Hellequin GB for the translation, and to Vlad Tepes and RAIR Foundation for the subtitling:
00:00 Our minister stated, from January,
00:03 when the vaccine is supposedly to be ready —
00:06 I believe it was ready a long time ago — but… when… he [the minister] said in January
00:12 they would have all information
00:15 which questions or criticizes the vaccine,
00:19 it would be deleted. They'd start a huge war to avoid
00:24 the carrying capacity… of the population…
00:28 …um… being somehow undermined
00:33 by critical information. So that's a real threat,
00:36 and we already see how bad it is with censorship.
00:40 But we reckon that we will really be silenced
00:45 …um… SOON. Today I published an article in "Rubicon" and "Multipolar".
00:52 And most likely the Article will show up on KenFm,
00:56 and maybe also in English. It's exactly about what they're trying to do now,
01:01 to set up large vaccination centers everywhere
01:04 That means the vaccine is not given to general practitioners
01:08 who would be able to advise their patients, like they did with the swine flu.
01:14 Back then with the swine flu the doctors said; "No, I will not give this vaccine to my patients."
01:19 In Germany there was hardly any vaccination, fortunately.
01:22 The doctors practically saved their patients from this bad vaccine.
01:27 They try to circumvent this now.
01:30 They are now trying to make big centers in Germany,
01:33 60 large centers. Huge cold storage facilities are being built.
01:38 Large cold stores are being built at the airports,
01:41 and the pretext for this is that this vaccine
01:44 has to be cooled very, very thoroughly, and you can't do that in a doctor's office,
01:48 and in this way there will be great centers,
01:51 similar to those PCR-test centers at the border,
01:56 at airports and such. These are big companies, big laboratories.
02:00 And exactly such companies will then also carry out the vaccination with some auxiliary workers;
02:05 that is the plan. And that the doctors put up with this,
02:09 that the medical chambers are allowing this,
02:12 the way this vaccine is then suddenly administered, by people who have no experience,
02:16 with no previous personal contacts with the patients —
02:19 How they can just watch that, when otherwise they always say,
02:22 the Robert Koch Institute, "You have to give informed consent for vaccination."
02:27 You have to be well-informed, you have to ensure that there are no side effects,
02:32 because patients react differently to a vaccination.
02:35 A medical history must be taken,
02:38 and all that's now through this planned mass action.
02:42 It's like factory farming: people are driven into large halls, large institutions,
02:47 and are [conveyor belt] vaccinated. Only with factory farming is it like this;
02:51 those animals are there for the slaughter.
02:55 That means they only live a few weeks or months; there ARE no late effects.
03:00 They end up on a plate. And that's different from people
03:03 who want to live for many, many years after the vaccination.
03:06 And all these late effects that can occur there,
03:09 such as autoimmune disease, cancer,
03:12 everything that disturbs the immune system, can cause serious chronic illnesses.
03:18 And when this vaccination is carried out en masse,
03:22 and only one per million in the population has side effects,
03:26 and then there will be millions of people who become seriously ill,
03:30 many more than have suffered from any epidemic so far.
03:34 I wrote this down in detail and,
03:38 I think this vaccination is really the pinnacle of the crime.
03:43 They can't do that, no way.
This entry was posted in Civil Liberties, Crazy Socialism, Culture Wars, Europe, Insanity, Legal action, News, Plagues, Politics by Baron Bodissey. Bookmark the permalink.
19 thoughts on "Dr. Wodarg: "I Think This Vaccination is Really the Pinnacle of the Crime""
Mark H on November 15, 2020 at 2:00 pm said:
What's his evidence? I'll happily have the vaccine when available (unlike some here), but voluntarily and from my GP.
Jeff on December 8, 2020 at 11:31 pm said:
Your GP will do what ever it takes to keep his license from being yanked. Even if it goes against what he believes is scientifically sound.
James on December 10, 2020 at 3:07 pm said:
Mark H you seriously are [grievously in error] if you're not willing to consider any potential health risks associated to the cv19 vaccine.
Andre on February 21, 2021 at 2:19 pm said:
It is not a vaccine, which would guarantee to give you immunity and non-transmission. It is not a vaccine when there is nothing of the original substance in it, like all vaccines do. It is a medical device to suppress the symptoms when you get infected, so more like a medication, but then done under the heading of an experiment. They by-pass the Nuermberg COde with it too as all experiments must meet the 10 points agreed on after WWII.
Anonymous on March 7, 2021 at 1:33 am said:
All of the injections available (Moderna and Pfizer are not real vaccines) have only been approved under "emergency use" which is why they determined it's a pandemic. Their test period is said to end in 2023 which means anyone injected is the equivalent of a lab rat.
Mary Thranow on March 20, 2021 at 7:54 pm said:
Mark H, we are three months into 2021, March 21st, 2021. If you are not yet well informed please allow me to share a video which in my opinion and the opinion of hundreds maybe thousands. This is the video; Human Genome 8 and mRNA vaccine; https://www.brighteon.com/59e20408-8324-4a1f-9de5-9c4f9d205394 . It is strongly recommended not to take the vaccine.
Blaž Kavčič on November 22, 2020 at 5:00 am said:
It is To Be or Not To Be moment fot the humanity. We need to wake up more people day by day. Stand up and fight!
Tom on December 4, 2020 at 5:24 am said:
'What's his evidence?'
He exposed the fake swine flu which used PCR and this is the same but far bigger. In November UK Liverpool had the army testing using the lateral flow, not PCR, this was on the back of a FOI request as to how many people had died of covid between Feb 2020 and Nov 2020 – it was 5 people. The lateral flow test showed pretty much no one had covid.
Anonymous on December 11, 2020 at 1:49 pm said:
Please send pdfs of recent papers!
Victor S. Alpher, Ph.D.
tim on December 14, 2020 at 12:41 pm said:
If this vaccine is so safe then why has the UK Government followed the US Government in making it impossible to sue the vaccine companies if it causes death or serious injury? The US Government has paid out $6,500,000.000 in compensation since this was enacted. Ever tried to sue a Government? Few succeed!
Ru4liminx on December 19, 2020 at 7:22 am said:
Reagan signed the Vaccines Act because manufacturer's were threatening to stop making the vaccines because of the lawsuits. The taxpayer now pays for these lawsuits.
Conner on December 31, 2020 at 12:48 pm said:
The death rate from covid for people UNDER 65 years old is 99.99 percent! Why would I take a vaccine that could kill me when the death rate is so low! Those who want to take it, fine, but we should NOT BE PRESSURED TO TAKE AN UNSAFE AND UNTESTED VACCINE! We are like guinea pigs and some have died from taking this vaccine. Please look up Tiffany Dover a nurse who collapsed within minutes of taking this. They tried to cover this up but people found her face book and found her death records online. She was 30 years old and a nurse in Tennessee.
Anonymous on January 3, 2021 at 10:44 am said:
You must mean the survival rate, as if 99.99% would die it would be pretty horrible. So I am assuming you meant the death rate is 0.01% for under 65yo.
it is me on January 3, 2021 at 10:46 am said:
Survival rate under 65yo 99.99% and death rate 0.01 you must have meant.
Janice King on January 12, 2021 at 8:24 am said:
I did look up Tiffany Dover.. saus she fainted when she got the vaccination and is now doing fine
Anonymous 2 on February 6, 2021 at 8:48 pm said:
No, she is dead.
Karli Cassidy on March 8, 2021 at 12:29 pm said:
This corona virus can be easily treated with ivermectin (check Dr Pierre Kory) and quercetin (search engine with covid 19). Doctors have lost their jobs using effective medicines while the Globalists push for everyone to roll up their sleeve and allow an anonymous person to inject an unknown substance into your body.
I did not understand this from a genuine Doctor's view point and am glad that good men like Dr Wolfgang Wodarg exist to sound the alarm and raise questions, as well as our awareness
susan smith on March 11, 2021 at 10:33 am said:
That is one of the pillars they have built this whole pandemic on, that there is no treatment, you will end up on a ventilator and might die etc.
Not only have doctors used Ivermectin there is also Hydroxychloroquine.
Hospitals in China have used Intravenous Vitamin C and also TCM herbal protocols to good effect.
Here you are taken down social media if you mention alternative treatments. So it has never been about keeping people safe from a virus, otherwise they would have told everyone to have a healthy diet and take Vitamins C, D and zinc as a prophylactic.
It has always been about a vaccine saving humanity. Never mind you have an immune system.
prepare on May 5, 2021 at 1:38 pm said:
Load up your guns!!!!
Prepare to kill without mercy if they come for you.


text:
This inclusive list of opera companies in Europe contains European opera companies with entries in Wikipedia plus other companies based there. Within the sections for each country, the arrangement is alphabetical by location. For a list of the most important opera companies in the world, see Lists of opera companies. For more inclusive lists of opera companies from other regions, see:
 List of Latin American and South American opera companies
 List of North American opera companies,
 List of opera companies in Africa and the Middle East
 List of opera companies in Asia, Australia, and Oceania

Albania

Armenia

Austria

Azerbaijan

Belarus

Belgium

Bosnia and Herzegovina

Bulgaria

Croatia

Cyprus

Czech Republic

Denmark

Estonia

European Union

Finland

France

Georgia

Germany

Greece

Hungary

Iceland

Republic of Ireland

Italy

Latvia

Liechtenstein

Lithuania

Luxembourg

Malta

Monaco

The Netherlands

North Macedonia

Norway

Poland

Portugal

Romania

Russia

Serbia

Slovakia

Slovenia

Spain

Sweden

Switzerland

Turkey

United Kingdom

England

Northern Ireland

Scotland

Wales

Ukraine

References

Companies

redpajama_set_name: RedPajamaWikipedia


Mike Kalmbach grew up in a forest near Lake Michigan. Spending his summers chasing wizards and fighting battles with evil ogres, Mike has always had a creative mind. He'll often share stories from his past, and some of them are even true.


text:
13/01/2015 Tue 09:54 in Global by Akankasha Dewan
Your employees' New Year's resolutions
Want to increase employee engagement and loyalty levels in your company? Help your staff manage their savings and expenditures, because that's what most of your staff want in 2015.
Saving more pay was the top New Year's resolution at work for 42% of employees surveyed by CareerBuilder.
Canvassing responses from 3,056 American workers across various industries, 34% also said they aim to be less stressed this year, followed by 26% who said they want to get a promotion or raise in 2015 (26%).
Eating healthier at work was also identified as a top resolution (25%), while 22% said they wished to learn something new (more courses, training etc.) in the next 12 months.
Mark Zuckerberg's 2015 New Year resolution is…
Staff want their bosses to get fired in the New Year
Unfortunately for majority of bosses, finding a new job was also among the top resolutions among employees this year.
While 30% of workers reported that they regularly search for job opportunities even though they're currently employed, 16% stated they are determined to land a new position in the New Year. Among workers aged 18 to 34, 23% also stated they expect to have a new job by year-end.
"While the majority of workers say they're satisfied in their jobs, an expanding economy and widespread employment gains are motivating them to consider bigger, better opportunities," Rosemary Haefner, vice president of human resources at CareerBuilder, said.
"Skilled workers will have more leverage this year as the competition for labor becomes more intense across a variety of job functions. Employers expect to increase salaries on initial job offers in 2015 and may be more willing to negotiate other perks such as flexible work arrangements."
RELATED READ: Happy New Year, I'm quitting
The survey also delved onto the type of additional perks bosses could provide to make their companies more satisfying for employees.
Half-day Fridays ranked as the top desired perk (40%), followed by an on-site fitness centre (22%), and daily catered lunches (21%).
Almost two out of 10 (16%) of respondents also stated they would like massages at work, while 15% voted for being able to wear jeans in the office.
The most and least happy industries in Singapore
Get prepared for pay for performance
06/21/2019 Fri 10:27 AM in China by Robert Blain
Skytrax評選2019全球最佳航空公司
亞洲及中東航空公司稱霸前10名,國泰航空排名上升..
04/10/2013 Wed 18:30 PM in Singapore by Staff Writer
CCL joins Human Resources Excellence Awards
The Center for Creative Leadership has joined the Human Resources Excellence Awards Singapore as the official sponsor for the Exce..
01/16/2020 Thu 11:50 AM in All markets by Priya Sunil
"How much do you make?" goes mainstream, and 9 more talent trends to watch in 2020
What used to be a taboo question is now being considered appropriate to ask by nearly 24% of respondents. Here are all the trends ..
HSBC: Why some Hongkongers are worried about their financial future
Hong Kong working women's tendency to succumb to parenthood, the highest in Asia. ..
01/20/2017 Fri 12:24 PM in All markets by Laura Fransen
MPF offset changes to cost employers up to HK$147m in first year
The government will subsidise severance and long service payments, in an arrangement designed to "mitigate the impact on enterpris..


1. Go to Preview Payroll and select the month for which you want to download the pay slips.
3. If you want to download pay slips of only selected employees, check the boxes before their names or check the box in the header to select all employees whose names are displayed on first page. Click on down arrow next to Download button and click on Single PDF (if you want to download pay slips of all employees in one single PDF file) or click on Multiple PDF (if you want a separate PDF file for pay slip of each employee. All PDF files will be downloaded in a zip format). Click on Next to go to next page and repeat the same process to download pay slips of employees whose names appear on that page.


text:
\section{Unitary Time Evolution for Non-Hermitian Hamiltonians}
\label{S1}

If for a time-independent Hamiltonian $H$ one constructs a time evolution operator of the form $U(t)=e^{-iHt}$, then if $H$ is Hermitian, the adjoint operator $U^{\dagger}(t)$ is given by $U^{\dagger}(t)=e^{iHt}$ and the unitarity of $U(t)$ immediately follows. Moreover, if one introduces right-eigenvectors of $H$ that obey
\begin{equation}
i\frac{d}{dt} |R_i(t)\rangle=H|R_i(t)\rangle,
\label{E1}
\end{equation}
then for Hermitian Hamiltonians the Dirac norm $\langle R_i(t)|R_i(t)\rangle$ is immediately preserved in time. However, if the Hamiltonian is not Hermitian, conjugation of (\ref{E1}) leads to
\begin{equation}
-i\frac{d}{dt} \langle R_i(t)|=\langle R_i(t)|H^{\dagger},
\label{E2}
\end{equation}
with $U^{\dagger}(t)$ now being given by $U^{\dagger}(t)=e^{iH^{\dagger}t}$, and with the Dirac norm then not being time independent. Despite this, one cannot conclude that the time evolution associated with a non-Hermitian Hamiltonian is not unitary. Rather, all one can conclude is that the standard derivation of unitarity for Hermitian Hamiltonians and the appropriateness of the Dirac norm do not apply when the Hamiltonian is not Hermitian.  While the above analysis shows that Hermiticity implies unitarity, one cannot conclude that lack of Hermiticity implies lack of unitarity. And indeed, a whole class of non-Hermitian Hamiltonians has been identified in which time evolution is unitary, namely those in which the Hamiltonian possesses a $\cal{P}\cal{T}$ symmetry and has a set of energy eigenvalues that are all real (see the review of  \cite{R1} and references therein). The purpose of this paper is to identify all possible classes of Hamiltonians for which time evolution is unitary, with Hermitian Hamiltonians being just one of the possible classes.

The key to finding the general rule is to recognize that if $|R_i(t)\rangle$ is an eigenstate of $H$ with some general complex energy $E_i=E^R_i+iE^I_i$, then on introducing some general time-independent operator $V$, the $V$-dependent inner product $\langle R_j(t)|V|R_i(t)\rangle$ will be given by
\begin{equation}
\langle R_j(t)|V|R_i(t)\rangle = e^{-i(E^R_i-E^R_j)t+(E^I_i+E^I_j)t}\langle R_j(t=0)|V|R_i(t=0)\rangle.
\label{E3}
\end{equation}
This inner product will be time independent for energies that obey the two conditions
\begin{equation}
E^R_i-E^R_j=0, \qquad E^I_i+E^I_j=0,
\label{E4}
\end{equation}
and will be time independent for states with energies that do not obey these conditions if an operator $V$ can be found so that for all of those states the matrix element $\langle R_j(t=0)|V|R_i(t=0)\rangle$ vanishes. The eigenstates of Hermitian Hamiltonians immediately obey these conditions with $E^I_i=0$, $E^I_j=0$ and $V=I$. However in the general case one needs a non-trivial $V$, and a thus non-Dirac norm.

To find the general conditions under which the needed $V$ will in fact exist, we note that from (\ref{E1}) and (\ref{E2}) we can evaluate the time derivative of $\langle R_j(t)|V|R_i(t)\rangle$ to obtain
\begin{equation}
i\frac{d}{dt} \langle R_j(t)|V|R_i(t)\rangle=\langle R_j(t)|(VH-H^{\dagger}V)|R_i(t)\rangle.
\label{E5}
\end{equation}
Thus if, just as is needed to establish unitarity for Hermitian Hamiltonians, we require that the set of states $|R_i(t)\rangle$ be complete for the general $H$, we see that all  matrix elements $\langle R_j(t)|V|R_i(t)\rangle$ will be time independent if $V$ obeys the relation
\begin{equation}
VHV^{-1}=H^{\dagger}
\label{E6}
\end{equation}
as an operator identity. The needed $V$ is thus the one that effects the transformation from $H$ to its Hermitian adjoint $H^{\dagger}$. Conversely, if a Hamiltonian has the property that $H$ and $H^{\dagger}$ can be related by an operator $V$ as in (\ref{E6}), it follows from (\ref{E5}) that all matrix elements $\langle R_j(t)|V|R_i(t)\rangle$ constructed with this $V$ are time independent. The condition that there exist an operator $V$ that effects $VHV^{-1}=H^{\dagger}$ is thus a necessary and sufficient condition for unitary time evolution. We note that as defined in (\ref{E6}) the operator $V$ depends on the Hamiltonian. Thus unlike the standard Dirac norm $\langle R_j(t)|R_i(t)\rangle$, the $\langle R_j(t)|V|R_i(t)\rangle$ norm cannot be preassigned, with it being dynamically determined by the Hamiltonian itself.

When there does exist an operator  $V$ for which (\ref{E6}) is satisfied, we can rewrite (\ref{E2}) as
\begin{equation}
-i\frac{d}{dt} \langle R_i(t)|V=\langle R_i(t)|VH.
\label{E7}
\end{equation}
In such a situation the state $\langle L_i(t)|=\langle R_i(t)|V$ is a left-eigenvector of $H$ as it obeys
\begin{equation}
-i\frac{d}{dt} \langle L_i(t)|=\langle L_i(t)|H,
\label{E8}
\end{equation}
with unitary time evolution thus being associated with Hamiltonians that have complete sets of both left- and right-eigenvectors. In terms of the left-eigenvectors the $\langle R_j(t)|V|R_i(t)\rangle$ inner product can be written as $\langle L_j(t)|R_i(t)\rangle$, with the inner product thus being the overlap of the left- and right-eigenvectors of the Hamiltonian, an overlap that is manifestly time independent because of (\ref{E1}) and (\ref{E8}). The general rule then is to define the inner product as the overlap of the left- and right-eigenvectors, and so we need to ascertain the conditions on $H$ for which a $V$ operator that satisfies (\ref{E6}) (and thus the left-eigenvectors that it then generates) will necessarily  exist.

\section{$\cal{P}\cal{T}$ symmetry and the $VHV^{-1}=H^{\dagger}$ condition}
\label{S2}

When $H$ and $H^{\dagger}$ are related according to the similarity transform $VHV^{-1}=H^{\dagger}$, the determinant condition for the eigenvalues of $H$ obeys ${\rm det}(H-\lambda I)={\rm det}(V^{-1}H^{\dagger}V-\lambda I)={\rm det}(H^{\dagger}-\lambda I)={\rm det}((H^{*})^{\rm TR}-\lambda I)={\rm det}(H^{*}-\lambda I)=0$, where ${\rm TR}$ denotes transpose. Consequently, $H$ and $H^{*}$ possess the same set of eigenvalues, with the secular equation ${\rm det}(H-\lambda I)=0$ thus being real. With the energies of a real secular equation either being real or appearing in complex conjugate pairs, one can immediately satisfy (\ref{E4}) non-trivially, just as required. Conversely, if the secular equation that determines the energy eigenvalues is real, then $H$ and $H^{\dagger}$ will possess the same set of eigenvalues and thus be related by an isospectral similarity transform. Reality of the secular equation is thus both necessary and sufficient for the existence of a $V$ operator that obeys (\ref{E6}). Reality of the secular equation is thus both necessary and sufficient for unitary time evolution.

The reality requirement on a secular equation is a condition that is encountered in $\cal{P}\cal{T}$-symmetric theories ($\cal{P}$ and $\cal{T}$ denote parity and time reversal). Specifically, it was noted in \cite{R2} that if a Hamiltonian is $\cal{P}\cal{T}$ symmetric, the secular equation would be real. Moreover, it is not specifically $\cal{P}\cal{T}$ invariance itself that is required for the proof. All one needs is that $H$ be invariant under the action of the product of a discrete linear operator and a discrete anti-linear operator. For a time-independent $H$, time reversal reduces to complex conjugation $K$ times a matrix that acts in the space of the eigenvectors of $H$, with $\cal{P}\cal{T}$ then acting as $AK$ where $A$ is a matrix. The essence of the proof of the reality of the secular equation is to note that if a Hamiltonian commutes with $AK$, the determinant condition then obeys ${\rm det}(H-\lambda I)={\rm det}(AKHKA^{-1}-\lambda I)={\rm det}(KHK-\lambda I)={\rm det}(H^{*}-\lambda I)=0$, with reality of the secular equation immediately following. Discussion of the reality of secular equations dates back to Wigner \cite{R3}, who considered invariance of a Hamiltonian under time reversal alone. Modern interest in the reality of secular equations was triggered by the surprising discovery that the non-Hermitian Hamiltonian $H=p^2/2m+ix^3$ had a completely real eigenspectrum \cite{R4,R5}, an outcome that was traced in \cite{R5} to the fact that while not time reversal invariant, $H$ was nonetheless invariant under the $\cal{P}\cal{T}$ product as $\cal{T}$ transforms $i$ into $-i$ while $\cal{P}$ transforms $x$ into $-x$. The utility of $\cal{P}\cal{T}$ invariance stems from the fact that complex potentials that are not $\cal{T}$ invariant might still be invariant with respect to a $\cal{P}\cal{T}$ product where $\cal{P}$ is an appropriate linear operator, and thus yield a real secular equation.

In \cite{R2} it was shown that if a Hamiltonian is $\cal{P}\cal{T}$ symmetric then its secular equation is real. More recently, the converse has been proven \cite{R6}, namely that if a Hamiltonian has a secular equation that is real, then one can always find appropriate $\cal{P}$ and $\cal{T}$ operators under which the Hamiltonian is $\cal{P}\cal{T}$ symmetric. Consequently, $\cal{P}\cal{T}$ symmetry of a Hamiltonian is both necessary and sufficient for reality of its secular equation, and thus $\cal{P}\cal{T}$ symmetry of a Hamiltonian is both necessary and sufficient for unitary time evolution. The power of this result is that one can determine whether or not a Hamiltonian can generate unitary time evolution entirely by examining its symmetry structure under the action of the product of a discrete linear operator and a discrete anti-linear operator.

Within the family of Hamiltonians that have real secular equations there are three cases of interest: (i) the energies are all real and the energy eigenvectors are complete, (ii) the energy eigenvectors are complete but the energies include one or more complex conjugate pairs, and (iii) the energies are real but the energy eigenvectors do not form a complete set and the Hamiltonian is in non-diagonalizable, Jordan block form. A possible fourth case, namely that the energy eigenvectors are not complete and the energies include one or more complex conjugate pairs, is not allowed since the energies of a Jordan-block matrix are all equal (they all share a single common eigenvector) and could thus not contain any complex conjugate pairs \cite{R6}. Moreover, in \cite{R6} criteria were also provided for determining to which of these three cases of interest any given $\cal{P}\cal{T}$-symmetric Hamiltonian belongs. Specifically, in the general analysis of $\cal{P}\cal{T}$-symmetric Hamiltonians it has been found to be very convenient \cite{R1} to introduce a linear operator, the $\cal{C}$ operator, that obeys the two conditions: $[{\cal{C}},H]=0$, ${\cal{C}}^2=1$. In \cite{R6} it was shown that if every $\cal{C}$ that non-trivially obeys these two conditions commutes with $\cal{P}\cal{T}$ then we are in case (i), that if there exists at least one $\cal{C}$ that does not commute with $\cal{P}\cal{T}$ then we are in case (ii), and if there is no $\cal{C}$ that obeys these two conditions at all then we are in case (iii). Thus as well as ascertain the unitarity structure of a Hamiltonian via a symmetry condition (i.e. whether or not $H$ commutes with $\cal{P}\cal{T}$), we can even determine which realization of the energy spectrum we are in by examining the structure of a commutator (viz.  that of $\cal{C}$ with $\cal{P}\cal{T}$). We now examine how the unitarity of time evolution works in each of these three cases in detail.

\section{Unitarity when energies are all real and complete}
\label{S3}

For the case of a $\cal{P}\cal{T}$-invariant Hamiltonian whose energy spectrum is both real and complete, it can be shown \cite{R1,R7,R6} that  the operator $V$ can always be written as $e^{-Q}$ where $Q$ is a Hermitian operator, and that the operator $e^{-Q}$ itself can always be written as $e^{-Q}=P\cal{C}$ where $\cal{C}$ is the $\cal{C}$ operator discussed above. The utility of the $Q$ operator is that its Hermiticity ensures that the operator $\tilde{H}=e^{-Q/2}He^{Q/2}$ is Hermitian \cite{R1,R8}. If for $\tilde{H}$ we introduce a standard set of right-eigenstates $|\tilde{n}^i\rangle$, the right-eigenstates of $H$ are thus related to those of $\tilde{H}$ by the mapping $|n_i\rangle=e^{Q/2}|\tilde{n}_i\rangle$. Since $Q$ is Hermitian and $e^{-Q/2}$ is a similarity transform but not a unitary one, the states  $\langle n_i|=\langle \tilde{n}_i|e^{Q/2}$ are not left-eigenstates of $H$. Rather, it is the states $\langle n_i|e^{-Q}$ that are the left-eigenstates. Moreover, since the eigenstates of the Hermitian $\tilde{H}$ obey the standard time-independent Dirac orthonormality condition $\langle \tilde{n}^i|\tilde{n}^j\rangle=\delta_{i,j}$, then by the mapping the eigenstates of $H$ obey the time-independent condition $\langle n^i|e^{-Q}|n^j\rangle=\delta_{i,j}$. With $V=e^{-Q}$, we recognize the inner product  $\langle n^i|e^{-Q}|n^j\rangle$ as being none other than the time-independent $V$-operator norm introduced above \cite{R9}.

The essence of the above analysis is the realization that when a Hamiltonian $H$ has an energy spectrum that is both real and complete, the Hamiltonian is either already Hermitian or can be brought to a Hermitian form $\tilde{H}$ by a similarity transformation. However, if a Hamiltonian $H$ is not Hermitian the needed similarity transformation will not be unitary and the basis states of $H$ will not be orthonormal with respect to the Dirac inner product. Rather, they will form a skew basis, with it being the similarity transform that puts the basis into an orthonormal form. $\cal{P}\cal{T}$-symmetric Hamiltonians that are not Hermitian but nonetheless have a real and complete eigenspectrum are thus Hermitian in disguise. Consequently, they are unitary in disguise too, with it being the $V$-operator norm that is the appropriate norm for the Hamiltonian.

It is instructive to recast the above discussion in the language of the $S$-matrix. For the above $|\tilde{n}_i\rangle$ basis first, we can define complete sets of in and out states that obey the standard closure relations $\sum_i|\tilde{n}^i_{in}\rangle\langle \tilde{n}_{in}^i|=I$ and  $\sum_i|\tilde{n}^i_{out}\rangle\langle \tilde{n}_{out}^i|=I$. Given these relations one can show that the scattering operator defined by $\tilde{S}=\sum_i|\tilde{n}_{in}^i\rangle\langle \tilde{n}_{out}^i|$ and thus by $\tilde{S}^{\dagger}=\sum_i|\tilde{n}_{out}^i\rangle\langle \tilde{n}_{in}^i|$ immediately obeys the unitarity relation  $\tilde{S}\tilde{S}^{\dagger}=I$.

Since the in and out states of $\tilde{H}$ can be mapped into the in and out states of $H$ by the mapping, an $S$-matrix operator in the $|n_i\rangle$ basis can thus be defined via the mapping as $\tilde{S}=e^{-Q/2}Se^{Q/2}$, with the adjoint $S^{\dagger}$ being given via $\tilde{S}^{\dagger}=e^{Q/2}S^{\dagger}e^{-Q/2}$ since the operator $Q$ is Hermitian. As constructed, the operator $S$ can be written as $S=e^{Q/2}\sum_i|\tilde{n}_{in}^i\rangle\langle \tilde{n}_{out}^i|e^{-Q/2}$, and from the mapping thus takes the form $S=\sum_i|n_{in}^i\rangle\langle n_{out}^i|e^{-Q}$ in the $|n_i\rangle$ basis. In addition, the $\tilde{S}\tilde{S}^{\dagger}=I$ relation obliges $S$ to obey $e^{-Q/2}Se^{Q/2}e^{Q/2}S^{\dagger}e^{-Q/2}=I$, i.e. to obey
\begin{equation}
Se^{Q}S^{\dagger}e^{-Q}=I,\qquad e^{-Q}Se^{Q}S^{\dagger}=I.
\label{E9}
\end{equation}
It is thus (\ref{E9}) that is the form that unitarity of a scattering process takes in a skew basis.

While we have derived (\ref{E9}) by transforming to the Hermitian basis and then transforming back, it  is possible to derive (\ref{E9}) directly in the $|n_i\rangle$ basis without needing to make any reference to the tilde basis at all. Moreover, there is a more general derivation that does not even require us to restrict to Hermitian $V$. Specifically, we note that for energy eigenstates, be they real or complex, the time independence of  $\langle R_j(t)|V|R_i(t)\rangle$ as required by (\ref{E5}) and (\ref{E6}) entails that states whose energies do not obey (\ref{E4}) have to obey $\langle R_j(t=0)|V|R_i(t=0)\rangle=0$. Consequently, such states are orthogonal with respect to the $V$-operator norm, and on normalizing the states appropriately, for all energy eigenstates we can thus set $\langle R_j(t)|V|R_i(t)\rangle=\delta_{i,j}$. With this orthonormality relation we obtain orthonormality and closure relations for the in and out states of the form
\begin{eqnarray}
&&\langle n_{in}^i|V|n_{in}^j\rangle=\langle n_{in}^j|V^{\dagger}|n_{in}^i\rangle=\delta_{i,j},\qquad \langle n_{out}^i|V|n_{out}^j\rangle=\langle n_{out}^j|V^{\dagger}|n_{out}^i\rangle=\delta_{i,j},
\nonumber\\
&&\sum_i|n^i_{in}\rangle\langle n_{in}^i|V=
\sum_iV^{\dagger}|n^i_{in}\rangle\langle n_{in}^i|=I,~~
\sum_i|n^i_{out}\rangle\langle n_{out}^i|V= \sum_iV^{\dagger}|n^i_{out}\rangle\langle n_{out}^i|=I.
\label{E10}
\end{eqnarray}
If we now define an operator $S=\sum_i|n_{in}^i\rangle\langle n_{out}^i|V$, from (\ref{E10}) we obtain
\begin{equation}
SV^{-1}S^{\dagger}V=\sum_i|n_{in}^i\rangle\langle n_{out}^i|VV^{-1}\sum_jV^{\dagger}|n_{out}^j\rangle\langle n_{in}^j|V=\sum_i|n_{in}^i\rangle\langle n_{in}^i|V=I.
\label{E11}
\end{equation}
Consequently, for $PT$-invariant Hamiltonians unitarity of the scattering process thus takes the equivalent forms
\begin{equation}
SV^{-1}S^{\dagger}V=I,\qquad VSV^{-1}S^{\dagger}=I.
\label{E12}
\end{equation}

As a simple check on (\ref{E12}), we note that if $S$ is written as the evolution operator $S=e^{-iHt}$, then because $H^{\dagger}=VHV^{-1}$, it follows that $VSV^{-1}$ is given as $e^{-iH^{\dagger}t}$. Then with $S^{\dagger}=e^{+iH^{\dagger}t}$, (\ref{E12}) immediately follows. The relation given in (\ref{E12}) is thus the unitarity relation we want. While we shall discuss the complex energy case in more detail below, as we had already noted, our derivation of (\ref{E12}) holds even if some energies are complex. The issue here is not whether or not we can prepare stable in and out states with them, but whether or not we need them for the closure relations given in (\ref{E10}). In other words, suppose we have a $PT$-invariant Hamiltonian with $N$ real energy eigenvalues and $M$ complex pairs. For such a situation, unitarity in the form given in (\ref{E12}) will only follow if in the closure relations in (\ref{E10}) we sum over $N+2M$ states (i.e. over $N+2M$ channels), and not over $N$ states alone.

As well as provide a formal derivation of our results, it is  instructive to see how our ideas work in a simple model. Since we can always diagonalize any Hamiltonian that possesses a complete set of eigenstates, and since complex congugate pairs would form a two-dimensional subblock in the diagonal basis, it will suffice to discuss a two-dimensional model. We thus follow \cite{R1} and introduce the Hamiltonian (the parameters $r$, $s$ and $\theta$ are real)
\begin{equation}
H=r\cos\theta\sigma_0+ir\sin\theta \sigma_3+s\sigma_1=\left(\matrix{r\cos\theta+ir\sin\theta&s\cr s&r\cos\theta-ir\sin\theta\cr}\right).
\label{E13}
\end{equation}
While not Hermitian, this $H$ is $\cal{P}\cal{T}$ invariant under ${\cal{P}}=\sigma_1$, ${\cal{T}}=K$ and thus has a real secular equation with energies being given by $E_{\pm}=r\cos\theta \pm (s^2-r^2\sin^2\theta)^{1/2}$. In the region where $s^2-r^2\sin^2\theta$ is positive the two energy eigenvalues are real and distinct. In this region we can define a Hermitian operator $e^{-Q/2}$ according to
\begin{equation}
e^{\mp Q/2}=\left({1+\sin\alpha\over 2\sin\alpha}\right)^{1/2}\sigma_0\pm \sigma_2\left({1-\sin\alpha\over 2\sin\alpha}\right)^{1/2},\qquad e^{\mp Q}={1 \over \sin\alpha}\sigma_0\pm\sigma_2 {\cos\alpha \over \sin\alpha},
\label{E14}
\end{equation}
where $\sin\alpha=+(s^2-r^2\sin^2\theta)^{1/2}/s$, $\cos\alpha=r\sin\theta/s$. Using the $e^{-Q/2}$ operator we construct
\begin{equation}
\tilde{H}=e^{-Q/2}He^{Q/2}=r\cos\theta\sigma_0+\sigma_1(s^2-r^2\sin^2\theta)^{1/2},
\label{E15}
\end{equation}
and confirm that $\tilde{H}$ is Hermitian when $s^2-r^2\sin^2\theta$ is positive. Similarly we construct $e^{-Q}He^{Q}$ and confirm that it is equal to $H^{\dagger}$. Finally, we construct an operator $C=e^{Q}P$, viz.
\begin{equation}
C={1 \over \sin\alpha}\left(\sigma_1+i\cos\alpha\sigma_3\right),
\label{E16}
\end{equation}
and confirm that it not only obeys $[{\cal{C}},H]=0$ and ${\cal{C}}^2=I$, it also obeys ${[\cal{C},\cal{P}\cal{T}]}=0$, just as it must since the energies are real.

In the region where $s^2-r^2\sin^2\theta$ is positive, eigenvector solutions that obey $idu_{\pm}/dt=Hu_{\pm}=E_{\pm}u_{\pm}$ are given as
\begin{equation}
u_+={e^{-i(r\cos\theta+\mu)t} e^{i\pi/4}\over (2\sin\alpha)^{1/2}}\left(\matrix{e^{-i\alpha/2}\cr -ie^{i\alpha/2}\cr}\right),\qquad
u_-={e^{-i(r\cos\theta-\mu)t} e^{i\pi/4}\over (2\sin\alpha)^{1/2}}\left(\matrix{ie^{i\alpha/2}\cr e^{-i\alpha/2}\cr}\right).
\label{E17}
\end{equation}
where $\mu=+(s^2-r^2\sin^2\theta)^{1/2}$. For the states in (\ref{E17}) the $e^{-Q}$ norms obey the time-independent and manifestly unitary orthonormality and closure relations
\begin{equation}
u_{\pm}^{\dagger}e^{-Q}u_{\pm}=+1,\qquad u_{\pm}^{\dagger}e^{-Q}u_{\mp}=0,\qquad u_{+}u^{\dagger}_{+}e^{-Q}+u_{-}u^{\dagger}_{-}e^{-Q}=I,
\label{E18}
\end{equation}
just as required. It is thus the $V=e^{-Q}$ norm that it is the appropriate one for the problem.

\section{Unitarity when energies are not all real but complete}
\label{S4}

To determine what happens when energies are complex, it is instructive to study the two-dimensional model in the regime where $s^2-r^2\sin^2\theta$ is negative. Now the energies are given by the complex conjugate pair $E_{\pm}=r\cos\theta\pm i\nu$ where $\nu=+(r^2\sin^2\theta-s^2)^{1/2}$.
In this region we can define a now non-Hermitian  operator $e^{-Q/2}$ according to
\begin{equation}
e^{\mp Q/2}=\left({1+i\sinh\beta\over 2i\sinh\beta}\right)^{1/2}\sigma_0\pm \sigma_2\left({1-i\sinh\beta\over 2i\sinh\beta}\right)^{1/2},\qquad e^{\mp Q}={1 \over i\sinh\beta}\sigma_0\pm\sigma_2 {\cosh\beta \over i\sinh \beta},
\label{E19}
\end{equation}
where $\sinh\beta=+(r^2\sin^2\theta-s^2)^{1/2}/s$, $\cosh\beta=r\sin\theta/s$. Using this $e^{-Q/2}$ operator we construct
\begin{equation}
\tilde{H}=e^{-Q/2}He^{Q/2}=r\cos\theta\sigma_0+i\sigma_1(r^2\sin^2\theta-s^2)^{1/2},
\label{E20}
\end{equation}
and see that $\tilde{H}$ is not Hermitian when $s^2-r^2\sin^2\theta$ is negative. Despite this,  we construct $e^{-Q}He^{Q}$ with this non-Hermitian $Q$ and confirm that it nonetheless is equal to $H^{\dagger}$, just as it must be. Finally, we construct an operator $C=e^{Q}P$, viz.
\begin{equation}
C={1 \over i\sinh\beta}\left(\sigma_1+i\cosh\beta\sigma_3\right)
\label{E21}
\end{equation}
and confirm that it while it obeys $[{\cal{C}},H]=0$ and ${\cal{C}}^2=I$, because of its overall factor of $i$ it does not obey ${[\cal{C},\cal{P}\cal{T}]}=0$, as must be the case since the energies are not real.

In the region where $s^2-r^2\sin^2\theta$ is negative, eigenvector solutions that obey $idu_{\pm}/dt=Hu_{\pm}=E_{\pm}u_{\pm}$ can be constructed by setting $\mu=i\nu$, $\alpha=i\beta$ in (\ref{E17}), and are given as
\begin{equation}
u_+={e^{-ir\cos\theta t+\nu t} \over (2\sinh\beta)^{1/2}}\left(\matrix{e^{\beta/2}\cr -ie^{-\beta/2}\cr}\right),\quad
u_-={e^{-ir\cos\theta t-\nu t} \over (2\sinh\beta)^{1/2}}\left(\matrix{ie^{-\beta/2}\cr e^{\beta/2}\cr}\right).
\label{E22}
\end{equation}
For the states in (\ref{E22}) the $e^{-Q}$ norms obey the time-independent orthogonality and closure relations
\begin{eqnarray}
&&u_{\pm}^{\dagger}e^{-Q}u_{\pm}=0,\qquad u_{-}^{\dagger}e^{-Q}u_{+}=+ 1,\qquad u_{+}^{\dagger}e^{-Q}u_{-}=- 1,
\nonumber\\
&&u_{+}u^{\dagger}_{-}e^{-Q}-u_{-}u^{\dagger}_{+}e^{-Q}=I.
\label{E23}
\end{eqnarray}
With the adjoints of the states in (\ref{E22}) having time dependences of the form $u_{+}^{\dagger}\sim e^{ir\cos\theta t+\nu t}$,  $u_{-}^{\dagger}\sim e^{ir\cos\theta t-\nu t}$, we see that in (\ref{E23}) those overlaps that are zero have to vanish through the $e^{-Q}$ matrix structure of the overlaps since the time dependences in $u_{\pm}^{\dagger}e^{-Q}u_{\pm}$ do not cancel each other once $\nu$ is non-zero. For the non-zero overlaps the time dependences in $u_{\mp}^{\dagger}e^{-Q}u_{\pm}$ do precisely cancel each other, just as required by (\ref{E4}). With the $u_+$ and $u_-$ states in (\ref{E22}) obeying ${\cal{P}}{\cal{T}}u_+=u_-$, ${\cal{P}}{\cal{T}}u_-=u_+$ ($\cal{T}$ effects $t\rightarrow -t$ as well as $i\rightarrow -i$), the non-vanishing overlaps in (\ref{E23}) represent transitions between energy eigenstates and their $\cal{P}\cal{T}$ partners \cite{R10}.

The most notable aspect of the overlaps is that the $u_{+}^{\dagger}e^{-Q}u_{-}$ overlap is negative. However, this does not herald the presence of a negative metric since the overlap is a transition matrix element between different states and not the overlap of a state with its own adjoint. Moreover, rather than being an indicator of a possible loss of unitarity,  this negative sign is actually needed for unitarity. Specifically, if we construct a propagator $D(E)$ for above Hamiltonian, it will have the form of matrix elements of the states divided by energy denominators:
\begin{equation}
D(E)=\frac{u_{-}^{\dagger}e^{-Q}u_{+}}{E-(E_R+iE_I)}+\frac{u_{+}^{\dagger}e^{-Q}u_{-}}{E-(E_R-iE_I)},
\label{E24}
\end{equation}
and thus evaluate to
\begin{equation}
D(E)=\frac{1}{E-(E_R+iE_I)}-\frac{1}{E-(E_R-iE_I)}=\frac{2iE_I}{(E-E_R)^2+E_I^2}.
\label{E25}
\end{equation}
Other than the overall factor of $2$, the imaginary part of this propagator is the same as that of a standard Breit-Wigner
\begin{equation}
D_{\rm BW}(E)=\frac{1}{E-(E_R+iE_I)}=\frac{E-E_R+iE_I}{(E-E_R)^2+E_I^2}.
\label{E26}
\end{equation}
The negative sign of $u_{+}^{\dagger}e^{-Q}u_{-}$ thus compensates for the negative sign of the imaginary part of the energy of the $u_{-}$ state,  with its contribution  to the imaginary part of $D(E)$ then being positive rather than negative \cite{R11}.

While it is nice to see that $D(E)$ recovers the standard Breit-Wigner form, our results actually go further than that as they provide some justification for the use of the standard $D_{\rm BW}(E)$ in the first place. Specifically, if one works with a general complex potential, i.e. with one for which (\ref{E4}) is not obeyed, one would not get unitary time evolution. If for instance we work with a complex potential that has just one energy eigenstate with wave function $\psi=e^{-iE_Rt+E_It}$, the probability would be given as  $\psi^*\psi=e^{-2E_It}$ and not be preserved in time, and would even grow in time if $E_I$ is negative. Hence, if we wish to describe absorption or decay processes in a time-preserving manner, we must augment this state with its complex conjugate partner and include the contribution of the partner to $D(E)$. Our approach is thus well-suited to a scattering process in which the in and out states long before and long after a collision are real eigenvalue eigenstates of a $\cal{P}\cal{T}$-invariant Hamiltonian $H_0$, with the states scattering through some short-range $\cal{P}\cal{T}$-invariant interaction $H_{\rm INT}$ for which $H_0+H_{\rm INT}$ has complex eigenvalues. In such a situation the interaction would generate two poles at $E_R\pm iE_I$ that would be on the same Riemann sheet and combine just as in (\ref{E25}) \cite{R12}.

The fact that the two complex conjugate poles are on the same Riemann sheet has an interesting consequence: it enables the two poles to be located within the same contour in the complex energy plane rather than be  in different contours. In consequence, the theory will be causal. Specifically, with two complex conjugate poles having opposite imaginary parts, one of the poles would have to appear above the real energy axis and one below. Now when one only has to deal with poles with real energies (such as the $D(E)=1/E_++1/E_-$ propagator associated with  (\ref{E18})), to construct a causal, retarded propagator, one locates all the poles slightly below the real axis, with a contour integration then giving no pole contribution if one closes the contour in the upper-half plane. If one simply repeats this prescription when there is a pole in the upper-half plane, on closing the contour above the real axis one then gets a non-zero pole contribution and causality violations result. However, as discussed for instance in \cite{R13}, for complex conjugate pairs of poles one can use an alternate contour instead. Specifically, one can deform the contour to pass above any  pole in the upper-half plane. Then when one closes this deformed contour in the upper-half plane, one still gets no pole contribution and the propagator is causal, and when one closes the deformed contour in the lower-half plane, both complex poles contribute, just as in (\ref{E25}). For $\cal{P}\cal{T}$ theories then, to maintain causality, the prescription is to make the choice of contour dynamics dependent (just as is done with the $\cal{P}\cal{T}$-theory Hilbert space metric), so that as interactions cause poles to move off the real axis the contour must move along with them so that all the poles remain below it, a meaningful procedure if all the poles are on the same Riemann sheet \cite{R14}.

\section{Unitarity when energies all real but incomplete}
\label{S5}

When a Hamiltonian is diagonalizable,  one does not need to distinguish between the eigenvalue solutions to the secular equation ${\rm det}(H-\lambda I)=0$ and the eigenvalue solutions to $H\psi=E\psi$ since the two sets of solutions coincide. However,  when a Hamiltonian is not diagonalizable, the number of eigensolutions to $H\psi=E\psi$ is less than the number of eigenvalue solutions to ${\rm det}(H-\lambda I)=0$, and the spectrum of $H$ is incomplete. A typical example of a non-diagonalizable, Jordan-block, matrix is the two-dimensional matrix $M$
\begin{eqnarray}
M=\pmatrix{a&1\cr 0&a}.
\label{E27}
\end{eqnarray}
Its secular equation $|M-\lambda I|=0$ has two solutions for $\lambda$, both of which are equal to $a$ (and incidentally both solutions are real when $a$ is real even though an $M$ with real $a$ is not Hermitian), but  $M$ has only one right-eigenvector and equally only one left-eigenvector, viz.
\begin{eqnarray}
\pmatrix{a&1\cr 0&a}\pmatrix{1\cr 0}=a\pmatrix{1\cr 0},\qquad a\pmatrix{0 & 1}=\pmatrix{0 & 1}\pmatrix{a&1\cr 0&a}.
\label{E28}
\end{eqnarray}

Despite the lack of completeness of its eigenstates, if the secular equation ${\rm det}(H-\lambda I)=0$ of a Hamiltonian is real, $H$ and its adjoint $H^{\dagger}$ will still be related by (\ref{E6}), i.e. still be related $VHV^{-1}=H^{\dagger}$ for some operator $V$. For the example of (\ref{E28}) the secular equation will be real when $a$ is real, and $V$ will then be given by $V=\sigma_1$ \cite{R15}. More  generally, for a non-diagonalizable matrix of arbitrary dimensionality, Jordan showed that via a sequence of similarity transformations any such matrix can always be brought to the Jordan canonical form in which all of the elements on the diagonal are equal to each other, and the only non-zero off-diagonal elements are all real and all lie on the superdiagonal immediately above the diagonal. With the non-zero elements on the superdiagonal not contributing to the secular equation since all the other non-diagonal elements of the matrix are zero, the elements on the diagonal of a Jordan block matrix are the eigenvalue solutions to the secular equation. Since all the eigenvalues of a Jordan-block matrix have to be equal to each other, the reality of the secular equation of a Jordan-block matrix requires that  all of its solutions be real, since any complex conjugate pair of solutions could not be equal to each other. Thus for any Jordan-block matrix whose secular equation is real, we see that all the elements of the matrix are real, with the Hermitian adjoint of the matrix thus being equal to its transpose. Since a transposition matrix always exists in any dimension (an explicit construction is given in \cite{R6}), the transposition matrix serves as $V$.  Thus for any Jordan-block matrix with a real secular equation, one can always find an operator $V$ that effects $VHV^{-1}=H^{\dagger}$.

Moreover, in the Jordan block case the converse also holds. Specifically  if one can find  a $V$ operator that effects $VHV^{-1}=H^{\dagger}$, the secular equation will be real since the invariance of a determinant under similarity transforms is insensitive to Jordan-block structures. Thus even in the Jordan block case $\cal{P}\cal{T}$ invariance is necessary and sufficient for the existence of a $V$ operator that effects $VHV^{-1}=H^{\dagger}$.

With (\ref{E5}) holding for any states that obey (\ref{E1}) and (\ref{E2}), (\ref{E5}) will hold for non-stationary as well as stationary solutions to (\ref{E1}). Now in the Jordan block case the lack of energy eigenstates is compensated for (see e.g. \cite{R16}) by the presence of non-stationary solutions that typically behave as powers of $t$. For every missing stationary solution one finds a power-behaved in $t$ solution \cite{R17}. The set of all stationary plus non-stationary solutions combined is thus complete \cite{R18}. Since the stationary plus non-stationary solutions are complete, we can use (\ref{E5}) to infer that in the Jordan block case time evolution of wave packets will be unitary if and only if one can find a $V$ operator that effects $VHV^{-1}=H^{\dagger}$. Thus, as noted in \cite{R16}, even though the non-stationary solutions are power-behaved in $t$, packets containing them and the stationary solutions will still evolve with a probability that is preserved in time \cite{R19}.

redpajama_set_name: RedPajamaArXiv


text:
Q: How would one describe a person who is not convinced by strong evidence in support of a theory I am looking for a word which best describes a person who cannot be convinced by strong evidence presented in support of a theory. He may or may not present counter-arguments, but he is adamant in his refusal to be convinced.
For example

I have shown her all the evidence which convinces me that the theory is
  correct, but she is still __________ and says that the arguments are flawed.

The word 'unconvinced' would fit the blank here, but my request is for a stronger word than 'unconvinced' because the person in question will not discuss the evidence I have presented, but will only argue the case from other standpoints.

A: Skeptical.
Source: https://www.merriam-webster.com/dictionary/skeptical

Relating to, characteristic of, or marked by skepticism.

Example:

She's highly skeptical of the researchers' claims.

Skepticism is defined as:

An attitude of doubt or a disposition to incredulity either in general or toward a particular object.

In this situation, this is the most apt word.  From the question's description,  it's not at all clear that this person has been presented with irrefutable proof.  He was simply presented with "all the facts".  These is no mention that these facts constitute irrefutable proof.  Thus other words such as zealous, intolerant, denier don't work because they convey the idea that the person is irrational, which cannot be implied based on the question.  Adamant and persistent don't work because they imply imply some sort of effort, where as it's not the skeptic that is putting in the effort, it is the other party who is presenting the evidence.

A: You might call them close-minded, but they would see themselves as being faithful to their consciences.
You might call them overly suspicious, but they would see others around them as too quick to believe, gullible or even deceived.
No matter what you call them, I guarantee the person would see it differently.  No matter how you spin it, they think they are being true to the evidence (unless the person is genuinely mentally disabled or they are lying).
What is obvious to you is obviously not obvious to the other.  Calling someone names -- if they are being true to their consciences -- is both mean and bigoted.  Have some respect.  Be patient.  Give them the benefit of the doubt.
You say "all the facts" have been presented, but I guarantee if the other person is not convinced they don't see it that way.
"Fallacies do not cease to be fallacies because they become fashions." - G.K. Chesterton

A: Here are three words from Merriam Webster that you may find useful
Adamant
adjective
1.
unshakable or insistent especially in maintaining a position or opinion.
Or for a belief (usually religious)
Zealous
adjective
marked by fervent partisanship for a person, a cause, or an ideal
Or if you want to describe someone who could conceivably change their opinion. you could use
Persistent
existing for a long or longer than usual time or continuously: such as
a :  retained beyond the usual period a persistent leaf
b :  continuing without change in function or structure persistent gills
c :  effective in the open for an appreciable time usually through slow volatilizing mustard gas is persistent
d :  degraded only slowly by the environment persistent pesticides
e :  remaining infective for a relatively long time in a vector after an initial period of incubation persistent viruses


text:
You are here: Home / News / Walz transition advisory board begins meeting at State Capitol (with AUDIO)
Walz transition advisory board begins meeting at State Capitol (with AUDIO)
November 27, 2018 By Bill Werner
A wide-ranging group that's advising the incoming Walz administration is off-and-running as Lieutenant Governor-elect Peggy Flanagan opened the first of three meetings at the State Capitol Monday. "We said consistently that we believe that people who are directly affected by policy should have a seat at the table, and we would like to think that this Transition Advisory Board is literally people being at the table," says Flanagan.
The group, comprised of over two dozen people from a variety of backgrounds, will first help the incoming Walz administration recruit commissioners and other top officials. At their next meeting, they'll discuss budget and policy priorities.
Education Minnesota teachers union President Denise Specht is on the advisory board and says, "Every door I knocked and every phone I picked up, people want to talk about public education — so I'm certainly hoping it's at the heart of the discussion." Jaylani Hussein with the Council on American Islamic Relations Minnesota says, "We want to see the community's smartest and brightest have the same amount of opportunity to lead the state and show that this community is not only part of the state, but also the part that's gonna help grow it." Hussein says he's "very encouraged" because it's the first time a governor-elect has called together such an advisory board.
Here are Lieutenant Governor-elect Peggy Flanagan's opening remarks:
https://cdn.minnesotanewsnetwork.com/wp-content/uploads/2018/11/bwflanagan112618edit.mp3