We use at present two systems for measuring the time: the sexagesimal system for the time of the day, the Gregorian system for the time of the year.
Two systems, it is one too many.
In a concern for efficiency and simplicity, the calendar reform this site is proposing consists in doing away with the Gregorian system (which intricacy is as phenomenal as useless) to retain only the sexagesimal system (already in use all over the world to count the minutes and the seconds) and to extend its use for measuring the time of the year.
The whole humanity would profit from meeting about this great plan.
If you want to support this design, please sign the petition in page support.
Translators who would like to voluntarily develop new versions of this site are welcome to use the contact page to make themself known.


text:
Friday Monsoon Turns Oklahoma into a Tale of Two Fairs
Wade Shows features over 74 rides on the midway
By: Timothy Herrick
Charles Dickens famously said it was the best of times; it was the worst of times.
When asked how the 2018 Oklahoma State Fair went, J. Scott Munz, Vice President, Marketing & Public Relations paraphrased Dickens. The 2018 edition of the annual celebration of everything Oklahoma was "Not the best, not the worst."
All things considered, not being the worst fair is not the worst that can happen to a fair. As to why it wasn't the best fair ever, the main culprit was mother nature – a cataclysmic downpour on a key day. "The Fair was doing quite well going into the second Friday when the local weathermen began predicting catastrophic rains, including heavy flooding, for the area," said Munz. "It rained from about nine in the morning until nine at night including some periods of heavier than usual rain. To say that the day was a 'wash' would be an understatement."
Overall, the fair attracted more than 850,000 attendees, which Munz described as down "slightly" compared to 2017. It is still a healthy enough attendance for the event with fairgoers making the most out to the non-deluge days, although the fair doesn't report revenue or record individual day attendance figures.
But one positive indicator was a noticeably improved economy compared to 2017. While it may be too early to declare that boom times are back, Oklahomans seem to be working with more disposable income this year. "Prior to the rains coming on the second Friday, we were in pretty good shape so I believe that we have turned the corner on the recession to some degree," he said. But, [we're] not completely out of it yet."
The advertising budget remained about the same as last year, with the media mix being 30 percent television, 25 percent radio, 15 percent print, 15 percent outdoor and 15 percent digital. The big shift in the media buys was towards digital, including an emphasis on social media. "We had had a strong presence on social media for quite a few years now so we didn't do much different in 2018 with the exception of maybe more contests," said Munz.
Talent buying remained a "seller's market" and the fair has tended to stay away from booking high-cost entertainment acts. Instead, the arena during the fair featured Disney On Ice presents Dare to Dream and the PRCA Xtreme Bulls, with openers Big & Rich one night and Aaron Watson the next night. Otherwise, the headline acts which are free shows with outside gate admission included: Colt Ford, Neal McCoy, Beatlemania LIVE!, Los Traileros Del Norte, Jordan Feliz, Herman's Hermits starring Peter Noon, Elvis Extravaganza, Dylan Scott, Foghat and Space Oddity – The ultimate David Bowie Experience.
The fair featured 145 food vendors, but indicative of a more positive economic outlook, Munz said that "even with the almost complete loss of the second Friday, the food gross was only about 6 percent off last year."
The imagination of food vendors were on full display with an extraordinary range of more than 25 new food items, which the Fair's publicity described as "Old Fashioned Fun at Our New Fashioned Fair. The innovative interpretations of fair cuisine included the more subtle, such as Drizzled Muffins – warm muffins with chocolate, caramel or white chocolate drizzled on top – at the A Latte Love Coffee House to the complex and outrageous: Cotton Candy Pie, Root Beer Float Pie, Cherry Limeade Pie; Deep-Fried Hot Pepper Rings; Mac-N-Cheese Topped with Ground Beef and Fries; BBQ Chicken and Bacon Calzone; Waffle Wrapped Snow Ice; Beer Cheese Bacon Fries; Cheese Curd Taco Flaming Hot Cheetos Fish Taco; Jalapeno Cheddar Sausage and Kit-Kat Fries.
Exemplifying both the old and new fashion ethos of this year's new food creations was the Funnel Cake Burger ("Everything you love about a half-pound burger…except the buns have been replaced by funnel cake! This unexpected combo is the perfect mixture of sweet and savory! Find it at Porky's!")
The food twists at the Oklahoma State Fair have a long history, with some returning favorites that included Watermelon Salsa; Wonder Boy Corn Dog: (a Cap'n Crunch battered corn dog served with honey mustard dipping sauce); Avocado Fries; Deep-Fried Coffee; Gator Burger & Gator Bites; Mac N Cheese Burger; Deep-Fried Watermelon; Caveman Turkey Leg; Pork Chop On-A-Stick; Funnel Cake Fries and Wonder Stick Ice Cream.
According to Munz, top selling dishes at the 2018 Oklahoma State Fair were: "Watermelon Pie, Honey Pepper Bacon Dog and Mac N Cheese Burger, he said. "And the why is because of their each unique tastes."
Destination Wheel
Wade Shows provides the midway at the Oklahoma State Fair, with a footprint of about 74 rides. Frank Zaitshik, President/CEO, Wade Shows Inc., shared the good fair except for the closing Friday flood assessment voiced by Munz. "It was a very good year, but we lost a significant day on Friday," he said. "We were up a quite a lot going into that Friday. The Saturday was down a little, but we had strong closing Sunday."
Wade Shows increased the price of its armband slightly for the fair. "We had discussed options whether or not to increase price of advanced sale," said Zaitshik. "We decided to increase the cost of the armbands, and we didn't hear any negatives about it."
Although Zaitshik explained that advance sales were off due to the loss of a distributor, any loss was made up by partnering with the fair for its group sales program. These group sales – typically directed to corporations – was one of the strongest among the fairs on his route. "They do an excellent group sales program and that helped put us over the top."
Highlights of the midway include The Fighter, which had not appeared last summer, Super Bumper Boats, RC48 Roller Coaster, New York/New York, Super Cycle and Magnum. "We had a very powerful lineup," said Zaitshik.
The centerpiece was the new Sky Eye Plaza, which featured Wade Show's and Wood Entertainment's Giant Wheel, considered to be North America's largest traveling observation wheel. The ride features more than 500,000 LED lights and 35 gondolas, holding up to six riders each, and escalates to a peak height of 155 feet, allowing views up to 15 miles.
The fair and Wade Shows designed a separate area for this spectacular ride, away from the regular midway. "They were great partners and we created an entertainment plaza for the Sky Eye Wheel, which we pushed as an observation wheel and made it a destination "for all fairgoers, it was a separate price from the midway tickets. We explored several locations, and presented it to them to promote as a special attraction. We combined entertainment and food concessions in the plaza."
Zaitshik admits to having a sentimental attachment to this fair – his parents were concessionaires at the fair and he's been the carnival company – in one form or another – since 1993. "It is near and dear to my heart," he said. "But it's a great facility and they are constantly improving the facility. They have real out of the box thinking for a state fair in the variety of entertainment and the exhibits they present. Everybody on the fair staff is dedicated to building attendance and giving great customer service."

redpajama_set_name: RedPajamaCommonCrawl


EGUIDE: In this review of the top 10 Computer Weekly articles focused on IT in Australia, we look at what the country is doing to cement its position as a leader in mastering and deploying advanced information and communications technology across a large segment of its economy.
EBOOK: Learn how to improve your company's data protection strategies, reduce security spending, and reevaluate your vulnerabilities with business risk and ROI assessments.
ESSENTIAL GUIDE: This report from IPS explains how businesses can use the Strategic Execution Framework to help their companies stay on track and align projects to desired business outcomes.
PRESENTATION: Nick Beighton , CFO of the online fashion retailer ASOS.com, draws on his experience in both IT and finance to offer tips to CIOs on building credibility with the board of directors.
PRESENTATION: David Matthewman CIO of The Open University gives his take on the value of no-and low-tech innovation in this PowerPoint presentation.
PRESENTATION: Ian Campbell, board advisor for Value Retail, talks about what CIOs need to do to ensure they are "on the same planet" as the CEO and board members of any organisation in this PowerPoint presentation.
ESSENTIAL GUIDE: This major study from IBM, which delves into the views of 884 global CEOs, assess the impact of technology on their organisations and strategy.
ESSENTIAL GUIDE: This major global C-level survey from IBM examines the changing role of the CIO and makes recommendations for CIOs who want to move from the back office to the front line of the business.
ESSENTIAL GUIDE: This ground breaking study from Deloitte, based on a survey of 700 CIOs world wide, gives you the latest trends in IT spending, technology and business priorities and CIO's career aspirations.
BOOK: Learn how to make your presentation stand out from the crowd and make 'death by slide presentation' a thing of the past with this book extract especially written for IT professionals.
PRESENTATION: Robin Young, COO Mitchells and Butlers and former CIO gives a candid appraisal of the boardroom's view of IT and offers tips to CIOs on building credibility with board members.
PRESENTATION: Jim Norton, former BCS president and chartered director, explains the 5 key roles of the CIO and offers tips to CIOs on building credibility with the board.
ESSENTIAL GUIDE: Tablet devices will give enterprises a competitive advantage according to this in-depth report from Booz&Co.
ESSENTIAL GUIDE: This study by Capgemini and the Economist Intelligence Unit report assess the impact of Big Data on businesses.
WHITE PAPER: In this paper, learn about the Smarter Commerce approach to marketing performance and profitability. Inside, discover the five steps to personalized and profitable marketing and better understand how to succeed in an ever-changing digital world.
WHITE PAPER: Access this fascinating fact sheet to discover the importance of the relationship between CEOs/CFOs and the heads of HR, and learn how to improve this relationship and ensure better HR and overall business results.
WHITE PAPER: In this report, find out whether the HR function is forging a close and robust relationship with the CEO, and about the nature of these working relationships. Read on to discover findings from a global survey of over 200 company executives and a series of in-depth interviews with senior execs and experts.
BROCHURE: The Gartner Outsourcing & Strategic Partnerships Summit 2013 this September allows you to rethink your outsourcing strategies and discuss best practices with your peers to help you achieve the most from your outsourcing efforts.


text:
Q: Actualizar Mysql funciona en Json y no en Android Studio Soy nuevo en la programación espero puedan ayudarme con mi problema. Estoy realizando una aplicación donde busco recolectar el contenido de varios editar texto y actualizar mi DB con esos valores. el problema es que mi php funciona bien cuando lo pruebo en Postman, pero cuando lo pruebo con el código no actualiza. espero puedan ayudarme
public void Actualizar_info (){

        String Url_EDIT = "https://url/UsuariosRDC/Actualizar.php";

        StringRequest stringRequest = new StringRequest(Request.Method.POST, Url_EDIT, new Response.Listener<String>() {
            @Override
            public void onResponse(String response) {

                try {
                    JSONObject jsonObject = new JSONObject(response);
                    String success = jsonObject.getString("success");

                    if (success.equals("1")){

                        Toast.makeText(getApplicationContext(),"Actualizado",Toast.LENGTH_LONG).show();

                    }

                } catch (JSONException e) {
                    e.printStackTrace();
                }
            }
        }, new Response.ErrorListener() {
            @Override
            public void onErrorResponse(VolleyError error) {

                Toast.makeText(getApplicationContext(),"error en actualizacion: "+error,Toast.LENGTH_LONG).show();

            }
        })

        {
            @Override
            protected Map<String, String> getParams() throws AuthFailureError {
                Map<String, String> params = new HashMap<>();
                params.put("placa",placaVal.getText().toString());
                params.put("beneficio1",beneficio1v.getText().toString());
                params.put("beneficio2",beneficio2v.getText().toString());
                params.put("beneficio3",beneficio3v.getText().toString());
                params.put("beneficio4",beneficio4v.getText().toString());
                params.put("beneficio5",beneficio5v.getText().toString());
                params.put("beneficio6",beneficio6v.getText().toString());
                params.put("beneficio7",beneficio7v.getText().toString());
                params.put("beneficio8",beneficio8v.getText().toString());

                return params;

            }
        };

        request.add(stringRequest);

A: Primero en android estas creando una peticion  de tipo POST
  StringRequest stringRequest = new StringRequest(Request.Method.POST, Url_EDIT, new Response.Listener<String>()

pero en PHP estas tratando de obtener las variables por metodo GET, si quieres mantener eso entonces tendrias que mandar en la url los parametros.
 StringRequest stringRequest = new StringRequest(Request.Method.GET, Url_EDIT, new Response.Listener<String>()

la url seria:
 String Url_EDIT = "https://javicheti.000webhostapp.com/UsuariosRDC/Actualizar.php?placa"=+placaVal.getText().toString()+"&beneficio1="+,beneficio1v.getText().toString();

lo siguiente lo debes usar si quieres enviar parametros en la cabecera de la peticion:
 @Override
        protected Map<String, String> getParams() throws AuthFailureError {

redpajama_set_name: RedPajamaStackExchange


text:
Q: How to allow for only one month-year combination in java sb How do I allow input for only one month-year combination in Java Spring Boot. I need to make sure that user (postman client) can input one recording (randomly generated value) per month of that year. So for example: month: February -> Year: 2020 -> generatedValue = something random. And when user goes to input February 2020 again it throws an exception. I've tried with storing years and months in seperate lists, to check if there's month with that year already present in the database, but to no avail. In RecordService in first if I'm trying to see if there isn't present year that user entered. For example if there is not a year 2021 then the "if" should add that year to a list so i can check the month-year combo. It works, but not what I need because the second if always throws a RuntimeException(), except when I enter a year that hasn't been entered (for example there are years 2020, 2021 and 2022 but there isn't a year 2023, so when user adds for example:
{
    "month": "March",
    "year": "2023",
    "readingTime": "1"
}

the code will work because there isn't a year 2023 in the list, but as soon as they try to enter
{
    "month": "May",
    "year": "2023",
    "readingTime": "1"
}

it will not work because the year is already present, even tho it should because there isn't may-2023 combo in the db. I've tried to have a boolean to check if the combo exists, but that doesn't make any sense to me. So please, please help :)
Here is my code.
RecordController.java
@PostMapping("/{client_id}")
    public Record add(@PathVariable Long client_id, @RequestBody Record record){
        return recordService.add(client_id, record);
    }

RecordService.java
public Record add(Long client_id, Record record){

       List<String> monthList = months();
       List<Integer> yearList = years();

        Record recordSave = new Record();
        recordSave.setId(client_id);
        recordSave.setYear(record.getYear());
        recordSave.setMonth(record.getMonth());
        recordSave.setReadingTime(record.getReadingTime());
        recordSave.setReadingValue(randomGenerate());

        //Does not work
        if (!yearList.contains(recordSave.getYear())){
            yearList.add(recordSave.getYear());
        }

        //Does not work
        if (monthList.contains(recordSave.getMonth()) && yearList.contains(recordSave.getYear())){
                throw new RuntimeException();
        }
        else {
                recordRepository.save(recordSave);
        }
        return null;
    }

Record.java
@Data
@Entity
@Table(name = "record")
@JsonIgnoreProperties({"hibernateLazyInitializer","handler","device"})
public class Record implements Serializable {
    @Id
    @GeneratedValue(strategy= GenerationType.IDENTITY)
    private Long id;

    String month;
    Integer year;
    String readingTime;
    Float readingValue;

    boolean isPresent;
}

RandomGenerateValue & month-year functions
public Float randomGenerate(){
        int max = 105, min = 14;

        float random_float = (float)Math.floor(Math.random()*(max-min+1)+min);

        return random_float;
    }

    public List<String> months(){
        List<String> monthList = new ArrayList<>();

        monthList.add("January"); monthList.add("February"); monthList.add("March"); monthList.add("April");
        monthList.add("May"); monthList.add("June"); monthList.add("July"); monthList.add("August");
        monthList.add("September"); monthList.add("October");  monthList.add("November"); monthList.add("December");

        return monthList;
    }

    public List<Integer> years(){
        List<Integer> yearList = new ArrayList<>();

        yearList.add(2020);
        yearList.add(2021);
        return yearList;
    }

A: Keep year & month together, as a single value
Your problem seems to stem from thinking of the year and the month as separate values. Instead, combine them. Think in terms of year-month, a single unit.
YearMonth class
Java includes a class for this concept. Its name is appropriate: YearMonth, in the java.time package.
YearMonth ym = YearMonth.of ( 2023 , 3 ) ;

Or use the Month enum, to ensure valid values.
YearMonth ym = YearMonth.of ( 2023 , Month.MARCH ) ;

You can represent your slots for each month and year by using a Map. Keep the keys in sorted order by using a NavigableMap.
NavigableMap< YearMonth , UUID > map = new TreeMap<>() ;
map.put(
    YearMonth.of ( 2023 , Month.MARCH ) ,
    UUID.randomUUID()
);
map.put(
    YearMonth.of ( 2023 , Month.FEBRUARY ) ,
    UUID.randomUUID()
);

Test if a value has already been put.
boolean alreadyPut2023March = map.containsKey( YearMonth.of ( 2023 , Month.MARCH ) ) ;

ISO 8601
For text purposes, use standard ISO 8601 format: YYYY-MM
The java.time classes use ISO 8601 formats by default when parsing/generating text.
String iso8601Output = YearMonth.of ( 2023 , Month.MARCH ).toString() ;

2023-03

Such a string could be used for storage in your database, assuming your database does not offer a year-month data type. I don't know of any database that does offer such a data type. So text will suffice.
Notice that when sorted alphabetically, the values are also sorted chronologically.
Your JSON would look like this:
{
    "year-month": "2023-03",
    "readingTime": "1"
}


Workshop manual pdf download Audi A4 B5 1997 along with hundreds of photos and illustrations, that guide you through each service and repair procedure. Not a scanned Workshop repair manual.
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With respect to eggs specifically, it seems that moderate consumption of eggs are not a health risk and may even be beneficial.
The characteristics of the two types of pain are usually quite different. Peptic ulcer pain is not induced by exercise and relieved by rest, and the gnawing pain accompanied by bloating and nausea is quite different from that of typical angina.
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Symmetrel and Lysovir capsules amantadine hydrochloride 100mg have been discontinued by Alliance Pharmaceuticals. Generic versions are available from Auden McKenzie. Further information on 01895 627420.
Vision issues rapidly deteriorate; many people will become completely blind. Complications from other symptoms, such as kidney problems, can become lifethreatening.
FDA. Cold, cough, allergy, bronchodilator, and antiasthmatic drug products for overthecounter human use.
TUESDAY, Aug. 16, 2011 HealthDay News For some gout patients afflicted with a particularly severe, crippling form of the disease who find standard treatments either intolerable or ineffective, a recently approved alternative appears to afford relief.
This refers to a condition where the thyroid gland is enlarged in size. Goiter can result from autoimmune Hashimotos and Graves diseases, iodine excess and deficiency, and nodular thyroid disease.
American Academy of Pediatrics and American Academy of Family Physicians Subcommittee on Management of Acute Otitis Media. Diagnosis and management of acute otitis media. Pediatrics.
As noted above, its most frequent use is in diseases of the liver. Viral hepatitis is perhaps the most important of these. Little evidence supports its clinical use in hepatitis B, but studies in hepatitis C HCV indicate that it may have some utility, although newer antivirals that eradicate HCV infection are now preferred. However, some study indicates that silymarin when given intravenously may inhibit viral replication.
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text:
Pocatello ID Witness Says UFO Chased Off Mountain By Helicopters
Greg Jannetta
Greg Jannetta Published: September 21, 2021
casinos.com
A Pocatello area resident recently contacted the National UFO Reporting Center after witnessing an unexplained object interacting with some helicopters last week. The witness claims to have watched the ordeal take place for close to 30-minutes.
The state of Idaho for the month of September has logged one incident of an unexplained aerial phenomenon with the National UFO Reporting Center to date. The center has been tracking these types of incidents in the United States for decades, and publishes its reports for public viewing. The NUFORC investigates all reports prior to publishing details on its website.
An incident shared by the NUFORC last Thursday details a sighting that reportedly took place in Pocatello, Idaho, during the week of September 13, 2021. The individual claims to have seen a "glowing light" land on an area mountain, and then get chased off shortly after by six helicopters with green lights. The information was published on the center's website on September 16.
The sighting allegedly continued for approximately 25-minutes, according to the report. The southeastern portion of Idaho has had many reports of unexplained aerial phenomenon in recent years, including two incidents that were recorded by witnesses.
Back in February, a large glowing object was recorded by a witness in Bonneville County. A man recorded what appeared to be a massive object hovering above city lights for close to a minute.
Another incident near Pocatello was reported in June of 2020. Several unexplained lights were seen in the sky moving erratically. The Boise area also gets of good deal of reports to the NUFORC annually.
Flying History: Maid in the Shade B-25J Bomber
Weird Southern Idaho Sights From Space
Pictures Of Twin Falls As A Tiny Planet
7 Most Haunted Places In Southern Idaho
Filed Under: idaho, National UFO Reporting Center, pocatello, reports, UFO


text:
Whether you're into orchestra or opera, these Hong Kong arts groups have to be on your radar
by Carly Wu | Mar 06, 2020
Here are some of the most celebrated Hong Kong arts groups, and they promise a mesmerising performance for y'all
Being one of the most dynamic cities in the world, Hong Kong is full of exciting art galleries, museums and historic buildings to feed your culture hunger. And if you're into live performance, here are some of the most distinguished Hong Kong arts groups that you need to check out.
Our favourite Hong Kong arts groups
Hong Kong Ballet
Established in 1979, Hong Kong Ballet is a dedicated performing arts organisation formed by a vibrant community. With almost fifty dancers from around the world, HKB has done internationally-acclaimed re-stagings of the classics by Nina Ananiashvili, Cynthia Harvey, Anna-Marie Holmes, as well as works by some of today's most sought-after choreographers including Alexei Ratmansky, Christopher Wheeldon and more. They are definitely one of the most beloved Hong Kong arts groups, even for those who know nothing about dancing!
Learn more about Hong Kong Ballet.
City Chamber Orchestra of Hong Kong
City Chamber Orchestra of Hong Kong (Photography: City Chamber Orchestra of Hong Kong via Facebook)
As one of Asia's leading chamber orchestras, City Chamber Orchestra of Hong Kong features experienced musicians from early music to tango, Bollywood and jazz background. The CCOHK has performed alongside internationally renowned artists such as Sir James Galway, Dame Evelyn Glennie, Dame Emma Kirkby since 1999 and has made its mark in Italy and China. Last but not least, they also host masterclasses, workshops and soirées featuring outstanding orchestral-theatre programmes like Magnificent Mozart and The Star Bach to educate kids as well.
Learn more about City Chamber Orchestra of Hong Kong.
Hong Kong Philharmonic Orchestra
Hong Kong Philharmonic Orchestra (Photography: Hong Kong Philharmonic Orchestra via Facebook)
The philosophy of Hong Kong Philharmonic Orchestra is to inspire through the finest music-making. Being recognised as one of Asia's most prominent classical orchestras, HKPhil presents more than 150 concerts over a 44-week season, attracting more than 200,000 classical music enthusiasts each year. They're also very keen to promote the work of Hong Kong and Chinese composers through an active commissioning programme, as well as community engagement programmes in schools, hospital and outdoor spaces – simply wonderful.
Learn more about Hong Kong Philharmonic Orchestra.
All the hottest upcoming HK concerts in 2019
Opera Hong Kong
Opera Hong Kong (Photography: Opera Hong Kong via Facebook)
When it comes to Hong Kong arts groups that can't be missed, look no further! Founded in 2003, Opera Hong Kong was the first opera company in the city. The company believes that opera productions deserve a permanent niche and recognition in this culturally vibrant city. Hoping to enhance the public's interest in the art of opera, this non-profit organisation delivers a wide variety of educational and outreach activities and opera productions including La Traviata, Turandot, Carmen, The Marriage of Figaro, Roméo et Juliette and many more. Now grab those opera glasses, dress up fancy and take a listen.
Learn more about Opera Hong Kong.
The Chinese Artists Association of Hong Kong
The Chinese Artists Association of Hong Kong, AKA Bar Wo Hong Kong (Photography: 香港八和會館 – 粵劇新秀演出系列 via Facebook)
Are you interested in one of Hong Kong's most distinctive forms of entertainment Cantonese Opera? Formed in the Qing Dynasty during the reign of Emperor Guangxu (1875-1908), the Chinese Artists Association of Hong Kong (AKA Bar Wo Hong Kong) has since been a professional organisation for Cantonese opera performances in Guangdong Province. Not only do they aim to preserve the art of traditional Cantonese opera, they also strive to guarantee the welfare of fellow performers. Being absolutely one of the most respected Hong Kong arts groups, they also offer a wide range of classes for those who would like to learn more about Cantonese opera.
Learn more about The Chinese Artists Association of Hong Kong.
Hong Kong Arts Centre
Hong Kong Arts Centre (Photography: Hong Kong Arts Centre via Facebook)
Hong Kong Arts Centre is the city's only independent multi-arts centre. Dedicated to facilitating artistic exchanges between artists and the public, the HKAC has built a strong local art ecosystem that makes art more accessible to local audience. They cover a range of programmes of arts, visual arts, film and video arts, public art projects, art festivals and more.
Learn more about Hong Kong Arts Centre.
Carly Wu
Carly knows all about the underground music scene and the greatest 90s shoegaze bands like Slowdive and My Bloody Valentine. She's also a vegan food lover who is obsessed with both cooking and eating out.
Read more from Carly Wu
Wellness holidays, your best holiday treat!
Throw a punch at these top boxing gyms
We got ourselves some Warhol-inspired nails


Today's fast pace in companies often leads to a lack of important HR management areas, e.g. a clear leadership.
Consequences are a lack of emotional ties to the employer and decreasing motivation to work. In the last resort this is leading to productivity losses, arguments between employees, loss of teamwork, caused by a lack of motivation. Decreasing sales figures lead to a stressed boss who is reacting impulsively by passing the pressure on to the "next in line". The employees are in a downward spiral faster than they think. Demotivation and pressure to perform lead to burn-out.
Don't let it get so far in your company!
All data is safe, locked and will never be used for other purposes without agreement of the client.
I also remain obliged to maintain confidentiality following the ending of the assignment. Confidentiality and trust are a matter of course for me.


Data visualization stream "Beauty of Data with SAP Lumira" by Skybuffer. Enjoy our vision of Electric Cars Comparison!
Renault Twizy makes this market group available!
Most of electrics cars are in this group!
Currently there are only Tesla models in this group.


Happy February bookaholics! Or should I say the month of lllloooovvvveeee??
I thought to kick things off with a tag (i haven't done one in forever!) and my OTP's. I also have a good excuse to share of wonderful fanart. Enjoy!
Here's where I found this tag. I don't think Cristina is the original owner though. But onward!
The biggest OTP in the Tiger's Curse fandom is Kelsey (the main character) and Ren. In the first book, I did ship Kelsey and Ren but I'm now reading the third book in the series (Tiger's Voyage) and finding Ren to be very possessive of Kelsey and rude. So I'm now shipping Kelsey and Kishan (Ren's brother) .. my unpopular opinion I guess. Also, yes, it's a love triangle. Honestly, this whole series is just giving me a headache so don't count on my opinion haha.
I'm actually really hesitant about sharing this but hey, I'm going to be truthful. I didn't ship pynch (Ronan and Adam from the Raven Cycle) for a while. Me, one of the biggest Raven Cycle fans ever, yet I didn't ship the biggest OTP.
I'm mortified right now everybody.
I don't even know why I didn't ship Ronan and Adam back then .. they clicked so well?! I was so ignorant. I can now tell you that I do, happily, ship pynch and I'm going about my business a-ok.
Cheating a little bit here but, I need to talk about this OTP. So, apparently, people ship Percival Graves and Credence Barebone from Fantastic Beasts and Where to Find Them. I am so disgusted with this ship! If you saw the movie, you would of saw Percival using Credence (for his evil plans) and abusing him. Turning this toxic relationship into a romantic one is so terrible. Credence doesn't need to lean on or gather comfort from Percival.
Yes, I'm pretty upset over this fictional ship but what really upsets me is what it's representing. People actually get stuck in these toxic relationships and they're not living their "happily ever after". I can't believe that people think this is okay.
Definitely Cress and Thorne from the Lunar Chronicles. I did love how their relationship wasn't rushed but some parts were like "come on you two! just kiss!". I never did lose hope for this OTP though.
I feel like Albus and Scorpius from the Cursed Child own this one. These two had so much potential to go forward, together! I'm still bitter about their ending but in my heart (and head), these two are living their days together.
The Dregs (from Six of Crows) for sure. This murderous gang gives me life. Ok - that doesn't make much sense .. just read the book ya'll.
I wouldn't say Margo and Quentin from Paper Towns is an OTP I adore but I did enjoy their relationship much more in the book than the movie. I despise the whole movie in fact. But that's a discussion for another day.
This may come across as surprising (because a) this is the biggest TMR ship and b) half of my ships are m/m ha) but I don't really ship Thomas and Newt from the Maze Runner. I saw these two (and Minho) as best bros, just trying to survive .. nothing romantic. And anyway *cough* spoiler newt is dead (still crying how about you) and guess who killed him?! thomas so *cough* just throwing that out there.
Currently (because I can't pick a favorite) it's Aristotle and Dante from Aristotle and Dante Discover the Secrets of the Universe because I'm aching for their sequel, their movie, their love and hugs plus warmer weather. Whenever I think of summer (aka warmer weather) I immediately think of Ari & Dan and then the world seems alright.
I can't pick an all time favorite OTP - no way. I can pick the first OTP that stole my heart! That would be Grace and Sam from Shiver. Such an adorable OTP.
Well, there you have it, the OTP tag! It took a while but I had fun with it. Now, who's your favorite BROTP? Most hated OTP? Fill me in!
I can't get over how much I want Albus and Scorpius to be canon. They're so cute, I'm so in love with them.
YOU DIDN'T SHIP PYNCH?! Omg Anna I never knew this piece of information from you LOL! Thank goodness you changed your mind haha! Gosh I agree with you so much here. Ari and Dante, the Dregs, Albus and Scorpius. Maybe I would have liked Cursed Child a whole lot more if they were a couple.
EMILY I KNOW IT'S TRAGIC WHO WAS I BACK THEN?! I'm so glad. Hmm understandable!
I didn't even realize that Credence and Graves was a ship... why, people?
I know right? I'm just disgusted with the fandom.
THERE'S A MOVIE FOR ARISTOLE AND DANTE AHHHHHHHHHH!!!! I'm so pumped for this. It was one of the first LGBT books I read (because of my book competition) and the writing was just SO. GOOD. Throne and Cress are also the most adorable things ever. I want to hug them so many times.
I KNOOOOOOW I'M SO EXCITED!! Yesss - AADDTSOTU is so beautiful. <3 Me too!
This is such a great tag!
I agree with you about Credence and Graves. Why would anyone ship them?
Yes, Cress and Thorne took forever to get together!
I wonder the same, Jollygirl.
Yay! Ari & Dante are so amazing.
Great answers! I also don't know how people can ship Credence and Percival, it's like shipping Hermione and Snape! (and yes, it exist). It's so toxic and Percival never once show kindness to Credence so how could people ship them??
Thank you! Uuuggghhhh I forgot about that ship (thanks goodness). So disturbing! I don't know why, Tasya. I wonder the same thing.
Haha me too! Aw thanks and yay!


A series of stamps bearing Syracusean coin (above left) were issued from 1953 to 1977 as above. In 1964 on 6th December, a set of stamps (right above) was issued to celebrate the 6th Stamp Day and depicted six Italian sports stamps within its own design.
My collection of stamps of Italy contains these two series and many others stamps that were issued in the period 1955-1970 as would be recalled by the collectors. If someone has more details on these stamps, I shall be too grateful and would update this post.


text:
Poland: Combi Systems on the Rise
Turkey: High-quality Solar Hot Waters across Earthquake Area
Serbia: "Conditions for Solar Thermal Continue to Improve"
Costa Rica: Training Course at EARTH University
Germany: No Upturn in 2012
ESTIF anniversary: 10 years of strengthening the solar heating and cooling sector
The European Solar Thermal Industry Federation (ESTIF) celebrated its ten-year anniversary with around 70 guests in Brussels, Belgium, at the end of November. The organisers of the event remembered the ESTIF founders presented them with the first pieces of the anniversary cake. The former and newly elected President, Robin Welling, also lauded the milestones of the young organisation. ESTIF has achieved great success in bringing solar heating and cooling on the agenda of the European Commission. It is now a good sign for ESTIF's future that a member of the German heating association BDH was elected to the ESTIF board the day after the celebration.
(Photo above ©Caroline Lessire)
by Marcin Czekanski
The Polish population is becoming more and more interested in combi solar thermal systems: the share of residential combi systems for hot water and space heating which are subsidised by the grant scheme of the National Fund for Environmental Protection and Water Management, NFOŚiGW, increased from 13% at the beginning of this year to 18% in October. The growth in absolute numbers was even more impressive. Whereas only 100 combi systems were installed in January, there were 377 - or more than three times as many - new installations in October, according to NFOŚiGW data. The total number of subsidised residential systems between January and October 2012 was 16,830, of which 16% were combi systems (2,730 systems).
Turkey: High-quality Solar Hot Water Systems across Earthquake Area
Turkish collector and tank manufacturer Ezinç Metal San supplied, installed and commissioned more than 11,000 of these systems. Another 1,355 systems came from solar thermal system producer Ouraset, while several other suppliers delivered and set up the remaining installations. "We are deeply saddened by this great human tragedy. We have put a lot effort into improving the quality of life of the survivors in the shortest time possible, in order to contribute to the normalisation of life in the city," Hakan Alas, General Manager of Ezinç, says. The project was initiated by the Housing Development Administration TOKI that required uncommonly quality standards for the domestic Turkish market: in addition to the local TSE certification, the collectors are closed-loop pressurised systems, which include highly selective copper absorbers and enamelled tanks, and have a Solar Keymark certification.
by Vladislava Adamenkova
The solar thermal market in Serbia has grown noticeably over the last two years. Most solar thermal projects are realised in the public sector, in which installations have been subsidised for a few years now. Solarthermalworld.org spoke with Miroslav Lambic, Chairman of the Serbian Solar Association Srbija Solar, about the market situation and the industry. The association estimates that more than 8,000 m2 of solar collector area have been installed in Serbia over the last five years. Lambic supervised the drafting of a 300-page study on the Serbian solar thermal market called "Solar Atlas". The study was published in Serbian in September 2011.
An excellent campus, a highly motivated group of professionals and an abundantly sunny country: Martin Schnauss is very satisfied with his Costa Rican training course, which took place in the middle of November at the international campus of the Earth University, a two-hour drive from the country's capital, San José. Together with his colleague Katie Brown, Schnauss held the one-week training course about solar heating and cooling technology in cooperation with the German Renewables Academy AG (RENAC). The workshop addressed trainers and professionals from Costa Rica, as well as from the neighbouring countries of Honduras, Mexico and Guatemala.
Despite a good start, 2012 has not seen any upturn in the German solar thermal industry, as latest figures show. Carsten Kuhlmann from the heating manufacturers association BDH expects a newly installed collector area of 1.2 million m², which would be 5% less than in 2011. The number was part of Kuhlmann's presentation at the Forum Solarpraxis, a conference in Berlin, Germany, at which scientists, associations and industry representatives discussed the future of solar heating and cooling at the end of November. The decline in the sales of solar thermal systems is not a result of low sales in the German heating sector in general, as Kuhlmann points out. The overall sales figure for new heating systems in Germany has increased by 6% between 2011 and 2012.
France: Solar District Heating with Energy Costs around 0.06 EUR/kWh
Cyprus: Increasing Efficiency Through Replacing old Systems
Canada: Total Collector Sales Drop by 29%
India: Flat Plate vs Vacuum Tube Technology
Italy: Conference Highlights Installers' Key Qualification Issues
Europe: 3,000 m² Collector Area at Three STACCATO Projects


You haven't mentioned any details about the problem that is troubling you. I would like to help you with first grade printable math homework as it was my favorite topic in math. I also recommend using a really good product called Algebrator. This is the best that I have encountered to help math students. But make sure you use it to learn the subject and not just to copy and submit your homework.
I fully agree with that. It truly is a great program. Algebrator helped me and my classmates a lot during our exam time. We went on to get a better grade than we could ever have thought of. It explains things in a lot more detailed manner, than a instructor ever could, in a class. Moreover, you can read one solution again and again till you actually understand it, unlike in a classroom where the teacher has to move on due to time constraints. Go ahead and try it.
Algebrator is the program that I have used through several math classes - Remedial Algebra, College Algebra and Remedial Algebra. It is a truly a great piece of math software. I remember of going through difficulties with function composition, system of equations and function composition. I would simply type in a problem from the workbook , click on Solve – and step by step solution to my math homework. I highly recommend the program.


text:
A scene from the SBS slow-TV documentary The Chocolate Factory: Inside Cadbury Australia. Supplied
Three hours of sweet viewing for chocolate lovers
WORDS: SEANNA CRONIN
Over the past three years SBS has encouraged viewers to slow down with its series of slow-TV programs.
Hours of footage of train and boat journeys made for a meditative experience in front of the telly and now there's a sweet new twist on the genre.
The Chocolate Factory: Inside Cadbury Australia, SBS's fourth slow-TV iteration, is a visual feast that will tantalise the tastebuds as well as educate.
Cameras follow the production of the Easter egg and bunny, the company's best-selling Easter products
To produce 477 million eggs and 14 million bunnies, Cadbury needs 6,014 tonnes of cocoa, 87 million litres of milk and 54 million kilograms of sugar.
"It was lovely being around the smell of the factory, but we couldn't touch anything. We did get the occasional bar of chocolate but it wasn't as alluring as one might think," says Mint Pictures' Adam Kay, who also produced the slow-TV programs The Ghan, The Indian Pacific and The Kimberley Cruise.
Chocolate Easter eggs take shape in a scene from the slow-TV documentary The Chocolate Factory: Inside Cadbury Australia. Supplied
"From a filming point of view it was absolutely a harder one to pull off. Going into a factory - and this was pre- COVID 19 - every time we moved rooms we had to wash down, change our overalls, put new gloves and hairnets on and wash down our equipment. I can only imagine what it would be like now.
"It was also incredibly challenging to select the right equipment to work in tight spaces and adhere to Cadbury's good food policy, which is pretty intense if you read the fine print.
"Without giving away trade secrets, there were lots of GoPros used and a lot of remote filming. Once we set up the cameras we couldn't get to them so we had to trust it. They couldn't stop production for more than a minute or two.
"For Cadbury to open their doors to this and allow small cameras to be put on those machines where a lot of IP (intellectual property) could potentially be an issue, they were absolutely amazing. "
The three-hour documentary takes a paddock-to-plate approach by following the chocolates' journey from the raw ingredients to the factory floor and, eventually, supermarket shelves.
A few of the 14 million Easter bunnies Cadbury will produce this year in a scene from the slow-TV documentary The Chocolate Factory: Inside Cadbury Australia. Supplied
"We go right back to the start of the hourney in the sugarcane fields in Mackay and the dairy farms in Tasmania," McKay says.
"When SBS set the challenge of moving the genre forward, as the director I wanted to maintain great production values and incorporate a journey - which is one of the founding principals of what slow TV is - with a multilayered storyline.
"Within this show are 60 graphics which tell the multicultural story of Australia through the prism of chocolate. For example, the Maltese workers were the first people who helped the sugar industry in Far North Queensland. They came from Malta and were pioneers of the sugar industry.
"It's a very clever way to tell the multicultural story of Australia."
While the documentary was always slated to air over the Easter long weekend, McKay says the slow TV concept has taken on a new meaning with much of the country homebound to combat the spread of the coronavirus.
"I think timing is everything in life. I think it really will rate very well with what's going on," he says.
"Not that you shouldn't be watching the news but how much can we take in? This is a real chance to sit with the family at a safe distance, of course, and enjoy it.
"Before with slow TV you could say what was in it for kids? Why would kids watch a cruise or a train? This one is perfect for the kids. It may make them eat more chocolate (laughs) but it's the ultimate family viewing.
"You must sit down with a bar of chocolate and watch it."
The Chocolate Factory: Inside Cadbury Australia airs tomorrow at 7.30pm on SBS.
Big Cadbury myth that's actually true
cadbury easter eggs easter weekend sbs television 2020


Due to continuous awareness drive carried out by Sakal Media Group, the sale of banned nylon, synthetic and glass-coated (Chinese) manja has gone down. On Thursday, a team of Sakal Times and Sakal reporters along with Pune Police carried out an investigation at Bohri Ali and Bhavani Peth.
Pune: Due to continuous awareness drive carried out by Sakal Media Group, the sale of banned nylon, synthetic and glass-coated (Chinese) manja has gone down. On Thursday, a team of Sakal Times and Sakal reporters along with Pune Police carried out an investigation at Bohri Ali and Bhavani Peth. However banned nylon thread was sold by not a single shop when a team of reporters posed as customers.
However, reporters found a group of young children hopping from shop to shop in search for 'Tungus' Manja, which is coated with glass powder and was banned by the National Green Tribunal in 2017. The group of youngsters said that this type of thread is being sold in the fringe areas and according to them, buying this thread is essential to win the kite fights. The youngsters seemed oblivious to the fact that many have lost their lives due to this deadly thread in the last one year.
Last year during Makar Sankranti, Suvarna Manohar Mujumdar (46), a manager with Sakal Media Group succumbed to injuries due to the banned manja.
Team Sakal Times carried out an exercise visiting shops of manja and kite vendors posing as customers seeking Chinese manja. The four shops selling manja and kites at Bohri Ali said they do not keep any stock of the banned manja, but a shop at Bhavani Peth told the team to give some cash in advance and collect the Chinese manja after some time.
The team went on investigating and reached Chaman Shah Chowk where they met a manja and kite seller. While interacting with him, the seller informed that the Chinese manja is being sold and manufactured at Bhavani Peth near Dulha Dulhan Qabristan (Muslim cemetery).
After getting this information, Team Sakal Times tried to find out whether the Chinese manja is really being manufactured in Bhavani Peth.
So on the next day, i.e, on Thursday, Team Sakal Times and Sakal along with Pune Police carried out a raid at Bhavani Peth near Dulha Dulhan Qabristan (Muslim cemetery) and found a bunch of manja with some raw materials for making manja on the cemetery premises.
They also carried out a raid at Bohri Ali, Raviwar Peth. After reaching the spot, the police told a shop owner to show them all the stock of manja in his warehouse. The police checked the entire warehouse but Chinese manja was not found. However, API Vaibhav Pawar has taken a sample from Raviwar Peth and will be further investigating it.
Meanwhile, Team Sakal Times heard that some young boys were looking for banned manja and to help them find the nylon manja, the children of that area took them to a store located near the raiding spot. Team Sakal Times followed them but they disappeared. This also proves that the banned manja is sold in the market but not openly.


text:
\section{Dumb Holes}
Black hole evaporation\cite{Hawking} was one
 of the most surprising predictions of the field of
quantum field theory in curved backgrounds.
Since the phenomenon has not
 been observed experimentally, it is of crucial
importance that the assumptions
 underlying the prediction be examined
especially carefully so as to try to understand the
process as deeply as possible.

One of the most unsettling features of the derivation is the
dependence of the  derivation on the behaviour
 of the fields at arbitrarily high frequencies. In fact, if we trace,
  in the usual derivation, the origin of the thermal emission
 from a solar mass sized black hole a second after the formation
 of the black hole, that thermal radiation has its origin in frequencies
 in the incoming (vacuum) radiation   of the order of $e^{10^4}$
 (where any units make only trivial changes in the exponent).
 Since $\hbar \omega$ for such frequencies correspond to
masses vastly larger that the mass of the universe, it seems
 certain that the quantum gravitational effects of such frequencies
 would completely alter the behaviour of the field at such scales.
 Would such quantum gravitational effects also destroy the thermal
 emission from the black hole?

Since we have no quantum theory of gravity, this question is
difficult to answer. However, the thermal emission is not only
 characteristic of black holes, it is also characteristic of dumb holes,
 the sonic analog of black holes\cite{Unruh}\cite{Jacobson}.
A dumb hole forms when the
 velocity of the fluid exceeds the velocity of sound at some
closed surface. That surface forms a sonic horizon, an exact
 sonic analog of a black hole horizon. As I showed in 1981,
the propagation of sound waves in such a hypersonic fluid
flow are exactly
 the same as the propagation of scalar waves in a black hole
spacetime.

Since the derivation is not commonly known, it worthwhile
repeating it here.
The isentropic equation for fluid flow in a medium which is has an
equation of state $p=p(\rho)$ is given by
\begin{eqnarray}
\rho \left(\dot {\bf v} +{\bf v}\cdot \nabla {\bf v} \right) = -\nabla
p(\rho)
\cr
\dot\rho + \nabla(\rho{\bf v})=0
\end{eqnarray}

I will assume that the flow is irrotational, so that we can write
\begin{equation}
{\bf v}= \nabla \Phi
\end{equation}
The first equation can then be written as
\begin{equation}
\nabla \left( \dot \Phi + {1\over 2} {\bf v\cdot v} + h(\rho)\right) =
0
\end{equation}
where $h(\rho) = \int {dp\over \rho} $, from which we get Bernoulli's equation
\begin{equation}
\dot \Phi + {1\over 2}{\bf v\cdot v} +h(\rho) =0
\end{equation}
(The time dependent constant of integration can be
absorbed into $\Phi$).
We now introduce the small perturbations of $\Phi$
and $\rho$ about the background flow, defining
$\phi=\delta\Phi$ and $\psi={\delta \rho\over \rho}$.
 We get the equations
\begin{eqnarray}
\dot\phi + {\bf v}\cdot\nabla \phi + c^2 \psi =0
\cr
\dot\psi +{\bf v}\cdot \nabla \psi +\nabla^2\phi
+\nabla ln(\rho)\cdot\nabla\phi=0
\end{eqnarray}

where $c^2 = { \rho} {dh\over d\rho}= {dp\over d\rho}$.
 Dividing the first equation by $c^2$ and adding taking
 the derivative with respect to
${d\over dt} +{\bf v}\cdot\nabla+\nabla\cdot {\bf v}$ we
 finally obtain
\begin{equation}
{1\over \rho}\left({d\over dt} +{\bf v}\cdot\nabla
+ \nabla\cdot {\bf v}\right) {\rho\over c^2}
 \left( {d\over dt} +{\bf v}\cdot\nabla \right) \phi
- {1\over \rho} \nabla \cdot \rho\nabla \phi=0
\end{equation}
Now, this is exactly the equation of motion
for a scalar wave in the metric

$$
\sqrt(-g) g^{\mu\nu} =
 \rho\left(\matrix{ c^{-2} & {v^i\over c^2}\cr {v^j\over c^2} & {v^iv^j\over
c^2}
- \delta^{ij}\cr}\right)
$$
or in four dimensions
$$
g_{\mu\nu}= \rho\left(\matrix{c^2-{v^2} & v^i\cr v^j & -\delta_{ij}\cr}\right)
$$
If the flow is stationary, we can define
the Killing vector
\begin{equation}
\zeta^\mu=\delta_0^\mu
\end{equation}
and find the Killing Horizon
at the point where
$c^2=v^2$. If ${v^i\over  {(c^2- v^2)}}$ is an integrable vector, we
can also define
$d\tau= (  dt+ {v^i\over {(c^2- v^2)}}dx^i)$ and  get
the metric
\begin{equation}
ds^2= \rho ((c^2-v^2)d\tau^2
- ( \delta_{ij} +{v^iv^j\over c^2-v^2})dx^idx^j
\end{equation}

If we furthermore assume that the flow is radial, ( in which case
 ${v^i\over  {(c^2- v^2)}}$ is always integrable) the metric becomes
$$
ds^2= \rho\left((c^2-v^2) d\tau^2
- {1\over 1-{v^2\over c^2}} dr^2 - r^2 d\Omega^2\right)
$$
where $d\Omega^2= d\theta^2 +sin^2\theta d\phi^2$
the usual angular metric.

By exactly the same arguments as for black holes,
one expects that this hypersonic flow will produce
thermal radiation with a temperature given by the
 ``surface gravity" at the black hole horizon, which
 in this case, results in a temperature
\begin{equation}
T= {1\over 2\pi} {dv\over dr}\vert_{v=c}
\end{equation}

However this prediction is again made on the assumption
 that these sonic equations are valid for arbitrarily short
wavelengths, a clearly ridiculous assumption. At wavelengths
 shorter than of order the intermolecular spacing,
the equations for sound waves
 deviate significantly from the low frequency
 continuum fluid approximation. Does this change in the fluid
equations at high frequency alter the prediction of thermal emission?
If it does, one begins to loose faith in the black hole predictions.
If it does not, perhaps it will give us a clue as to the real origin of
the
radiation.

While an exact solution of the fluid equations which fully took into account
the atomic nature of the fluid would be most welcome, I am unable to
supply it. However one of the most
 significant of the deviations from continuum fluid flow is the change
in the
 dispersion relation for sound waves. Typically at
 wavelengths approaching the inter atomic spacing, the group
velocity of the sound waves drops to values much
less than the low frequency value. Can this change
in the dispersion relation change the prediction of a
 thermal spectrum of sound waves emitted from such a dumb hole?

Thus the model I want to test is a model for sound waves
 within a fluid flow with a sonic horizon, or for scalar waves in
a background metric, in which
the dispersion relation at high frequencies differs from the
 usual low frequency form. In particular the model will
contain a high frequency cut off, i.e., a frequency above
which there are no normal modes for the propagation of
sound waves. As Jacobson has argued, a naive cutoff leads to not only a
suppression of the thermal emission, but also a suppression of all
waves and vacuum fluctuations from the hole. In our model however the cutoff
is to  arises naturally in the theory.

Because I am interested in the effects of changes at high frequencies
to the thermal emission, not in the detailed behaviour of a real fluid,
I will simplify the model so as to make the solution as easy as possible
while still retaining the features responsible for the thermal emission
in the
naive theory. Thus, to make the calculations easy, I will look at a two
dimensional model
(i.e., one space and one time) of the propagation of waves
 in a flowing medium and one in which the high frequency
 dispersion relation is non-standard.  I will also assume a
 constant velocity of sound (c=1), and
I will assume that
the background density $\rho$ is a constant. (Note that although a two
dimensional background flow cannot have a constant density and
a varying velocity, this assumption does not change the location
of the horizon, nor does it significantly alter the propagation
equation of sound waves  except at the very lowest frequencies.)
 The model equation of motion of the scalar waves I will use in examining
the effects of alteration of the high frequency behaviour of the theory
is

\begin{equation}
\left({\partial_t} + \partial_x v \right)
\left( \partial_t + v\partial_x\right)
\phi - F^2(\partial_x) \phi =0
\end{equation}
where the function $F(\kappa)$ is such that
 $F$ is an odd analytic function of $k$,
 $F(\kappa)=\kappa$ for small $\kappa$ and
 $F(\kappa)=Const$ for large $\kappa$. I.e.,
the dispersion function for the fluid ( taking v=0) is
$$\omega^2 = F^2(k)$$
Note that if $F(\kappa)=\kappa$ for all $\kappa$,
 then we have the simple equation
\begin{equation}
\left[(\partial_t +\partial_x v)(\partial_t+v\partial_x)
- \partial_x^2 \right] \phi=0
\end{equation}
for which we can make the change of variables
 $\tau= t+\int {vdr\over (1-v^2)}$ to get
\begin{equation}
\left[(1-v^2)\partial_\tau^2 - {1\over 1-v^2}\partial_x^2 \right]\phi =
0
\end{equation}
which has as solution
\begin{equation}
\phi(\tau,x) = f(\tau-z) +g(\tau+z)
\end{equation}
where $z= \int {dx\over 1-v^2}$
This is just the equation for a scalar field in a two dimensional black
hole
spacetime, where near the horizon, we can write
\begin{equation}
ds^2=2{dv\over dx}\vert_{v=1} (x-x_0) d\tau^2
 - {dx^2\over 2 {dv\over dx}\vert_{v=1} (x-x_0)}
\end{equation}

Just as for the black hole spacetime this leads to the
conclusion that the temperature of the emitted radiation is given by
\begin{equation}
T={1\over 2 \pi} {dv\over dx}\vert_{v=1}
\end{equation}

Alternatively, one can use the analytic continuation
 arguments to imaginary $\tau $ time and demand
regularity of the Green's function at the horizon in the regular Euclidean
metric
\begin{equation}
ds^2 = (1-v^2) d{\cal T}^2 + {1\over 1-v^2} dx^2
\end{equation}
with the identification
\begin{equation}
{dv\over dx}{\cal T} +2\pi = {dv\over dx}{\cal T} \label{identification}
\end{equation}
to arrive at the same conclusion.

However, as soon as we alter the dispersion function $F$, this
 analyticity argument fails. Under the analytic continuation
of $\tau= i{\cal T}$, the equation of motion for the field becomes
 complex, rather than real. One can draw no
conclusion from
 the behaviour of the Green's function for this complex metric,
 nor does one have any reason to demand that one make the
identification of the Euclidean ${\cal T}$ coordinate of eqn. \protect\ref{identification},
 since the equation of motion no longer has a  metric that
this identification makes regular.

\section{Numerical Solution}
In order to determine the consequence to the thermal emission
process of the  altered dispersion relation, we must go back to
 basic principles and calculate the Bogoliubov coefficients for
the conversion of ingoing positive frequency modes to outgoing
 negative frequency modes. I have carried out this calculation
numerically for a couple of  dispersion functions $F$.

As is usual, the particle production rate is equal to the overlap
integral between a negative frequency final mode and a positive
 frequency initial mode.
One can either start with a  positive frequency initial mode, propagate
this
through the region containing the black or dumb hole,
and calculate the negative frequency component of the final mode,
 or start with a  negative frequency final mode and calculate the
positive frequency initial component of this by propagation backwards in
time. It turns out that
 the latter is the easier to do numerically. Thus I start with some
outgoing purely negative frequency wave packet. I then propagate
 it backwards in time toward the horizon  until it is converted
to an initial pulse, and calculate the positive
frequency component of that initial packet.

It is here necessary to state, in the case of the non-trivial dispersion
relation, what I mean by positive and negative frequency.
 This is important because the  dispersion
relation implies that the notion of positive frequency  does not refer
to positive or negative sign of the frequencies {\it  per se}.
The
dispersion relation for constant velocity of fluid flow  looks like
\begin{equation}
\omega_\pm = vk \pm |F(k)| \label{disp}
\end{equation}
Even if $v$ is less than unity, there are values of positive $k$ for which
$\omega_\pm$ both are
positive, and values of negative $k$ for which both are positive.
In particular if $k>k_{c}$,
where $k_c$ is the solution to $F(k_c)=vk_c$, then both possible values,
$\omega_\pm$, are positive. ($k_c$ represents the wave vector at which the
phase velocity of the wave is zero.) Thus, in the sense of the sign of
 $\omega$, there are no positive frequencies at all for $k>k_c$ and no
negative frequencies at all for $k<-k_c$. However, the term `positive
 frequencies' or `negative frequencies' refers not to the sign of $\omega$ (although there is a
correlation for free fields) but to fixed frequency modes which
 have positive or
negative norm.

The field equations for the simplified two dimensional model for sound
waves (with constant density) can be derived from the action
\begin{equation}
I= {1\over 2} \int |\partial_t \phi + v(t,x) \partial_x \phi|^2 - |(F(\partial_x)
\phi|^2 dx
\end{equation}
which leads to a momentum
\begin{equation}
\pi(t,x)= \partial_t\phi + v(t,x)\partial_x\phi
\end{equation}
and an inner product
\begin{equation}
<\phi,\phi'>=-{i\over 2}\int (\phi^*(t,x) \pi'(t,x) - \pi^*(t,x)\phi'(t,x))
dx
\end{equation}
If we assume a solution with a definite frequency and wave number
 $\phi_{\omega,k}(t,x)=\tilde \phi(\omega,k) e^{i\omega t +kx}$
and  with constant $v$, we find that
\begin{equation}
<\phi_{\omega,k}(t,x),\phi_{\omega,k}(t,x)>
= \pm F(k) \int |\phi_{\omega,k}|^2
dx
\end{equation}
where $\omega$ is given by equation \protect\ref{disp}.
The definition of a positive frequency mode is that the mode have a
definite frequency and that the inner product be
positive, and thus that $\pm F(k)$ be positive. This selects the positive
sign for $k>0$ and the negative for $k<0$ and independent of the sign of
$\omega$.

One can rephrase the above discussion by stating that one is definig positive
frequency by the sign of the frequency in the co-moving frame. Defining
$x'=x-vt$, the mode $e^{i(\omega_pm t +k x)} $ becomes
$e^{i((\omega_pm-kv)t+kx)}= e^{i(\pm|F(k)| t +kx')}$.

In the case of the usual black hole situation, or the case in
which the dispersion relation is linear for all frequencies for
 the dumb hole,  we must propagate the packet backward in
time until it enters the region of black (or dumb) hole formation.
 During that back propagation, the packet is constantly blue shifting,
 so that the frequency of the wave by the time it reaches the formation
 time is absurdly high.  This is clearly not calculable numerically, but
 the process has been well understood analytically
 since Hawking's original calculation. In the case
 in which the dispersion relation is such that $\omega$
 becomes a constant
 at high frequencies, however, the calculation can be
 done numerically, and the positive and negative frequency
overlap integral can be computed numerically.

The dispersion function $F$ is taken to be given by
\begin{equation}
F(k) = k_0\tanh(\left({k\over k_0}\right)^n) ^{1\over n}
\end{equation}
where $k_0$ is the spatial frequency at which the dispersion
function changes from linear to constant.
This gives the length scale over which the dispersion
function leads to  a non-locality in the propagation equations of about
$2\pi/k_0$.
 The parameter $n$
determines the sharpness of the transition, with large $n$ implying
a very fast transition between the two regimes . I have studied what happens
 with $n=1$ and $n=4$ in most detail.
  A calculation with $n=\infty$ was also
 carried out and the results were essentially the same as those for $n=4$.
I will first describe the $n=1$ case in some detail, and then briefly
present the results for $n=4$.

 \figloc1{The soft  dispersion function ($n=1$) and corresponding group
velocity (dotted line) at zero fluid velocity. The transition wave number
$k_0$ is 512.}

A non-linear dispersion function means that the group velocity of the wave
when the fluid velocity,$v$ is $0$, namely
\begin{equation}
v_g = {d\omega\over d k},
\end{equation}
is not a constant, but depends on frequency. In figure \protect\ref{fig1}
 is plotted
$\omega $ and $v_g$, the group velocity, as a functions of $k$ for
the value of $n=1$.   One can now give a hand waving description
 of the effect of this non-trivial
dispersion function on the behaviour of a wave packet. I will describe
( and in the next section analyze) the problem by propagating an
outgoing packet backward in time.  Consider a long wavelength packet which
is an outgoing packet at late times. It travels outward away from the sonic
 horizon and against the fluid flow. As we go backward in time, it approaches
nearer and
nearer the horizon, until when it is sufficiently close it begins to blue
shift exponentially.
 Eventually the frequency becomes
 sufficiently high that the group velocity of the
wave is less that the velocity of the fluid at the horizon.
The fluid therefore
drags this outgoing packet in toward the hole ( or, since we are examining
the
system backward in  time, the packet at earlier times is further and further
from the horizon).  The packet seems to bounce off the horizon because of
the chage in the relation of the group and the fluid velocity of the
packet.

The naive picture is however complicated by the fact that the
 blue shift of the wave near the horizon is spatially very non-uniform.
 The front edge of the wave, the edge nearest the horizon, is blue
 shifted to a much larger extent ( at any given time) than
 the trailing edge of the wave. In fact the leading edge is blue shifted
to the final frequency long before the tail of the pulse has come near
the sonic horizon. Thus, it seems dangerous to   simply analyze the process
either in position space, or in momentum space.

\figloc2{ The velocity profile of the fluid used. The system is
assumed to have periodic boundary conditions. Note that $x\approx .7$
corresponds to the horizon. $x\approx .8$ is a Cauchy horizon.}

However, the numerical calculation seems
 to support this naive picture. In the numerical calculations, I have chosen
my space to have periodic boundary conditions with $x=0$ identified with
$x=1$. This was done primarily because of the difficulty of specifying
any other boundary conditions with the non-trivial wave equation with its
unusual dispersion relations. The velocity field is chosen to be given
by the
function
 \begin{equation}
v(x)= 1- .2 \tanh\left( 24\cos(2\pi(x-.25))+23\right)
\end{equation}
which is plotted in figure   \protect\ref{fig2}.
This function, which is constant with value of .8 ( in units where the
low wave number velocity of sound in a still fluid is unity) over most
of the range, was chosen precisely  to have a broad  range of constant
value with a smooth transition
to a region where $v>1$.
Although the region where $v>1$ is small, this turns out to be
irrelevant because the wave never penetrates that region.
The horizon occurs where $v(x)=1$, which is where $\cos(2\pi(x-.25))= -23/24$,
or
$x\approx .75\pm .046$. It is the lower value ($x\approx .7$) which represents
the horizon, while the other represents an irrelevant Cauchy horizon.

Another value of interest is the derivative of velocity with respect
to position, ${dv\over dx}$ at the horizon, since this gives the temperature.
 This is given by
\begin{equation}
{dv\over dx}\vert_{v=1} = .2(48\pi\sqrt(1-(23/24)^2)=.4\pi \sqrt(47)\approx
8.6
\end{equation}
 giving a temperature of
\begin{equation}
T={1\over 2\pi}{dv\over dx}= 1.37.
\end{equation}
(Recall that our units are such that $v_g(k=0)=1$, so that the thermal
wave number is $k_T\approx 1/T$ and the thermal wave length is  thus approximately
8, which is longer than the whole spatial domain.

  The final (late in time) wave  packets
 (recall that we will be propagating the packets
backward in time), chosen to be purely
negative frequency packets,  are
 thus complex, and are traveling away from the horizon. They are
confined as much as is possible to the region
 where the velocity
 is constant. They now travel (backwards
 in time) toward the
 horizon of the dumb hole, where
they begin to blue shift.
  Eventually their frequency becomes
sufficiently high that the group
velocity drops to less than unity and they
are dragged backward out of the region of
the hole to the region where the fluid
velocity is constant. In this region we can again
analyze the wave into its positive and
negative frequency parts, and determine the
Bogoliubov transformation quantity for this
particular wave packet.

This analysis must be carried out in the constant
velocity regions. Whether or not
a wave is "positive frequency" depends on its
time dependent behaviour. However,
both because of the finite size of the system,
 and because of the finite time for which one
can reliably carry out the integration, the
 temporal behaviour is difficult to use in
determining whether or not the wave is
positive frequency. However, in regions where the
fluid velocity is constant, one can directly
compare the relation between the field and its
first time derivative to determine its positive
and negative frequency components. We have
\begin{eqnarray}
(\partial_t-v \partial_x)\phi=\pi
\nonumber\\
(\partial_t-v\partial_x)\pi= F^2(\partial_x)\phi
\end{eqnarray}
Fourier transforming under the assumption that $v$ is a constant,
we have
\begin{eqnarray}
(\omega_\pm -vk) \tilde\phi_\pm(k)=\tilde\pi_\pm(k)
\nonumber\\
(\omega_\pm -vk)\tilde\pi_\pm(k)= F^2(k) \tilde\phi_\pm(k)
\end{eqnarray}
We can solve for $\omega$ and choose that
\begin{equation}
\omega_\pm= vk \pm |F(k)|
\end{equation}
with $\omega_+$ the positive frequency branch  for all values of $k$ (independent
of
the sign of $\omega_+$).

Now, given $\tilde \phi(t,k)$ and $\tilde\pi(t,k)$ we can split it into
its positive and negative frequency parts by
$\tilde\phi(k)=\tilde\phi_+(k)+\tilde\phi_-(k)$ and
$\tilde\pi(k)=\tilde\pi_+(k)+\tilde\pi_-(k)$, and the $\pm$ subscript
denotes the positive and negative frequency component.
Solving for the positive frequency part, we get
\begin{eqnarray}
\tilde\phi_+(k)= {1\over 2}\left(  (-i\tilde\pi(k)/|F(k)|
  +\phi(k)\right)
\nonumber\\
\tilde\pi_+(k)= {1\over 2}\left((\tilde\pi(k)
  -i|F(k)|\phi(k)\right)
\end{eqnarray}

The procedure now is to set up the initial (late time) wave as
a purely negative frequency wave,
propagate it backward in time until the
 resultant wave is again entirely (or as much as is possible) in the
 constant velocity regime. The resultant
wave is then analyzed into
 its positive and negative frequency
 parts, and the inner product of each of these
parts separately is calculated.  Note
 that the inner product of the full wave itself is
conserved, and this can be used as a
test of the integration routine. We finally get
 the actual Bogoliubov coefficients
for the wave from the future to the past (and thus also from the past to
the future) and can compare this with the thermal hypothesis.

One can  also calculate the expected
 Bogoliubov coefficient under the assumption that
the outgoing mode is thermally distributed,
as would be expected from the naive application
of the Hawking procedure to the wave.
 The wave packets used are not plane wave states,
and thus one must integrate the thermal
 factor over the spectrum of the outgoing wave to
find the expected amplitude of the thermal Bogoliubov coefficient.
 It this thermal factor equals the Bogoliubov
 coefficient calculated from
the evolution equations, then the
thermal radiation for dumb holes hypothesis is validated
even with this non standard high frequency dispersion function.

\figloc3{ The Real (solid line) and Imaginary (dotted line) parts of a
final pulse emerging
from the
dumb hole. The dispersion function has $n=1$ and $k_0=512$.}

 \figloc4{ An intermediate stage in the evolution backward in time of the
real part
of the pulse of figure \protect\ref{fig3}. Note that the front
 of the wave has crashed into
the horizon,
and been blue shifted to a high frequency pulse whose group velocity is
less than the fluid
velocity. The dotted line is the same calculation but at half the spatial
resolution as the solid line.}

\figloc5{ The pulse as it must have been initially to produce the outgoing
pulse of
figure \protect\ref{fig3}.  Note that it is an outgoing
 pulse but is being dragged in toward
the horizon by the
inflowing fluid. Again the dotted line is at half the resolution as the
solid line to give an estimate of the numerical errors.}

Figures 3  gives the real (solid line) and
imaginary (dotted line) parts of the wave packet
at the final time.  In figures \protect\ref{fig4} and \protect\ref{fig5}
 I show  the real part of the
 wave at two separate earlier times. In figure \protect\ref{fig4}
the wave is just interacting
with the horizon. Part of the wave has been blue shifted (going backwards
in time) and part is still at the final low frequency. Figure 6 gives the
incoming wave in the constant velocity region as it must have been in order
to produce the outgoing wave of
 figure \protect\ref{fig3}.  We note in figure \protect\ref{fig4}
that the front edge of the
wave has already crashed into the ``horizon" ($v=1$), been
 blue-shifted and begun to be dragged back out of the dumb hole
by the inflowing (which in the
reverse time direction is outflowing) fluid because its group velocity
 has decreased at the higher frequencies.
At the same time the trailing edge of the pulse is still traveling toward
the hole.

In figures \protect\ref{fig4} and \ref{fig5} I also show the outcome
of the numerical evolution for two
different grid spacings (the dotted is at half the
resolution of the solid
line)
 to give a feeling for the accuracy
of the integration. The key difference is in the
 phase velocity of the wave being dragged out
 of the hole. This is expected, because of
the finite differencing of the term $v\partial_x$
term in the equations.
The centered differencing scheme converts
 this term to $iv \sin(2k\Delta_x)/2\Delta_x$
instead of the exact $ivk$. This means that at
large $k$, the effective velocity of the fluid is
decreased by $sin (2k\Delta_x)/2k\Delta_x$.
 I.e., at high frequencies,
the effective fluid velocity is less leading to
a slightly smaller dragging velocity
for the high frequency wave, as is seen in the simulation.

\figloc6{ The spectrum of the final pulse of figure \protect\ref{fig3}.
Note that it is
purely positive wave number
and negative frequency.}

\figloc7{ The spectrum of the initial pulse of figure \protect\ref{fig5}.
The solid line is positive frequency components
while the dotted line is negative frequencies.
Since positive frequencies correspond to positive
wave number and vice versa, this still represents a purely outgoing wave.}

In figure \protect\ref{fig6} I give the  spectrum
 ( in k space) of the final outgoing wave
packet.
This wave has been designed to be  purely negative
 frequency, left traveling and concentrated in the region where the
velocity is constant. It represents a wave
packet traveling  away from  the hole against the inflowing fluid flow.
 In figure \protect\ref{fig7} we have the spectrum corresponding to figure
\protect\ref{fig6}
, divided into
positive and negative frequency parts, again
in $k$ space. The dotted line is the negative frequency components
while the solid line represents the positive frequency components.
We note that to very good accuracy,
the interaction with the horizon has left
the wave as a wave purely traveling to the left
( even though
 the fluid velocity is now sufficiently high to drag
the left traveling wave to the right). The positive $k$ modes
are negative frequency while the negative $k$ modes are positive frequency.

\figloc8{ A narrower final pulse but otherwise the same as in Figure
\protect\ref{fig3}.}

\figloc{9}{ The initial pulse which must have produced figure
\protect\ref{fig8}.}

\figloc{10}{The spectrum of the final pulse of figure \protect\ref{fig8}.}

\figloc{11}{ The positive and negative frequency spectrum corresponding
to
figure
\protect\ref{fig9}.  Note the much smaller positive frequency
 components than in Figure
\protect\ref{fig7}. Note that the
power which has not been blue shifted corresponds to components of the
initial packet whose
group velocity was already of the order of or less than .8, the minimum
velocity of the
fluid.}

Figures \protect\ref{fig8} and \protect\ref{fig9}
 give the final and initial wave
 packets for another higher frequency pulse
while figures \ref{fig10} and \ref{fig11} give the spectra of these
 pulses again split into positive and negative frequency parts.
We see in figure \protect\ref{fig11} a much smaller conversion
of positive to negative frequency, as would
have been expected from the higher frequency of the initial pulse.
All of these cases are for the $n=1$ dispersion function.

Let us now compare the above with the value
for the total Bogoliubov transformation
expected on the thermal hypothesis.

Given the final mode represented by figure \protect\ref{fig3}
or \protect\ref{fig8}, the expected number
of particles resident in this mode in a thermal state of temperature $T$
is given by
\begin{equation}
\beta_T={1\over {\cal N}}\int {e^{-\omega T}\over 1- e^{-\omega T}}
\left(\tilde\pi^*(k)\tilde\phi(k)-\tilde\phi^*(k)\pi(k) \right)dk
\end{equation}
where $\cal N$ is the normalization factor
\begin{equation}
{\cal N} = \int \left(\tilde\pi^*(k)\tilde\phi(k)
-\tilde\phi^*(k)\pi(k)\right) dk
\end{equation}
On the other hand, the expected number of particles in this mode, $\beta$,
if we assume that the
input state was in the vacuum state is just given by the positive frequency
portion of the initial wave form ( the Bogoliubov coefficient).
This is just the norm of the
positive frequency part of the normalized wave.

Comparing the two values, we find for the low frequency pulse in
 the soft ($n=1$ ) dispersion function case  that
\begin{equation}
\beta_T= .02302; ~~~~~~~~ \beta= .02336
\end{equation}
while for the high frequency pulse
\begin{equation}
\beta_T=.0005364;~~~~~~~~ \beta=.0005545
\end{equation}
In each case the Bogoliubov estimate of the particle
 production in that particular pulse is essentially the
same as the thermal estimate. The change in high
frequency behaviour of the theory makes little or
no difference to the expected thermal output from
 the dumb hole. ( I suspect the error to be related to the
fact that the final wave pulse is not entirely contained within the
constant velocity region.)

\figloc{12}{  The relation between $\omega$, the temporal frequency, and
$k$ the wave number in the constant velocity ($V=.8$) region . The various
branches  (positive and negative frequency and right and left moving) of
the dispersion relation are labeled.}

Moreover, in addition to the integrated Bogoliubov transformation, one can
test whether the full spectrum itself of the outgoing radiation is thermal.
Since
the
velocity in the simulation is time independent, the frequency of any wave
in the
continuum, infinite spatial section case is conserved.  Consider an final
left moving pulse, contained entirely in the constant velocity region,
with components
$\tilde \phi(k)$. For any value of k, there are two possible
 values for the frequency $\omega$ as given in figure \protect\ref{fig12}.
Since the pulses are left moving pulses, the relation between
the frequency  $\omega$ and $k$ is given by the
left-moving branch labeled as such in the figure. Since the final
pulse is chosen to be a purely negative frequency pulse, it is, as mentioned
previously, composed of purely positive values of k. Now evolve the wave
backward in time until one has evolved it past its interaction with the
horizon and back out into the region where the velocity is a constant.
Because the problem is time independent, the frequency $\omega$ is conserved.
Thus the amplitude of the wave over some finite frequency regime must be
the same.
Furthermore, we have already noted that the left moving wave remains a
left moving wave, and thus remains on the same left moving branch of
the dispersion relation.

This amplitude is given by
\begin{equation}
\int \tilde\pi^*(t,k) \tilde\phi(t,k) dk
\end{equation}
However, on the left moving branch, we have a definite relation between
$\omega$ and $k$, and between $\tilde\pi(t,k)$ and $\tilde\phi(t,k)$. In
particular for the left moving branch, $\tilde\pi(t,k)= +F(k)\tilde\phi(t,k)$.
Thus, we have that the magnitude of the wave over a frequency interval
$d\omega$ is
\begin{equation}
\int F(k) |\phi(t,k)|^2 {dk\over d\omega}d\omega
\end{equation}
where the integral is over all values of $k$ for which $\omega(k)$ has
the desired
value. From the plot we see that along the left moving branch there are
three
values of $k$ for any value of $\omega$ near zero. If we choose our initial
pulse to have $k$ positive, two of these lie on the negative frequency
branch, and one lies on the positive frequency branch. Now the initial
pulse is chosen to be non- zero only for small values of $k$. After the
interaction with the horizon, the pulse
has been blue shifted, and has non-zero values for $k$ lying near $\pm k_c$,
the
wave number where the phase velocity of the waves in the constant velocity
regions ($\omega(k)/k$) is zero.

Let us define the three values of $k$ at which the value of $\omega$ is
the same as $k_i$, for the value of k nearest $k=0$, $k_n$ for the nearest
value of $k$ to $+k_c$ and $k_p=-k_n$ for the value nearest $-k_c$.  Under
the thermal hypothesis, the initial pulses, obtained by transporting the
final pulse backward in time, will be composed of positive and negative
frequency components, with the two magnitudes in a frequency interval related
by
\begin{equation}
|F(k_p)\tilde\phi(k_p)^2/v_g(k_p)|
= e^{-\omega(k_i)/T} |F(k_n)\tilde\phi(k_n)^2/v_g(k_n)|
\end{equation}
where $v_g(k)= {d\omega(k)\over dk}$ is the group velocity at wave vector
$k$.
Furthermore, we should have
\begin{equation}
|F(k_p)\tilde\phi(k_p)^2/v_g(k_p)|= {e^{-\omega(k_p)/T} \over 1-e^{-\omega(k_p)/T}}
|F(k_i) \tilde \phi(k_i)^2/v_g(k_i)|
\end{equation}
Only if these relations hold will the Bogoliubov transformation satisfy
the thermal hypothesis for all final wave forms.

\figloc{13}{  The comparison between the thermal predictions for the positive
frequency component of the outgoing pulse and the actual positive frequency
component of the outgoing pulse.}

In figure \protect\ref{fig13} I have plotted the three functions
$|F(k_p)\hat\phi_i^+(k_p)^2/v_g(k_p)|^{1/2}$, the positive frequency part of the
initial pulse,
$|{e^{-\omega(k_p)/T}
 \over 1-e^{-\omega(k_p)/T}} F(k_i) \hat \phi_f(k_i)^2/v_g(k_i)|^{1/2}$,
the predicted positive frequency part of the inital pulse from the final pulse
and $|e^{-\omega(k_i)/T} F(k_n)\hat\phi_i^-(k_n)^2/v_g(k_n)|^{1/2}$, the prediction of
the positive frequency part of the final pulse from the negative frequency part
of the final pulse. These are plotted against the frequency $\omega$.
 These are for the final pulse of figure \protect\ref{fig3} and
associated initial pulse of figure \protect\ref{fig6}.  Note that
if the first two agree, the last one's agreeing is a test
of the conservation of the norm by the evolution.
  Because of the finite size of
the region and the periodic boundary conditions, only a finite number of
$k$ values are calculated, but it is clear that these three curves are
identical to numerical accuracy. Note that the temperature is of order
1.3, and this
graph thus represents about 10 e-foldings of the thermal function. Thus
 we can conclude that not only are
the two particular final wave forms chosen for the soft dispersion relation
thermal, but that any final wave form would be thermal. Thus despite the
change in the high frequency dispersion function, the output of the dumb
hole will continue to be thermal. The  spectrum, and not just the integrated
intensity,
 is a thermal spectrum.

 \figloc{14}{ The sharp dispersion function ($n=4$) and group velocity (dotted
line) at zero fluid velocity. The transition wave number here is taken
to be 1024. }

\figloc{15}{ The velocity profile for the sharp dispersion function. It
is scaled by a factor of 2 from that of figure
\protect\ref{fig1} to allow more room for the
constant velocity region}

\figloc{16}{The final pulse for the sharp dispersion function--- it is scaled
by a factor or 2 from figure \protect\ref{fig3}}

\figloc{17}{The inital pulse which would have produced the final pulse
of figure \protect\ref{fig4}
 rescaled by a factor of 1.5. Note that the initial pulse is more monochromatic
than that
of figure \protect\ref{fig6} because of the much sharper dispersion function.}

\figloc{18}{ The intensity of the positive frequency component of the initial
pulse of fig. \protect\ref{fig15}
together with the thermally scaled negative frequency spectrum of figure
\protect\ref{fig16} and that of
the final pulse of figure \protect\ref{fig3} (rescaled).
Note that the thermal hypothesis
does accurately
predict the relations between the various components of the spectrum of
the ingoing
and outgoing pulses. }

The dispersion function with $n=1$ present a relatively gentle transition
from the low
frequency linear regime to the high frequency constant regime. If we alter
the dispersion
function to give a much more sudden transition, namely the dispersion function
with $n=4$ (see fig. \protect\ref{fig14}),
does this alter the thermal spectrum of the emitted radiation? The answer
is no.
The sharp dispersion function has a much longer initial pulse for the same
situation as used above for the $n=1$ case. In order to allow the initial
pulse to be contained entirely within the constant velocity region, I have
scaled the problem by a factor of 2. Thus the transition $k_0$ in figure
\protect\ref{fig14} is larger by 2 to 1024, the velocity profile of figure
\protect\ref{fig15} has been rescaled by a factor of 2,
increasing the temperature to approximately 2.7. The
final pulse of figure \protect\ref{fig16} is just
 figure \protect\ref{fig3} rescaled by a faxtor of 2.
In figure \protect\ref{fig17} I present the initial
 pulse which must have produced the final
pulse of figure \protect\ref{fig16}
in the case in which $n=4$. Despite the far more sudden transition
between the regimes in the
dispersion function, the relation between the final and the initial pulses
is
 again accurately given by a thermal
relation as plotted in figure \protect\ref{fig18}.
Again the final positive and negative frequency components of the initial pulse
can be accurately predicted from the final pulse using the thermal hypothesis.

\section{Discussion}

Why are the results thermal, and what lessons can we learn from this simple
problem
for the more interesting one of black hole evaporation? The crucial lessons
seems
to be that, despite the naive derivations, black hole evaporation depends
neither
on the ultra high frequency behaviour of the fields near the black hole,
nor on
the behaviour of the field theory in imaginary time. The process of the
thermal particle
creation appears to be primarily a low, not high, energy phenomenon.
The black hole and dumb hole have  natural time scales- the the mass in
the former case, and the inverse gradient of velocity in the latter. The
behaviour of the fields near the horizon of the holes is governed by these
relatively (compared with Plank or atomic) time scales. In the vicinity
of
the hole, the fields experience changes on these scales. However,  as far
as the high frequency parts of the field are concerned, these time scales
are
very long and the changes are slow. The high frequency phenomena simply
adjust adiabatically to these slow changes. If the state is the vacuum
state at
high frequencies, it remains the vacuum. One would expect this to remain
true
no matter what the form of the theory was at those high frequencies and
energies.
It is only in the regime where the natural time scale of the hole is of
the same
order as the time scale of the field theory that these slow changes near
the hole
can make their influence felt. I.e., it is only for those
 wave whose frequencies are of
the order of 1/M for the black hole that anything happens.

On that time scale, the structure near the black hole is that the null
geodesics diverge
exponentially. The time between neigbouring outgoing
geodesics is exponential in the
 affine parameter along the geodesics. It is this exponential divergence
 ( shared by both the black hole and the dumb hole) that leads to the
thermal spectrum emitted by the hole. It is this exponential divergence
at the low frequency
time scale, and not at the highest frequencies of the theory that matters
for the thermal
emission.

One can encapsulate this freedom of the low frequency thermal
 emission from traces of the high freqeuncy
 behaviour of the theory by the phrase that
dumb holes (and thus by hypothesis also black holes)  have no
 quantum hair.
Just as the red shift at the horizon wipes out all traces of
 the rich complexity of classical material which could have
formed the black hole, it also seems to wipe out all traces
 of the quantum structures at high frequencies wich are red
shifted to form the thermal radiation from the black hole.

\section*{Acknowledgments}
I would like to thank Ted Jacobson who revived my interest in dumb holes,
and
pointed out in conversations and in ref.\cite{Jacobson} that one of the
crucial
effects of the atomic nature of matter is to alter
the high frequency dispersion
relation of the sound waves. Conversations with him
 have been very helpful to me
in understanding dumb holes.
I would also like to thank Matt Choptuik
who insisted through the years on
thinking about the stability of the solution scheme
 before coding rather than when the numerical
instabilities become obvious. Without the lessons
 he taught me   I would not have
solved this problem. In addition a conversation with
 him on the numerical techniques needed for this problem gave me the
courage to attack it. This research was
carried out under a Fellowship from
 the Canadian Institute for Advanced Research and with an NSERC research
grant.

redpajama_set_name: RedPajamaArXiv


Lawyer by day, Whimsy by night, owner Crystal loves mixed media, disco and lint. She believes every person has an artist inside them. Her motto she lives by, "never, never, never give up." Self-taught, she dances to the beat of her own bongo drum. In her alternate life she believes she is a country western singer.
Her art can be viewed at thequeenoftorts.blogspot.com.


Paresh has spent his career specialising in fintech, primarily in front office trading – working for global, tier-one investment banks across the UK and South Africa. Moving into the digital forefront, he is now the Blockchain Strategist for Standard Bank based in South Africa, ex-Chairman of Technology for the South African Financial Blockchain Consortium and Co-Founder of a blockchain startup. He also drives blockchain initiatives and communities across the country and is heavily embedded within the entrepreneurship and technology start-up sectors.


text:
Program helps low-income parents in Springfield become teaching assistants
SPRINGFIELD — The Department of Transitional Assistance recently announced a public-private partnership that would allow some recipients of its assistance in the Springfield area to intern and eventually become teaching assistants.
The department, which provides cash and food assistance to low-income residents, created the program after people with dependent children said they wanted more "career preparation programs that lead to direct hire," according to the announcement. from the Department.
And so he created two tracks: a program to prepare people for office jobs in health care institutions and another, in Springfield, that would prepare people to become teaching assistants, also known as paraeducators.
Anne Kandilis, director of the Springfield Works, said her organization, which seeks to connect low-income people with services, partnered with the Transitional Assistance Department's Works Coordinator to bring the program to the area. Springfield Public Schools and Holyoke Community College also accepted the program.
"We agreed that the paraeducator track was a great career and a much-needed program for our community," Kandilis said in a statement. "The DTA Works internship program will serve as a scalable model in building career pathways to living wage jobs in other occupations of opportunity' in our region."
The Department of Transitional Assistance also offers a six-week health management training program that includes a three-month paid internship in partnership with Massachusetts General Brigham and Project Hope.
Both are designed to be intensive preparatory programs created to bring people directly into high-demand jobs and economic mobility.
"The program is attractive because it prepares participants for an entry-level job with clear paths to continuing education, at no cost, as a first step towards a meaningful career and related to the participants' skills, interests and background, said Robert Frye. , a workforce development instructor at Holyoke Community College.
Interns will also work with a mentor, financial coach, and receive a monthly stipend, in addition to other supports such as childcare and transportation.
In addition, the Paraeducator Training and Internship class is a five-week job readiness training with two weeks of paraeducator job-specific training and an internship at a public school.
According to Frye, the program will prepare participants who do not have an associate's degree or college credits to enter the workforce as teaching assistants.
Internships provide practical job-readiness skills such as career search, resume building, interviewing, and networking, along with soft skills such as digital and financial literacy.
Frye said there is specific pre-skills training for paraeducators that will include legal, development and pedagogy, diversity, equity and inclusion, trauma-informed education, social-emotional skills and more.
Participants will prepare to achieve qualifying scores on the teaching assistant certification tests that they must pass before they are eligible to be hired by school districts.
Internships began this month and another round will begin in April.
"We are aiming for around 20 registrants," he said.
Interested families can check eligibility or complete an online application.
Translated by Damaris Pérez-Pizarro
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