Feb 19, 2015 After the formation of SIMA i.e. Sponge Iron Manufacturers . All input costs (administered pricing) are higher in India than overseas.
Find here Sponge Iron Plants manufacturers, suppliers & exporters in India. a range of sponge iron plant and other equipment to our clients at optimum prices.
Abstract. The author tries to foresee the future of Sponge Iron Making in India and forecasts that the metallur down the cost of steel making by a sizeable mar.
Jan 25, 2017 number of Sponge Iron Plants, Mini Blast Furnace units, Hot liquid steel by BOF and EAF/IF routes. Prices of steel are provided in Table6.
Abstract Iron ore and coal together account for about 72% of cost of input materials in Indian steel plants. integrated steel plants and Scrap / DRI / Sponge Iron route in . Major steel plants in India consume medium to high grade iron.
Sep 9, 2008 CCCMC reference prices for Indian iron ore imports. ANNEXURE Iron Ore CLO at Plant and Sponge Iron Gas Based price Trend. 0. 5000.
Indian Steel Industry SPONGE IRON MANUFACTURERS ASSOCIATION. 2. In India, DRI mainly used in India as a substitute of steel melting scrap in steel making increased maintenance cost with capital repairs of vital equipments.
Thanks to the high capital cost and a higher gestation period in setting thousands of induction furnace based steel plants are operating in India India has been highly successful in substituting steel scrap with sponge iron for steel making.
sponge iron Latest Breaking News, Pictures, Videos, and Special Reports from Steel manufacturing cost to rise as power out of GST Steel Ministry to PMO.


Disability Articles By Midwest Disability, P.A.
If you are like many people seeking disability benefits, you have questions about the process, your medical impairments and other aspects of life with an illness or injury. The attorneys at Midwest Disability, P.A., provide information about many common issues with Social Security disability benefits and medical impairments. To learn more, review the links to our articles below. You can also check out our blog or review our resources.
To find out more about your case, ask for a free disability evaluation from our law firm. Call our lawyers at 888-351-0427 or contact us online.


text:
Use the Jekyll and [Ironsummitmedia theme](http://ironsummitmedia.github.io/startbootstrap-clean-blog-jekyll/) to build my blog.

###[My blog  →](http://Marsrocky.github.com/)
=======
Marsrocky.github.io
===================

redpajama_set_name: RedPajamaGithub


text:
Page Links: https://fcsca.mizoram.gov.in/page/bpl-aay-aplp
AAY (Antyodaya Anna Yojana) Under AAY scheme the poorest among the BPL families are selected and issued AAY ration cards. Households having this card are issued 35 kgs (rice) at the rate of Rs. 3 per kg. The scheme initially targeted the 5% of the population who couldn't have 2 square meals a day. It now also brings into consideration BPL households headed by widows, terminally ill persons, disabled persons or persons above 60 years with assured means of subsistence or societal support. The identification of AAY families and issuing of distinctive ration cards is the responsibility of the state government. The village councils finalize the list of AAY families in the village.
PHH (Priority Households) Households having PHH ration cards are issued 8 kgs of rice monthly per Beneficiaries at the rate of 5 Kgs at the rate of Rs. 3/- and 3 kgs at the rate of Rs. 15/- per kg. 5 kgs is Central Scheme under National Security Act-2013 and 3 kgs is the state scheme. The scheme targets the really poor and vulnerable sections of the society such as landless laborers, marginal farmers and wage earners of the informal sections of the economy. The identification of PHH families is the preview of the state government and identification is made as per the estimates adopted by the central Government and distinctive ration cards issued. The village councils/ local councils finalize the list drawn up by the designated authorities.
Non-NFSA (Non-National Food Security Act) As the Department of Food, Civil Supplies & Consumer Affairs is entrusted with ensuring that essential commodities are under the Public Distribution System reach all citizens so as to ensure food security regardless of the individual's position in economically or otherwise, all those households who are not covered under PHH or AAY are issued ration cards nonetheless. Non-NFSA ration card holders are issued 8 Kgs of rice per beneficiaries at the rate of Rs. 15/- per Kg. This is to make the basic necessities of life within the grasp of all the citizens.
Page Created On: 8th Sep 16 12:13 PM
Updated On: 25th Jun 19, 4:54 PM

redpajama_set_name: RedPajamaCommonCrawl


text:
Événements
 22 février : découverte de l'antibiotique « streptomycine », le premier efficace pour le traitement des affections tuberculeuses.

Publication
 19 octobre : Joshua Lederberg et Edward Tatum publient leur découverte de la conjugaison bactérienne, un mécanisme de transfert horizontal de gènes entre bactéries .

Naissances

Décès
 20 février : Friedrich Ernst Krukenberg (né en 1871), ophtalmologiste allemand.
 28 mai : mort par pendaison du médecin et criminel de guerre Claus Schilling (né en 1871).

Références

Santé
Chronologie de la santé et de la médecine

redpajama_set_name: RedPajamaWikipedia


text:
Baltimore MD, Clean Water Action, Crude By Rail, Crude Oil, Derailment, Explosion, Keeping Watch on Earth News, Local land use authority, Local Regulation, Oil refineries
Baltimore council members propose ban on new crude oil facilities
October 20, 2017 Roger Straw
From an email by Jennifer Kunze, Maryland Program Organizer,
Clean Water Action
[See also the Baltimore Sun story, below]
Just wanted to share the exciting news that the Baltimore zoning code change to prohibit new or expanded crude oil terminals has been officially introduced! You can download the bill here, and here is some coverage of it in the Baltimore Sun and our local NPR station. Taylor and I would be happy to answer any questions about it!
Jennifer Kunze
Maryland Program Organizer
Website – Facebook – Twitter
Repost from The Baltimore Sun
By Ian Duncan, October 16, 2017
Two members of the Baltimore City Council want to ban new crude oil terminals from the city as part of an effort to limit the number of oil trains traveling through the area.
Council members Mary Pat Clarke and Ed Reisinger introduced a proposed change to the city's zoning laws Monday that would add the oil terminals to a list of banned facilities, ranking them alongside nuclear power plants and incinerators.
"Crude oil shipments are potential hazards to residents and entire neighborhoods," Reisinger said in a statement.
The council members said they were turning to the zoning code because federal law stops city authorities from directly regulating rail. They hope limiting the terminal capacity will mean there will be less interest in sending oil trains to Baltimore.
Two existing facilities in Baltimore would be allowed to stay but could not expand in any way under the proposal.
For years environmental activists have been sounding the alarm about crude oil that is transported by rail, which can lead to deadly explosions in the case of an accident. In 2013, 47 people died when a train carrying crude oil exploded in Canada.
Precise details of the shipments are scarce, but with the price of oil low, the practice is widely believed to currently be at a low ebb. Rob Doolittle, a spokesman for CSX Transportation, said no oil trains have operated in Baltimore or anywhere else on the company's network for months. Doolittle also said the company has never run dedicated oil trains through the city, but had moved small amounts of crude on mixed trains.
Clarke said the dip in the market meant it was the right time for the council to take up the proposed restrictions.
"It doesn't put jobs in jeopardy," she said. "We don't know when the marketplace may change. If it does we want to have already capped out the capacity of Baltimore facilities."
The operator of one of the existing terminals declined to comment; the other did not respond to questions.
Environmental groups say there's reason to think that if the price of oil picks up again, companies would seek to expand the number of terminals in Baltimore. That's what happened during the last boom several years ago, but the plans were blocked.
Jennifer Kunze, an organizer with Clean Water Action, said it makes sense to put limits in place now.
"This is really a preventative measure," she said.
Previous PostTrump Names Climate Denier to Head White House Environmental CouncilNext PostSturgeon County Canada: neighborhoods evacuated after train carrying crude oil derails


text:
Dec 23, 2015|Court Reporter, Court Reporters San Jose
Court Reporter: An Invaluable Resource
Court reporting agencies near San Jose provide a wide range of services to both attorneys and courts. Court reporters are highly trained professionals who undergo several years of skills training, which allows them to type accurately at incredibly high speeds. In addition to transcription services, court reporters can also provide the latest in video technology. Read on to learn more about why court reporters are invaluable to law firms and businesses alike.
Legal Depositions
Depositions are an essential part of litigating civil cases. For example, a law firm handling a medical malpractice case may need to depose countless witnesses, including physicians, nurses, hospital supervisors and staff, injured patients, and anyone else who may bear responsibility for the negligent act. Court reporters can accurately transcribe depositions for use later in court. In addition, a court reporter can certify and testify to the accuracy of a record. The ability to provide reliable and precise transcriptions at unparalleled speeds makes court reporters essential for law firms.
Court reporters can also convert transcripts into many different formats, making life easier for attorneys—and for the court. It is standard in court reporting to provide both paperless and electronic copies of a transcript. But court reporters can also create special condensed transcripts in many different formats. Thanks to new developments in court reporting technology, court reporters can also create CDs with scanned exhibits and file-formats including YesLaw, E-Transcript, PDF, LEF, and ACSII.
Corporate Assistance
Court reporters do much more than just provide litigation services, making them invaluable resources for many businesses. For example, court reporters also frequently offer notary services and interpreting services. Many court reporting companies offer document depository and reproduction services, as well. For example, court reporters can assist with document scanning and duplication and can Bates stamp documents. If your business has a great deal of paperwork and needs organization assistance, consider contacting a court reporter.
Are you a San Jose attorney searching for a trustworthy court reporting service? Look no further than Talty Court Reporters. Whenever and…


text:
Q: WPF Button icon gets mirrored, why? This Button looks fine (see screenshot) when defining the image as done below. Note that the shield shaped icon with the letter 'T' is visualized correctly.
<Button Command="w:MainWindow.BrowseTorrentSite">
    <StackPanel>
        <Image Source="../icons/kickasstorrent.png" />
    </StackPanel>
</Button>

When I want to rely on the buttons enabled state, the icon gets mirrored.
<StackPanel
      Orientation="Horizontal"
      FlowDirection="RightToLeft">
        <Button
            x:Name="KatButton"
            Command="w:MainWindow.BrowseTorrentSite">
            <StackPanel>
                <Image>
                    <Image.Style>
                        <Style TargetType="Image">
                            <Style.Triggers>
                                <DataTrigger
                                    Binding="{Binding Path=IsEnabled, RelativeSource={RelativeSource Mode=FindAncestor, AncestorType=Button}}"
                                    Value="True">

                                    <Setter Property="Source" Value="../icons/kickasstorrent.png" />
                                </DataTrigger>
                                <DataTrigger
                                    Binding="{Binding Path=IsEnabled, RelativeSource={RelativeSource Mode=FindAncestor, AncestorType=Button}}"
                                    Value="False">

                                    <Setter Property="Source" Value="../icons/kickasstorrent_disabled.png" />
                                </DataTrigger>
                            </Style.Triggers>
                        </Style>
                    </Image.Style>
                </Image>
            </StackPanel>
        </Button>
</StackPanel>

Note the shield shaped icon with the letter 'T' is now mirrored.
What is responsible for mirroring the icon?
If somebody has tips to debug this in whatever way possible, feel free to point me in the right direction!

A: The problem is in the parent StackPanel. If the StackPanel is defining the FlowDirection from right to left, the Image definition inherits this property which results in the flipped icon.
To solve this problem redefine left to right on the image itself.
    <StackPanel
        Orientation="Horizontal"
        FlowDirection="RightToLeft">
        <Button>
            <Image FlowDirection="LeftToRight">
                <Image.Style>
                    <!-- etc etc -->
                </Image.Style>
            </Image>
       </Button>
    </StackPanel>

redpajama_set_name: RedPajamaStackExchange


Check out our new building!
Modern and state of the art.
Same great food for amazing times with friends and family!
Plenty of fun for the entire family!
Great menu with Burgers, Wings and so much more! Cold Beer on tap and 8 HDTV's - There is not a bad seat in the house!!! Your home for ESPN College sports and NFL Sunday Ticket! Live music and karaoke!
A great place to enjoy a delicious meal with friends and family!
Make sure you ask your host/server about our daily specials!!
Visiting from Indiana and was impressed with the service, quality and taste of food. Loved the atmosphere and open to the elements design of the bar.
Always friendly, food is served quickly, and is oh so good!
Check out these great photos of our new building and menus!


text: export default <any>{};


text:
Q: asp.net C# evento onblur recarga pagina completa Buen día, tengo una página .aspx donde, dentro de un asp:UpdatePanel, existe un asp:TextBox al que le asigné un evento onblur, de la siguiente forma:
.aspx:
<asp:UpdatePanel ID="updatePanel1" runat="server" UpdateMode="Conditional">
  <ContentTemplate>
    <asp:TextBox ID="txt1" runat="server"></TextBox>
    <asp:Button ID="btn1OnBlur" runat="server" Visible="false" OnClick="btn1OnBlur_Click"></asp:Button>
  </ContentTemplate>
</asp:UpdatePanel>

.aspx.cs:
protected void Page_Load(object sender, EventArgs e) {
  //Asignar evento onblur
txt1.Attributes.Add("onblur",Page.ClientScript.GetPostBackEventReference(btn1,""));
}

protected void btn1OnBlur_Click(object sender,EventArgs e){
  if(txt1.Text.Equals("")){
    LlenarControles(); //...
  }
}

El evento funciona bien, pero el problema es que recarga la página completa, y no sólo el UpdatePanel. Si tengo otra función con otro control y se dispara el mismo evento, recarga la página una vez más y borra los cambios que había hecho el evento anterior...

A: No se alcanza a ver si tienes el ScriptManager definido
<asp:ScriptManager ID="ScriptManager1" runat="server">
</asp:ScriptManager>

Por otro lado puede ser la ausencia del trigger, te recomendaría realizar hoy en día esta clase de trabajos con el ajax convencional y no con los controles de Microsoft, pero en caso que sea necesario usarlo, esta página explica claramente como deberias realizarlo.

A: (Además de agregar el ScriptManager tal como menciona el usuario manu_rit en su respuesta), debes declarar en tu UpdatePanel el elemento Triggers y a su vez, el elemento AsyncPostBackTrigger.
Modificando tu código, quedaría así:
<%-- Recuerda colocar la etiqueta ScriptManager: -- %>
<asp:ScriptManager ID="ScriptManager1" runat="server">
</asp:ScriptManager>
<asp:UpdatePanel ID="updatePanel1" runat="server" UpdateMode="Conditional">
  <ContentTemplate>
    <asp:TextBox ID="txt1" runat="server"></TextBox>
    <asp:Button ID="btn1OnBlur" runat="server" Visible="false" OnClick="btn1OnBlur_Click"></asp:Button>
  </ContentTemplate>
  <Triggers>
    <asp:AsyncPostBackTrigger ControlID="btn1OnBlur" EventName="Click" />
  </Triggers>
</asp:UpdatePanel>

Revisa este enlace para que comprendas mas sobre el uso del UpdatePanel.
Understanding ASP.NET AJAX UpdatePanel Triggers

A: El problema que puedes tener es debido a que no esta encontrando la referencia al control. Tal vez con esta pequeña modificación sea la respuesta.
    txt1.Attributes.Add("onblur",Page.ClientScript.GetPostBackEventReference(btn1OnBlur,""));

Espero y funcione. Saludos.


Elevation Aerial Design and Consulting Inc. is an Accredited Training Provider of the Infrastructure Health and Safety Association (IHSA) offering the Ministry of Labour approved Working at Heights certification training. Public Working at Heights courses are offered on a regular basis or our professional instructors can come to your workplace to provide Working at Heights or customized fall protection courses that meet the OHSA standards with adaptations to your site specific needs.
Please contact us for a quote and needs assessment if you would like to book group training for your employees.
Personal Protective Equipment: All participants are required to bring CSA certified hard hat, steel toed boots and eye protection for the practical portion of the training.
Notebook, Pen and Highlighter: Taking notes and highlighting key sections of your workbook will aid in your retention of the information provided on this course.
Food and Nutrition: Participants are responsible for their own food. It is recommended you bring your own lunch, snacks and water for the day as leaving the facility for lunch may delay your return and ability to review class notes that lead into afternoon practical training sessions. The course will proceed on schedule and many participants benefit from networking with other trainees to share their experience over the lunch period.
Personal Fall Protection Equipment: We encourage you to bring your personal harness and any fall restraint or fall arrest devices. This is not mandatory as all fall protection equipment will be available, however, it is important you are familiar with inspecting and maintaining your own personal safety equipment. This is an ideal opportunity to compare new products available and evaluate the effectiveness of your personal equipment for different applications.
Elevation Aerial Design and Consulting appreciates that there are times when our customers need to cancel or make changes to their training. Due to the high demand for our courses, we have developed a cancellation policy that we feel is fair and allows our customers to cancel or reschedule their training when advanced notice is provided.
* Elevation will move your scheduled course date to another day, without penalty, when provided with 5 business days' notice.
* To receive a full refund, Elevation must receive notice at least 5 business days prior to the scheduled course date. Cancellations made with less than 5 business days' notice will not be refunded.
* For our customers booking private group training sessions (group minimum of 8 participants), a charge of $800.00 will apply if 7 business day's notice are not provided when cancelling the course.
If you need to move or cancel your course date, please notify our office immediately by calling 1 800-739-4992 during regular business hours (Monday to Friday, 8:30 am to 4:30 pm). If you are not able to speak with someone directly, please leave a voice message. We also ask that you clearly state in an email to info@elevationaerial.com the request to move or cancel your course or registration, and the reason for the move or cancellation.
We value the partnership with our customers and it is at the discretion of Elevation to modify this policy based on each individual circumstance.
The health and safety of our participants and our instructor is always our number one priority. Elevation reserves the right to waive all fees for cancelling or moving your program, given special weather conditions, that are beyond our/your control or are in the best interest of our instructor and your staff.
Elevation has an emergency number that allows you to speak to our Director of Training if there is a problem that requires immediate attention outside of regular office hours. Please use this number for urgent situations that cannot wait until the next business day.


"Gigant" Open tip container with automatic emptying device.For handling loads in different types of waste. Fully welded design and fitted to a robust bottom frame with fork pockets. Safe tipping design with heavy-duty gears, that control container tipping. Handle on the side that permits emptying manually.
The tip container up to a volume of 1100 L is powder coated in a very durable, structured finish, blue RAL 5005. Frame in grey RAL 7037. Volumes from 1600 L are wet enamelled in blue RAL 5005.
At an extra charge all tip containers are available in the following colours: Red RAL 3020, White RAL 9010, Orange RAL 2008, Yellow RAL 1018, Brown RAL 8017, Green RAL 6032, Grey RAL 7037 and Black RAL 9005.
Also available in a fully welded design: request a quote.
Possibility of a corrosion protection finish, approved for outdoor use. Request offer.
Flat or high cover in powder coated, grey RAL 7037 sheet steel.
Set of castors consisting of 2 fixed and 2 swivel solid rubber castors, diameter 160 mm and overall height 200 mm.


text:
module Dynflow
  module Semaphores
    class Aggregating < Abstract

      attr_reader :children, :waiting

      def initialize(children)
        @children = children
        @waiting  = []
      end

      def wait(thing)
        if get > 0
          true
        else
          @waiting << thing
          false
        end
      end

      def get_waiting
        @waiting.shift
      end

      def has_waiting?
        !@waiting.empty?
      end

      def save
        @children.values.each(&:save)
      end

      def get(n = 1)
        available = free
        if n > available
          drain
        else
          @children.values.each { |child| child.get n }
          n
        end
      end

      def drain
        available = free
        @children.values.each { |child| child.get available }
        available
      end

      def free
        @children.values.map(&:free).reduce { |acc, cur| cur < acc ? cur : acc }
      end

      def release(n = 1, key = nil)
        if key.nil?
          @children.values.each { |child| child.release n }
        else
          @children[key].release n
        end
      end

    end
  end
end


text:
−0 (ujemne zero) i +0 (dodatnie zero) – symbole używane w informatyce (dla odróżnienia dwóch reprezentacji zera w niektórych kodowaniach) i matematyce (do oznaczenia granic jednostronnych w zerze) oraz w architekturze i budownictwie.

Architektura i budownictwo
W architekturze i budownictwie symbolu ±0 używa się do oznaczania poziomu 0 budynku (zera budynku), tj. najczęściej poziomu posadzki parteru, względem innego układu odniesienia (np. n.p.m.).

Matematyka
W matematyce zapisy −0 i +0 oznaczają po prostu 0 (liczbą przeciwną do 0 jest 0). Czasami jednak symbolu −0 używa się w celu oznaczenia lewostronnej granicy funkcji w zerze, a +0 – do oznaczenia prawostronnej granicy funkcji w punkcie zero. Innymi często spotykanymi symbolami oznaczającymi wspomniane granice są 0− i 0+.

Informatyka
W informatyce symbolami −0 i +0 oznacza się dwa alternatywne sposoby zapisu liczby zero w liczbach zmiennoprzecinkowych oraz w niektórych kodowaniach liczb całkowitych (np. ZM i U1).

W arytmetyce liczb zmiennoprzecinkowych operacje na zerze ze znakiem określone są zwykle tak:

Pierwsze z tych działań może być wykorzystane do odróżnienia zera dodatniego od ujemnego. Sprawdzenie, czy dwa zera są równe, da nam zawsze prawdę, niezależnie od znaku tych zer.

Wynikiem poniższych operacji może być zarówno +0 jak i −0, zależy to od sposobu zaokrąglania (zwykle domyślnie jest to +0):

Poniższe operacje są niewykonalne i zwrócą NaN (nie-liczba) niezależnie od znaków zer i nieskończoności:

Zobacz też
 0 – zero

Komputerowe reprezentacje danych
Granice


two more vintage clothespin necklaces.
« a new take on an original design.
now i'm nostalgic. these little wooden objects tucked me into a time machine and whisked me not so far but away.
i'm thinking of summer. i'm thinking of sunshine and clean sheets. i'm thinking about the real "fresh scent", you know what i mean? i'm thinking of working hands, stiff socks, and sweet-smelling grass. i'm thinking of ballets of color rippling in the wind. i'm thinking of my grandmother. i'm thinking of women and work and tradition. i'm thinking of time.
i've made a couple of these necklaces in the past. and when they found homes, several people expressed interest in them. but since they're not an especially common object, at least ones this small, i only make them as they present themselves to me in my treasure-hunting…and the mood has to strike just right.
one vintage clothespin, capped with silver, hangs gently from an oxidized sterling silver chain, lightly buffed to add variation in the links. a silver "lace" detail that i made with the pressed print of cloth offsets the chain for the sweetest little interruption. wear this in the back or off to the side.
another vintage clothespin, capped with silver, hangs gently from the lightest of lavender silk cord. a silver disc allows the silk to move freely adjusting to the length that suits you best.
available in the shop until they're not.


text:
Appraiser Defense
Health Care Defense
Insurance Agent Defense
Realtor/Real Estate Defense
Expert Analysis and Opinions
Lawyer Ethics Advice
Florida Bar Discipline Defense
Florida Bar Admission
Other Defense
Call us for a consultation 727-799-1688
Home / Blog / Law Firm's Contact With Both Sides in Illinois Divorce Case Results in a Denial of all Attorney's Fees
Law Firm's Contact With Both Sides in Illinois Divorce Case Results in a Denial of all Attorney's Fees
Welcome to this JACPA Ethics Alert which will discuss an Illinois appeals court case that addresses the area of conflicts of interest in family law cases. In an October 14, 2011 opinion, an Illinois appellate court affirmed the trail court which found that a law firm which represented the wife in a divorce after initially consulting with the husband had a conflict of interest which voided its fee agreement with the wife from the outset and; therefore, the law firm forfeited all fees. The case is: In re Marriage of Newton, Ill. App. Ct. 1st Dist., No. 1-09-0683, 6/30/11 (published 10/14/11).
David Newton filed a motion to disqualify attorney David J. Grund and the law firm Grund & Leavitt from representing his wife Hadley Newton in their divorce action in 2007. After hearings, the trial court subsequently disqualified the lawyer and the law firm, concluding that Grund had previously represented Mr. Newton in the same matter. According to the court's order, Mr. Newton had met the lawyer at his law office for one or two hours and discussed his impending divorce, children, and financial situation.
The lawyer testified that he told Mr. Newton at the meeting that the representation would not begin unless he actually signed a contract; that no attorney-client privilege would attach during their meeting; and that Newton should not disclose anything to him that could not appear in the public record. The lawyer also testified that he did not believe that Mr. Newton would actually hire him, that he couldn't recall anything that Mr. Newton told him, and that he didn't take any notes. The lawyer subsequently was retained by Ms. Newton and represented her in the divorce proceedings. She testified that when she approached the lawyer, he told her there was a conflict of interest but that he agreed to represent her despite the conflict and she later executed a fee agreement.
After hearing the evidence, the trial court concluded that both of the Newtons were credible and that Mr. Newton's meeting with the lawyer created an attorney-client relationship that disqualified the firm from representing Hadley Newton in the divorce. The court further found that the representation of Ms. Newton violated Illinois Rule of Professional Conduct 1.9(a) which addresses conflicts of interest involving former clients; therefore, the law firm was disqualified and prohibited from collecting any fees for the services it had previously provided since the retainer agreement for Ms. Newton was void and unenforceable from its inception. The law firm then appealed.
The Illinois appellate opinion held that the trial court correctly ruled that the law firm should be disqualified for violating Rule 1.9, particularly since both of the Newtons' interests were so obviously in conflict. The opinion noted that Illinois Rule 1.9(a) (which is substantially similar to Rule 4-1.9(a), Rules Regulating The Florida Bar) clearly states that a lawyer who has represented a client in a matter shall not take on a client in the same or a substantially related matter if the new client's interests are materially adverse to those of the former client, unless the former client consents.
The opinion further found that, notwithstanding the lawyer's disclaimers, Mr. Newton's consultation with lawyer created an attorney-client relationship since he was seeking advice about his impending divorce. Further, since the Newtons were adverse parties in the same case, there was clearly a substantial relationship between the two representations and, as a result of the lawyer's meeting with Mr. Newton, an irrebuttable presumption was created that Mr. Newton shared confidential information with the lawyer and was sufficient grounds for the disqualification.
The appellate opinion also rejected the argument that the law firm was entitled to be paid for the services the firm provided before it was disqualified since the retainer agreement was void ab initio and unenforceable due to the conflict for reasons of public policy for the following reasons:
1) as a result of the Illinois Rule 1.9 violation, the law firm's fee agreement with Ms. Newton was not a "contract which meets applicable requirements of court rules" as required by the Illinois Marriage and Dissolution of Marriage Act.
2) the fee contract was void and unenforceable from its inception since it violated Illinois public policy which is set forth in Rule 1.9. Further, case precedent indicated that attorneys' fees should not be allowed if a lawyer is disqualified due to conflict of interest.
The court also rejected the law firm's alternative argument that it was entitled to the fees since it acted in good faith since "purported good faith is irrelevant".
Finally, the court also upheld a contempt order issued by the trial court against the lawyer for failing to step away from the bench when ordered to do so because the failure could not be justified as a good faith effort to secure "clarification of an uncertainty" since Rule 1.9 makes it abundantly clear that representing clients with conflicting interests is prohibited, the court said.
Bottom line: As I have said many times, the practice of family law is fraught with potential peril with regard to potential (or actual) conflicts of interest and other issues. As side note, current (and fairly recent) Florida Bar Rule 4-1.18 addresses the issue of conflict when one party attempts to consult with the lawyer and the lawyer (or law firm) declines the representation and is approached by the opposing party for representation.
…be very careful out there!
As always, if you have any questions about this Ethics Alert or need assistance, analysis, and guidance regarding these or any other ethics, risk management, or other issues, please do not hesitate to contact me.
THE LAW OFFICE OF JOSEPH A. CORSMEIER, P.A.
PROVIDES ETHICS ADVICE AND EXPERT OPINIONS TO LAWYERS AND LAW FIRMS
DEFENDS LAWYERS IN BAR ADMISSION AND DISCIPLINE CASES
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text:
arXiv.org > quant-ph > arXiv:2004.09405
arXiv:2004.09405 (quant-ph)
[Submitted on 20 Apr 2020]
Title:Algebraic and geometric properties of local transformations
Authors:Denis Rosset, Ämin Baumeler, Jean-Daniel Bancal, Nicolas Gisin, Anthony Martin, Marc-Olivier Renou, Elie Wolfe
Abstract: Some properties of physical systems can be characterized from their correlations. In that framework, subsystems are viewed as abstract devices that receive measurement settings as inputs and produce measurement outcomes as outputs. The labeling convention used to describe these inputs and outputs does not affect the physics; and relabelings are easily implemented by rewiring the input and output ports of the devices. However, a more general class of operations can be achieved by using correlated preprocessing and postprocessing of the inputs and outputs. In contrast to relabelings, some of these operations irreversibly lose information about the underlying device. Other operations are reversible, but modify the number of cardinality of inputs and/or outputs. In this work, we single out the set of deterministic local maps as the one satisfying two equivalent constructions: an operational definition from causality, and an axiomatic definition reminiscent of the definition of quantum completely positive trace-preserving maps. We then study the algebraic properties of that set. Surprisingly, the study of these fundamental properties has deep and practical applications. First, the invariant subspaces of these transformations directly decompose the space of correlations/Bell inequalities into nonsignaling, signaling and normalization components. This impacts the classification of Bell and causal inequalities, and the construction of assemblages/witnesses in steering scenarios. Second, the left and right invertible deterministic local operations provide an operational generalization of the liftings introduced by Pironio [J. Math. Phys., 46(6):062112 (2005)]. Not only Bell-local, but also causal inequalities can be lifted; liftings also apply to correlation boxes in a variety of scenarios.
Comments: 46 pages split in three independent parts (8+21+11). Numerous figures
Subjects: Quantum Physics (quant-ph)
Cite as: arXiv:2004.09405 [quant-ph]
(or arXiv:2004.09405v1 [quant-ph] for this version)
From: Denis Rosset [view email]
[v1] Mon, 20 Apr 2020 16:01:31 UTC (380 KB)
quant-ph


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text:
\section{Introduction}

The generalized variational problem proposed
by Herglotz in 1930 \cite{Guenther1996,Herglotz1930}
can be formulated as follows:
\begin{equation}
\label{PH_1}
\tag{$P_H$}
\begin{gathered}
z(b)\longrightarrow \text{extr}\\
\text{with }\dot{z}(t)=L(t,x(t),\dot{x}(t),z(t)), \quad t \in [a,b],\\
\text{subject to } x(a)=\alpha, \quad z(a)=\gamma, \quad \alpha, \gamma \in \mathbb{R}.
\end{gathered}
\end{equation}
It consists in the determination of trajectories $x(\cdot)$ and corresponding trajectories
$z(\cdot)$ that extremize (maximize or minimize) the value $z(b)$,
where $L \in C^1([a,b]\times \mathbb{R}^{2n}\times \mathbb{R};\mathbb{R})$.
While in \cite{Guenther1996,Herglotz1930,Simao+NM+Torres2013} the admissible functions
are $x(\cdot) \in C^2([a,b];\mathbb{R}^n)$ and $z(\cdot) \in C^1([a,b];\mathbb{R})$,
here we consider \eqref{PH_1} in the wider class of functions
$x(\cdot) \in PC^1([a,b];\mathbb{R}^n)$ and $z(\cdot) \in PC^1([a,b];\mathbb{R})$.

It is obvious that Herglotz's problem \eqref{PH_1} reduces to the classical fundamental problem
of the calculus of variations (see, e.g., \cite{vanBrunt}) if the Lagrangian $L$
does not depend on the $z$ variable: if
$\dot{z}(t)=L(t,x(t),\dot{x}(t))$, $t \in [a,b]$,
then \eqref{PH_1} is equivalent to the classical variational problem
\begin{equation}
\label{eq:class:Funct}
\int_a^b L(t,x(t),\dot{x}(t))dt \longrightarrow \textrm{extr},
\quad x(a) = \alpha.
\end{equation}
Herglotz proved that an Euler--Lagrange optimality
condition for a pair $\left(x(\cdot),z(\cdot)\right)$ to be an extremizer
of the generalized variational problem \eqref{PH_1} is given by
\begin{multline}
\label{eq:gen:EL}
\frac{\partial L}{\partial x}\left(t,x(t),\dot{x}(t),z(t)\right)
-\frac{d}{dt}\frac{\partial L}{\partial \dot{x}}\left(t,x(t),\dot{x}(t),z(t)\right)\\
+\frac{\partial L}{\partial z}\left(t,x(t),\dot{x}(t),z(t)\right)
\frac{\partial L}{\partial \dot{x}}\left(t,x(t),\dot{x}(t),z(t)\right) = 0,
\end{multline}
$t \in [a,b]$. The equation \eqref{eq:gen:EL} is known as the generalized
Euler--Lagrange equation. Observe that for the fundamental problem
of the calculus of variations \eqref{eq:class:Funct} one has
$\frac{\partial L}{\partial z}=0$ and the differential equation
\eqref{eq:gen:EL} reduces to the classical Euler--Lagrange equation
$$
\frac{\partial L}{\partial x}\left(t,x(t),\dot{x}(t)\right)
-\frac{d}{dt}\frac{\partial L}{\partial \dot{x}}\left(t,x(t),\dot{x}(t)\right) =0.
$$

Since the celebrated work \cite{Pontryagin} by Pontryagin et al.,
the calculus of variations is seen as part of optimal control.
One of the simplest problems of optimal control, in Bolza form,
is the following one:
\begin{equation}
\label{problem P}
\tag{$P$}
\begin{gathered}
\mathcal{J}(x(\cdot),u(\cdot))=\int_a^b f(t,x(t),u(t))dt+\phi(x(b))\longrightarrow\text{extr}\\
\text{subject to } \dot{x}(t)=g(t,x(t),u(t)) \text{ and }  x(a)=\alpha, \quad \alpha \in \mathbb{R},
\end{gathered}
\end{equation}
where $f \in C^1([a,b]\times \mathbb{R}^{n}\times \Omega;\mathbb{R})$,
$\phi \in C^1(\mathbb{R}^{n};\mathbb{R})$,
$g \in C^1([a,b]\times \mathbb{R}^{n}\times \Omega;\mathbb{R}^n)$,
$x \in PC^1([a,b]; \mathbb{R}^n)$ and $u\in PC([a,b];\Omega)$,
with $\Omega \subseteq \mathbb{R}^r$ an open set. In the literature
of optimal control, $x$ and $u$ are called the state
and control variables, respectively, while $\phi$ is known
as the payoff or salvage term. Note that the classical
problem of the calculus of variations \eqref{eq:class:Funct}
is a particular case of problem \eqref{problem P}
with $\phi(x) \equiv 0$, $g(t,x,u)=u$ and $\Omega=\mathbb{R}^n$.
In this work we show how the results on Herglotz's problem
of the calculus of variations \eqref{PH_1} obtained in
\cite{Georgieva2002,Simao+NM+Torres2013}
can be generalized by using the theory of optimal control.
The main idea is simple and consists in rewriting the generalized variational
problem of Herglotz \eqref{PH_1} as a standard optimal control problem \eqref{problem P},
and then to apply available results of optimal control theory.

The paper is organized as follows. In Section~\ref{sec:prelim}
we briefly review the necessary concepts and results from optimal control theory.
In particular, we make use of Pontryagin's maximum principle (Theorem~\ref{PMP});
the DuBois--Reymond condition of optimal control (Theorem~\ref{thm DB-r opt});
and the Noether theorem of optimal control proved in \cite{Torres2001}
(cf. Theorem~\ref{thm opt cont Noether}).
Our contributions are then given in Section~\ref{sec:MainRes}:
we generalize the Euler--Lagrange equation and the transversality condition
for problem \eqref{PH_1} found in \cite{Simao+NM+Torres2013} to admissible
functions $x(\cdot) \in PC^1([a,b];\mathbb{R}^n)$ and $z(\cdot) \in PC^1([a,b];\mathbb{R})$
(Theorem~\ref{Thm:MR1}); we obtain a DuBois--Reymond necessary optimality condition for problem \eqref{PH_1}
(Theorem~\ref{Thm:DR}); and a generalization of the Noether theorem \cite{Georgieva2002}
(Theorem~\ref{thm noether PH1}) as a corollary of the optimal control results of Torres
\cite{Torres2002,Torres2001,Torres2004}.
We end with Section~\ref{sec:conc} of conclusions and future work.

\section{Preliminaries}
\label{sec:prelim}

The central result in optimal control theory is given by Pontryagin's maximum principle,
which is a first-order necessary optimality condition.

\begin{theorem}[Pontryagin's maximum principle for problem \eqref{problem P} \cite{Pontryagin}]
\label{PMP}
If a pair $(x(\cdot),u(\cdot))$ with $x \in PC^1([a,b]; \mathbb{R}^n)$ and $u\in PC([a,b];\Omega)$
is a solution to problem \eqref{problem P}, then there exists $\psi \in PC^1([a,b];\mathbb{R}^n)$
such that the following conditions hold:
\begin{itemize}
\item the optimality condition
\begin{equation}
\label{prob P opt condt}
\frac{\partial H}{\partial u}(t, x(t),u(t), \psi(t))=0;
\end{equation}
\item the adjoint system
\begin{equation}
\label{prob P adj syst}
\begin{cases}
\dot{x}(t)=\frac{\partial H}{\partial \psi}(t, x(t),u(t), \psi(t))\\
\dot{\psi}(t)=-\frac{\partial H}{\partial x}(t, x(t),u(t), \psi(t));
\end{cases}
\end{equation}
\item and the transversality condition
\begin{equation}
\label{prob P tr condt}
\psi(b)=\nabla\phi(x(b));
\end{equation}
\end{itemize}
where the Hamiltonian $H$ is defined by
\begin{equation}
\label{eq:def:Hamiltonian}
H(t,x,u,\psi)=f(t,x,u)+\psi\cdot g(t,x,u).
\end{equation}
\end{theorem}

\begin{definition}[Pontryagin extremal to \eqref{problem P}]
A triplet $(x(\cdot),u(\cdot), \psi(\cdot))$ with
$x \in PC^1([a,b]; \mathbb{R}^n)$, $u\in PC([a,b];\Omega)$ and
$\psi \in PC^1([a,b];\mathbb{R}^n)$ is called a Pontryagin extremal
to problem \eqref{problem P} if it satisfies the optimality condition
\eqref{prob P opt condt}, the adjoint system \eqref{prob P adj syst}
and the transversality condition \eqref{prob P tr condt}.
\end{definition}

\begin{theorem}[DuBois--Reymond condition of optimal control \cite{Pontryagin}]
\label{thm DB-r opt}
If $(x(\cdot),u(\cdot), \psi(\cdot))$ is a Pontryagin extremal
to problem \eqref{problem P}, then the Hamiltonian \eqref{eq:def:Hamiltonian}
satisfies the equality
\begin{equation*}
\frac{d H}{dt}(t,x(t),u(t),\psi(t))=\frac{\partial H}{\partial t}(t,x(t),u(t),\psi(t)),
\end{equation*}
$t \in [a,b]$.
\end{theorem}

Noether's theorem has become a fundamental tool
of modern theoretical physics \cite{MR3072684},
the calculus of variations \cite{MR2099056,MR2098297},
and optimal control \cite{Torres2002,Torres2001,Torres2004}.
It states that when an optimal control problem is invariant
under a one parameter family of transformations,
then there exists a corresponding conservation law:
an expression that is conserved along all the Pontryagin
extremals of the problem \cite{Torres2002,Torres2001,Torres2004,Torres2006}.
Here we use Noether's theorem as found in \cite{Torres2001}, which is formulated
for problems of optimal control in Lagrange form, that is, for problem
\eqref{problem P} with $\phi \equiv 0$. In order to apply the results of \cite{Torres2001}
to the Bolza problem \eqref{problem P}, we rewrite it in the following equivalent Lagrange form:
\begin{equation}
\label{eq:prob:Lag}
\begin{gathered}
\mathcal{I}(x_0(\cdot),x(\cdot),u(\cdot))
=\int_a^b \left[f(t,x(t),u(t))+ x_0(t)\right] dt \longrightarrow\text{extr},\\
\begin{cases}
\dot{x}_0(t)=0,\\
\dot{x}(t)=g\left(t,x(t),u(t)\right),
\end{cases}\\
x_0(a)= \frac{\phi(x(b))}{b-a}, \  x(a)=\alpha.
\end{gathered}
\end{equation}
The notion of invariance for problem \eqref{problem P} is obtained
by applying the notion of invariance found in \cite{Torres2001}
to the equivalent optimal control problem \eqref{eq:prob:Lag}.
In Definition~\ref{def inv OC} we use the little-o notation.

\begin{definition}[Invariance of problem \eqref{problem P}]
\label{def inv OC}
Let $h^s$ be a one-parameter family of $C^1$ invertible maps
\begin{equation*}
\begin{gathered}
h^s:[a,b]\times \mathbb{R}^n\times \Omega \rightarrow\mathbb{R}\times\mathbb{R}^n\times \mathbb{R}^r,\\
h^s(t,x,u)=\left(\mathcal{T}^s(t,x,u), \mathcal{X}^s(t,x,u),\mathcal{U}^s(t,x,u)\right),\\
h^0(t,x,u)=(t,x,u) \text{ for all } (t,x,u)\in [a,b]\times \mathbb{R}^n\times \Omega.
\end{gathered}
\end{equation*}
Problem \eqref{problem P} is said to be invariant under transformations $h^s$
if for all $(x(\cdot),u(\cdot))$ the following two conditions hold:
\begin{enumerate}
\item[(i)]
\begin{multline}
\label{eq inv OC 1}
\left[f \circ h^s(t,x(t),u(t))+\frac{\phi(x(b))}{b-a} + \xi s + o(s)\right]\frac{d\mathcal{T}^s}{dt}(t,x(t),u(t))\\
= f(t,x(t),u(t)) + \frac{\phi(x(b))}{b-a}
\end{multline}
for some constant $\xi$;
\item[(ii)]
\begin{equation}
\label{eq inv OC 2}
\frac{d\mathcal{X}^s}{dt}\left(t,x(t),u(t)\right)
=g\circ h^s(t,x(t),u(t))\frac{d\mathcal{T}^s}{dt}(t,x(t),u(t)).
\end{equation}
\end{enumerate}
\end{definition}

\begin{theorem}[Noether's theorem for the optimal control problem \eqref{problem P}]
\label{thm opt cont Noether}
If problem \eqref{problem P} is invariant
in the sense of Definition~\ref{def inv OC}, then the quantity
\begin{equation*}
(b-t) \xi + \psi(t) \cdot X(t,x(t),u(t))
-\left[H(t,x(t),u(t),\psi(t)) + \frac{\phi(x(b))}{b-a}\right]\cdot T(t,x(t),u(t))
\end{equation*}
is constant in $t$ along every Pontryagin extremal $(x(\cdot),u(\cdot), \psi(\cdot))$
of problem \eqref{problem P}, where
\begin{equation*}
\begin{gathered}
T(t,x(t),u(t))=\frac{\partial \mathcal{T}^s}{\partial s}(t,x(t),u(t))\biggm\vert_{s=0},\\
X(t,x(t),u(t))=\frac{\partial \mathcal{X}^s}{\partial s}(t,x(t),u(t))\biggm\vert_{s=0},
\end{gathered}
\end{equation*}
and $H$ is defined by \eqref{eq:def:Hamiltonian}.
\end{theorem}

\begin{proof}
The result is a simple exercise obtained by applying
the Noether theorem of \cite{Torres2001}
and the Pontryagin maximum principle (Theorem~\ref{PMP})
to the equivalent optimal control problem \eqref{eq:prob:Lag}
(in particular using the adjoint equation corresponding to the multiplier
associated with the state variable $x_0$ and the respective
transversality condition).
\end{proof}

\section{Main Results}
\label{sec:MainRes}

We begin by introducing some basic definitions for the
generalized variational problem of Herglotz \eqref{PH_1}.

\begin{definition}[Admissible pair to problem \eqref{PH_1}]
We say that $(x(\cdot),z(\cdot))$ with $x(\cdot) \in PC^1([a,b];\mathbb{R}^n)$
and $z(\cdot) \in PC^1([a,b];\mathbb{R})$ is an admissible pair to problem
\eqref{PH_1} if it satisfies the equation
\begin{equation*}
\dot{z}(t)=L(t,x(t),\dot{x}(t),z(t)), \quad t \in [a,b],
\end{equation*}
and the initial conditions $x(a)=\alpha$ and $z(a)=\gamma$, $\alpha, \gamma \in \mathbb{R}$.
\end{definition}

\begin{definition}[Extremizer to problem \eqref{PH_1}]
We say that an admissible pair $(x^*(\cdot),z^*(\cdot))$ is an extremizer
to problem \eqref{PH_1} if $z(b)-z^*(b)$ has the same signal for all admissible
pairs $(x(\cdot),z(\cdot))$ that satisfy $\|z-z^* \|_0< \epsilon$ and $\|x-x^* \|_0< \epsilon$
for some positive real $\epsilon$, where $\|y\|_0=\smash{\displaystyle\max_{a\leq t \leq b}}|y(t)|$.
\end{definition}

We now present a necessary condition for a pair $(x(\cdot),z(\cdot))$
to be a solution (extremizer) to problem \eqref{PH_1}. The following result generalizes
\cite{Guenther1996,Herglotz1930,Simao+NM+Torres2013} by considering a more general class of functions.
To simplify notation, we use the operator $\langle\cdot,\cdot\rangle$ defined by
$$
\langle x, z \rangle(t):=(t,x(t),\dot{x}(t),z(t)).
$$
When there is no possibility of ambiguity,
we sometimes suppress arguments.

\begin{theorem}[Euler--Lagrange equation and transversality condition for problem \eqref{PH_1}]
\label{Thm:MR1}
If $(x(\cdot),z(\cdot))$ is an extremizer to problem \eqref{PH_1}, then the Euler--Lagrange equation
\begin{equation}
\label{PH1_EL}
\frac{\partial L}{\partial x}\langle x, z \rangle(t)
-\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{x}}\right)\langle x, z \rangle(t)
+\frac{\partial L}{\partial z}\langle x, z \rangle(t)
\frac{\partial L}{\partial \dot{x}}\langle x, z \rangle(t) = 0
\end{equation}
holds, $t \in [a,b]$. Moreover, the following
transversality condition holds:
\begin{equation}
\label{PH1_tr_cdt}
\frac{\partial L}{\partial \dot{x}}\langle x,z\rangle(b)=0.
\end{equation}
\end{theorem}

\begin{proof}
Observe that Herglotz's problem \eqref{PH_1} is a particular case
of problem \eqref{problem P} obtained by considering $x$ and $z$ as state variables
(two components of one vectorial state variable),
$\dot{x}$ as the control variable $u$,
and by choosing $f\equiv 0$ and $\phi(x,z)=z$.
Note that since $x(t)\in \mathbb{R}^n$,
we have $u(t)\in \mathbb{R}^n$ (i.e., for Herglotz's problem \eqref{PH_1} one has $r=n$).
In this way, the problem of Herglotz, described as an optimal control problem, takes the form
\begin{equation}
\label{PH_1_OC}
\begin{gathered}
z(b) \longrightarrow \text{extr},\\
\begin{cases}
\dot{x}(t)=u(t),\\
\dot{z}(t)=L(t,x(t),u(t),z(t)),
\end{cases}\\
x(a)=\alpha, \  z(a)=\gamma,
\quad \alpha, \gamma \in \mathbb{R}.
\end{gathered}
\end{equation}
It follows from Pontryagin's maximum principle (Theorem~\ref{PMP})
that there exists $\psi_x \in PC^1([a,b];\mathbb{R}^n)$
and $\psi_z \in PC^1([a,b];\mathbb{R})$ such that the following conditions hold:
\begin{itemize}
\item the optimality condition
\begin{equation}
\label{opt_cond PH1}
\frac{\partial H}{\partial u}(t,x(t),u(t),z(t),\psi_x(t),\psi_z(t))=0;
\end{equation}
\item the adjoint system
\begin{equation}
\label{adj_syst PH1}
\begin{cases}
\dot{x}(t)=\frac{\partial H}{\partial \psi_x}(t,x(t),u(t),z(t),\psi_x(t),\psi_z(t))\\
\dot{z}(t)=\frac{\partial H}{\partial \psi_z}(t,x(t),u(t),z(t),\psi_x(t),\psi_z(t))\\
\dot{\psi}_x(t)=-\frac{\partial H}{\partial x}(t,x(t),u(t),z(t),\psi_x(t),\psi_z(t))\\
\dot{\psi}_z(t)=-\frac{\partial H}{\partial z}(t,x(t),u(t),z(t),\psi_x(t),\psi_z(t));
\end{cases}
\end{equation}
\item and the transversality conditions
\begin{equation}
\label{tr_cond PH1}
\begin{cases}
\psi_x(b)=0,\\
\psi_z(b)=1,
\end{cases}
\end{equation}
\end{itemize}
where the Hamiltonian $H$ is defined by
$$
H(t,x,u,z,\psi_x,\psi_z)=\psi_x \cdot u+\psi_z \cdot L(t,x,u,z).
$$
Observe that the adjoint system \eqref{adj_syst PH1} implies that
\begin{equation}
\label{adj_syst_double}
\begin{cases}
\dot{\psi}_x=-\psi_z\frac{\partial L}{\partial x}\\
\dot{\psi}_z=-\psi_z\frac{\partial L}{\partial z}.
\end{cases}
\end{equation}
This means that $\psi_z$ is solution of a first-order linear differential equation,
which is solved using an integrand factor to find that
$\psi_z=ke^{-\int_a^t\frac{\partial L}{\partial z}d\theta}$ with $k$ a constant.
From the second transversality condition in \eqref{tr_cond PH1}, we obtain that
$k=e^{\int_a^b\frac{\partial L}{\partial z}d\theta}$ and, consequently,
$$
\psi_z=e^{\int_t^b\frac{\partial L}{\partial z}d\theta}.
$$
The optimality condition \eqref{opt_cond PH1} is equivalent to
$\psi_x+\psi_z\frac{\partial L}{\partial u}=0$ and, after derivation, we obtain that
\begin{equation*}
\dot{\psi}_x=-\frac{d}{dt}\left(\psi_z\frac{\partial L}{\partial u}\right)
=-\dot{\psi}_z\frac{\partial L}{\partial u}-\psi_z\frac{d}{dt}\left(\frac{\partial L}{\partial u}\right)
=\psi_z\frac{\partial L}{\partial z}\frac{\partial L}{\partial u}
-\psi_z\frac{d}{dt}\left(\frac{\partial L}{\partial u}\right).
\end{equation*}
Now, comparing with \eqref{adj_syst_double}, we have
$$
-\psi_z\frac{\partial L}{\partial x}
=\psi_z\frac{\partial L}{\partial z}\frac{\partial L}{\partial u}
-\psi_z\frac{d}{dt}\left(\frac{\partial L}{\partial u}\right).
$$
Since $\psi_z(t)\neq 0$ for all $t \in [a,b]$ and $\dot{x}=u$,
we obtain the Euler--Lagrange equation \eqref{PH1_EL}:
$$
\frac{\partial L}{\partial x}-\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{x}}\right)
+\frac{\partial L}{\partial z}\frac{\partial L}{\partial \dot{x}} = 0.
$$
Note that from the optimality condition \eqref{opt_cond PH1} we obtain that
$\psi_x=-\psi_z\frac{\partial L}{\partial u}=-\psi_z\frac{\partial L}{\partial \dot{x}}$,
which together with transversality condition \eqref{tr_cond PH1} for $\psi_x$
leads to the transversality condition \eqref{PH1_tr_cdt}:
\begin{equation*}
\frac{\partial L}{\partial \dot{x}}(b,x(b),\dot{x}(b),z(b))=0.
\end{equation*}
This concludes the proof.
\end{proof}

\begin{definition}[Extremal to problem \eqref{PH_1}]
We say that an admissible pair $(x(\cdot), z(\cdot))$ is an extremal to problem
\eqref{PH_1} if it satisfies the Euler--Lagrange equation \eqref{PH1_EL}
and the transversality condition \eqref{PH1_tr_cdt}.
\end{definition}

\begin{theorem}[DuBois--Reymond condition for problem \eqref{PH_1}]
\label{Thm:DR}
If $(x(\cdot), z(\cdot))$ is an extremal to problem \eqref{PH_1}, then
\begin{equation*}
\frac{d}{dt}\left( -\psi_z(t)\frac{\partial L}{\partial \dot{x}}\langle x, z \rangle(t)
\dot{x}(t)+\psi_z(t) L\langle x, z \rangle(t)\right)
=\psi_z(t)\frac{\partial L}{\partial t}\langle x, z \rangle(t),
\end{equation*}
$t \in [a,b]$, where
$\psi_z(t)=e^{\int_t^b\frac{\partial L}{\partial z}\langle x,z \rangle(\theta)d\theta}$.
\end{theorem}

\begin{proof}
The result follows from Theorem~\ref{thm DB-r opt},
rewriting problem \eqref{PH_1}
as the optimal control problem \eqref{PH_1_OC}.
\end{proof}

We define invariance for \eqref{PH_1} using Definition~\ref{def inv OC}
for the equivalent optimal control problem \eqref{PH_1_OC}.

\begin{definition}[Invariance of problem \eqref{PH_1}]
\label{def inv_PH1}
Let $h^s$ be a one-parameter family of $C^1$ invertible maps
\begin{equation*}
\begin{gathered}
h^s:[a,b]\times \mathbb{R}^n  \times \mathbb{R}
\rightarrow \mathbb{R}\times \mathbb{R}^n  \times \mathbb{R},\\
h^s(t,x(t),z(t))=(\mathcal{T}^s\langle x,z \rangle(t),\mathcal{X}^s\langle x,z \rangle(t),
\mathcal{Z}^s\langle x,z \rangle(t)),\\
h^0(t,x,z)=(t,x,z),
\quad \forall (t,x,z) \in [a,b]\times \mathbb{R}^n  \times \mathbb{R}.
\end{gathered}
\end{equation*}
Problem \eqref{PH_1} is said to be invariant under the transformations $h^s$
if for all admissible pairs $(x(\cdot),z(\cdot))$ the following two conditions hold:
\begin{enumerate}
\item[(i)]
\begin{equation}
\label{eq inv ph1_1}
\left(\frac{z(b)}{b-a}+\xi s + o(s)\right)\frac{d\mathcal{T}^s}{dt}\langle x,z \rangle(t)
=\frac{z(b)}{b-a}
\end{equation}
for some constant $\xi$;
\item[(ii)]
\begin{multline}
\label{eq inv ph1_2}
\frac{d \mathcal{Z}^s}{dt}\langle x,z \rangle(t)\\
= L\left(\mathcal{T}^s\langle x,z \rangle(t),\mathcal{X}^s\langle x,z \rangle(t),
\frac{d\mathcal{X}^s}{d\mathcal{T}^s}\langle x,z \rangle(t),
\mathcal{Z}^s\langle x,z \rangle(t)\right)\frac{d\mathcal{T}^s}{dt}\langle x,z \rangle(t),
\end{multline}
\end{enumerate}
where
$$
\frac{d\mathcal{X}^s}{d\mathcal{T}^s}\langle x,z \rangle(t)
=\frac{\frac{d\mathcal{X}^s}{dt}\langle x,z \rangle(t)}{\frac{d\mathcal{T}^s}{dt}\langle x,z \rangle(t)}.
$$
\end{definition}

Follows the main result of the paper.

\begin{theorem}[Noether's theorem for problem \eqref{PH_1}]
\label{thm noether PH1}
If problem \eqref{PH_1} is invariant in the sense
of Definition~\ref{def inv_PH1}, then the quantity
\begin{multline}
\label{quantity PH1}
\psi_z(t)\biggl[\frac{\partial L}{\partial \dot{x}}\langle x,z \rangle(t) X\langle x,z \rangle(t)
-Z\langle x,z \rangle(t)\\
+\left(L\langle x,z \rangle(t)-\frac{\partial L}{\partial \dot{x}}\langle x,
z \rangle(t) \dot{x}(t)\right)T\langle x,z \rangle(t)\biggr]
\end{multline}
is constant in $t$ along every extremal of problem \eqref{PH_1}, where
\begin{equation*}
\begin{gathered}
T\langle x,z \rangle(t)=\frac{\partial \mathcal{T}^s}{\partial s}\langle x,z \rangle(t)\biggm\vert_{s=0},\\
X\langle x,z \rangle(t)=\frac{\partial \mathcal{X}^s}{\partial s}\langle x,z \rangle(t)\biggm\vert_{s=0},\\
Z\langle x,z \rangle(t)=\frac{\partial \mathcal{Z}^s}{\partial s}\langle x,z \rangle(t)\biggm\vert_{s=0}
\end{gathered}
\end{equation*}
and $\psi_z(t)=e^{\int_t^b\frac{\partial L}{\partial z}\langle x,z \rangle (\theta)d\theta}$.
\end{theorem}

\begin{proof}
As before, we rewrite problem \eqref{PH_1} in the equivalent optimal control form \eqref{PH_1_OC},
where $x$ and $z$ are the state variables and $u$ the control.
We prove that if problem \eqref{PH_1} is invariant in the sense
of Definition~\ref{def inv_PH1}, then \eqref{PH_1_OC} is invariant in the sense of Definition~\ref{def inv OC}.
First, observe that if equation \eqref{eq inv ph1_1} holds, then \eqref{eq inv OC 1} holds
for \eqref{PH_1_OC}: here $f \equiv 0$, $\phi(x,z) = z$ and \eqref{eq inv OC 1} simplifies to
$\left[\frac{z(b)}{b-a} + \xi s + o(s)\right]\frac{d\mathcal{T}^s}{dt}\langle x,z \rangle(t)
= \frac{z(b)}{b-a}$.
Note that the first equation of the control system of problem \eqref{PH_1_OC} ($u(t) = \dot{x}(t)$) defines
$\mathcal{U}^s:=\frac{d\mathcal{X}^s}{d\mathcal{T}^s}$, that is,
\begin{equation}
\label{eq U^s}
\frac{d \mathcal{X}^s}{dt}\langle x,z \rangle(t)
=\mathcal{U}^s\langle x,z \rangle(t)\frac{d\mathcal{T}^s}{dt}\langle x,z \rangle(t).
\end{equation}
Hence, if equation \eqref{eq inv ph1_2} and \eqref{eq U^s} holds, then
there is also invariance of the control system of \eqref{PH_1_OC} in the sense of \eqref{eq inv OC 2}
and consequently problem \eqref{PH_1_OC} is invariant in the sense of Definition~\ref{def inv OC}.
We are now in conditions to apply Theorem~\ref{thm opt cont Noether} to problem \eqref{PH_1_OC}, which
guarantees  that the quantity
\begin{multline*}
(b-t)\xi +
\psi_x(t)\cdot X(t,x(t),u(t),z(t)) + \psi_z(t)\cdot Z(t,x(t),u(t),z(t))\\
-\left(H(t,x(t),u(t),z(t),\psi_x(t),\psi_z(t)) + \frac{z(b)}{b-a}\right) \cdot T(t,x(t),u(t),z(t))
\end{multline*}
is constant in $t$ along every Pontryagin extremal of problem \eqref{PH_1_OC}, where
\begin{equation*}
H(t,x,u,z,\psi_x,\psi_z)=\psi_x u +\psi_z L(t,x,u,z).
\end{equation*}
This means that the quantity
\begin{multline*}
(b-t)\xi +
\psi_x(t) X\langle x,z \rangle(t) + \psi_z(t) Z\langle x,z \rangle(t)\\
-\left(\psi_x(t) \dot{x}(t) +\psi_z(t) L\langle x,z \rangle(t)
+ \frac{z(b)}{b-a}\right)T\langle x,z \rangle(t)
\end{multline*}
is constant in $t$ along all extremals of problem \eqref{PH_1}, where
$$
\psi_x(t)=-\psi_z(t) \frac{\partial L}{\partial u}\langle x,z \rangle(t)
=-\psi_z(t) \frac{\partial L}{\partial \dot{x}}\langle x,z \rangle(t).
$$
Equivalently,
\begin{multline*}
(b-t)\xi - \frac{z(b)}{b-a}T\langle x,z \rangle(t)
-\psi_z(t)\biggl[\frac{\partial L}{\partial \dot{x}}\langle x,z \rangle(t) X\langle x,z \rangle(t)
-Z\langle x,z \rangle(t)\\
+\left(L\langle x,z \rangle(t)-\frac{\partial L}{\partial \dot{x}}\langle x,
z \rangle(t) \dot{x}(t)\right)T\langle x,z \rangle(t)\biggr]
\end{multline*}
is a constant along the extremals.
To conclude the proof, we just need to prove that the quantity
\begin{equation}
\label{eq:constant}
(b-t)\xi - \frac{z(b)}{b-a}T\langle x,z \rangle(t)
\end{equation}
is a constant.
From the invariance condition \eqref{eq inv ph1_1} we know that
\begin{equation*}
\left(z(b)+\xi (b-a) s + o(s)\right)\frac{d\mathcal{T}^s}{dt}\langle x,z \rangle(t) =z(b).
\end{equation*}
Integrating from $a$ to $t$, we conclude that
\begin{multline}
\label{exp:prv:ad}
\left(z(b)+\xi (b-a) s + o(s)\right)\mathcal{T}^s\langle x,z \rangle(t)\\
=z(b)(t-a)+\left(z(b)+\xi (b-a) s + o(s)\right)\mathcal{T}^s\langle x,z \rangle(a).
\end{multline}
Differentiating \eqref{exp:prv:ad} with respect to $s$, and then putting $s=0$, we obtain
\begin{equation}
\label{eq:relation}
\xi (b-a) t + z(b) T\langle x,z \rangle(t) =\xi(b-a)a+z(b)T\langle x,z\rangle(a).
\end{equation}
We conclude from \eqref{eq:relation} that expression \eqref{eq:constant} is the constant
$(b-a)\xi - \frac{z(b)}{b-a}T\langle x,z\rangle(a)$.
\end{proof}

\section{Conclusion}
\label{sec:conc}

We introduced a different approach to the generalized variational principle of Herglotz,
by looking to Herglotz's problem as an optimal control problem.
A Noether type theorem for Herglotz's problem
was first proved by Georgieva and Guenther
in \cite{Georgieva2002}: under the condition of invariance
\begin{equation}
\label{def inv georg}
\frac{d}{ds}\left[L\left(\mathcal{T}^s\langle x,z \rangle(t),\mathcal{X}^s\langle x,z \rangle(t),
\frac{d\mathcal{X}^s}{d\mathcal{T}^s}\langle x,z \rangle(t),z(t)\right)
\frac{d\mathcal{T}^s}{dt}\langle x,z \rangle(t)\right]\bigg\vert_{s=0}=0,
\end{equation}
they obtained
\begin{equation}
\label{quant georg}
\lambda(t) \Biggl[\frac{\partial L}{\partial \dot{x}}\langle x,z \rangle(t) X\langle x,z \rangle(t)
+\left(L\langle x,z \rangle(t)-\frac{\partial L}{\partial \dot{x}}\langle x,z \rangle(t) \dot{x}(t)\right)T\langle x,z \rangle(t)\Biggr],
\end{equation}
where $\lambda(t)=e^{-\int_a^t\frac{\partial L}{\partial z}\langle x,z \rangle (\theta)d\theta}$,
as a conserved quantity along the extremals of problem \eqref{PH_1}.
Our results improve those of \cite{Georgieva2002} in three ways:
(i) we consider a wider class of piecewise admissible functions;
(ii) we consider a more general notion of invariance
whose transformations $\mathcal{T}^s$, $\mathcal{X}^s$
and $\mathcal{Z}^s$ may also depend on velocities, i.e.,
on $\dot{x}(t)$ (note that if \eqref{eq inv ph1_2} holds
with $\mathcal{Z}^s\langle x,z \rangle = z$, then \eqref{def inv georg} also holds);
(iii) the conserved quantity \eqref{quant georg}, up to multiplication by a constant,
is a particular case of \eqref{quantity PH1} when there is no transformation in $z$
($Z=\left.\frac{\partial \mathcal{Z}^s}{\partial s}\right\vert_{s=0}=0$).
The results here obtained can be generalized to higher-order variational problems of Herglotz type.
This is under investigation and will be addressed elsewhere.

\section*{Acknowledgments}

This work was supported by Portuguese funds through the
\emph{Center for Research and Development in Mathematics and Applications} (CIDMA)
and the \emph{Portuguese Foundation for Science and Technology} (FCT),
within project PEst-OE/MAT/UI4106/2014. The authors would like to thank
an anonymous Reviewer for valuable comments.

redpajama_set_name: RedPajamaArXiv


text:
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Polishology: Happy First Birthday, Polishology!
Happy Blog Birthday! What an unusual mani, love it!
Felice compleanno! the manicure you did is perfect and cute!
Happy blogiversary and I love your nails!!
Can't go wrong with cupcakes, congrats!
Happy one year! Cupcake manicures always win!
Happy blog birthday! Your mani is very cute. I thought it water marble at first!


text:
<?php

namespace ResaSystem\Controllers;

use Doctrine\Instantiator\Exception\InvalidArgumentException;
use ResaSystem\Services\CachingService;
use Slim\Http\Request;
use Slim\Http\Response;
use Sumeko\Http\Exception\BadRequestException;

class CacheController extends BaseController
{
    /**
     * @var CachingService
     */
    private $cachingService;

    /**
     * CacheController constructor.
     *
     * @param CachingService $cachingService
     */
    public function __construct(CachingService $cachingService)
    {
        $this->cachingService = $cachingService;
    }

    /**
     * Gets data from the cache.
     *
     * @param Request  $request
     * @param Response $response
     * @param          $args
     *
     * @return Response
     * @throws BadRequestException
     */

    public function getData(Request $request, Response $response, $args)
    {
        try {
            return $this->jsonDataResponse($response, $this->cachingService->get($args['key']));
        } catch (InvalidArgumentException $e) {
            throw new BadRequestException($e->getMessage());
        }
    }

    /**
     * Saves data in the cache.
     *
     * @param Request  $request
     * @param Response $response
     * @param          $args
     *
     * @return Response
     * @throws BadRequestException
     */
    public function setData(Request $request, Response $response, $args)
    {
        try {
            $key = $args['key'];
            $ttl = $request->getParam('ttl') ?: 0;
            $data = $request->getParam('data');
            $this->cachingService->set($key, $data, $ttl);

            return $this->jsonDataResponse($response, $data, ['ttl' => $ttl]);
        } catch (InvalidArgumentException $e) {
            throw new BadRequestException($e->getMessage());
        }
    }

}


Dame Elizabeth Marvyn Charity. Ufton Court, Ufton Nervet, Berkshire 1974. . The dole is given to all residents who attend when they are called, one loaf of bread per head to each home of an agricultural worker, and one loaf to each other home in the parish. About one hundred and fifty loaves of bread are distributed.


text:
Services & Apps »
technical abilities
Now, manage your mental health and chronic conditions with an app
The app takes patients through 10 sessions over a period of three months, covering topics such as stress, vulnerability and illness.IANS | August 17, 2017, 14:49 IST
NEW YORK: Researchers have developed a smartphone app to help middle-aged and older adults self-manage their mental illness and other chronic conditions, suggests new research.
First, the researchers determined the technical abilities and needs of middle-aged and older adults with serious mental illnesses using smartphones. The researchers then developed the content and modified an existing smartphone platform.
The app takes patients through 10 sessions over a period of approximately three months, covering topics such as stress vulnerability and illness, medication adherence and strategies, and substance and medication abuse, according to the study published in the American Journal of Geriatric Psychiatry
Physicians can remotely monitor app use, and intervene when problems are detected, facilitating telemedicine for less accessible populations.
The researchers found that even patients with limited technical abilities could use this app successfully.
"The use of mobile health interventions by adults with serious mental illness is a promising approach that has been shown to be highly feasible and acceptable," explained lead investigator Karen Fortuna of Geisel School of Medicine at Dartmouth in the US.
"These technologies are associated with many advantages compared with traditional psychosocial interventions, including the potential for individually tailored, just-in-time delivery along with wide dissemination and high population impact," Fortuna said.
"Nevertheless, the process of adapting an existing psychosocial intervention to a smartphone intervention requires adaptation for a high-risk group with limited health and technology literacy," Fortuna added.
Tags : Services & Apps, smartphone app, mental illness, chronic conditions, smartphone, app, technical abilities, healthcare
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(For Super Game Boy only.) On the title screen, hold any direction on the Control Pad and press Start. Keep holding the Control Pad until the screen border color changes. Depending on the direction held, a different color border will appear.


H-I Idibia, Former member of defunct music group "Da Natives" and younger brother of African pop star Tuface Idibia has announced on his Facebook page that he has been denied entry into the United States of America.
H-I Idibia who has been living in Woodbridge, Virginia for years now with his family made the announcement as his fans on Facebook could not withhold their surprises.
You may recall that barely 48 hours ago, the Senior Special Assistant to the President on Foreign Affairs and Diaspora, Abike Dabiri-Erewa, advised Nigerians who have no compelling or urgent reason to travel to the US to postpone their travel plans until the new administration's policy on immigration is clear. Dabiri-Erewa said that the warning became imperative due to series of reports her office has received in recent times .
"In the last few weeks, the office has received a few cases of Nigerians with valid multiple-entry US visas being denied entry and sent back to the Nigeria. In such cases reported to the office, such affected persons were sent back immediately on the next available flight and their visas were cancelled".
Onyeama spoke with newsmen in Abuja and asked Nigerians to dismiss the advise given by Dabiri-Erewa. He said there are no reports of Nigerians being turned back at any US airport.
He added that he had spoken to the US ambassador to Nigeria and high level US officials who said nothing of such had happened.


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I use the materials and techniques of katazome (paste-resist stencil dyeing) to capture my experience of nature. My materials—cloth, rice paste resist, soymilk, natural dyes and pigments—engage my senses. The process creates a centering rhythm and a space for reflection. This blog is a journal of that process.
These small works range from approx. 6"x 9" to 10" x 12." I am experimenting with Japanese Katazome techniques on washi (handmade kozo). I first learned these techniques on fabric from John Marshall. My goal with this work is to achieve differentiation between the various stenciled and painted layers, hopefully giving the work depth and surface interest. The results you see here are inconsistent, and I think I understand which variables to change next time. I am excited about the possibilities of this technique and intend to explore it further!
©Kit Eastman 2007-2019. All Rights Reserved.


text:
After Modi, Amit Shah Also Denied Working On Nationwide NRC
Did PM Narendra Modi contradict the December 9 statement of Home Minister Amit Shah in Lok Sabha. Amit Shah said that the government would implement NRC on pan-India basis. But PM Modi denied working on all-India NRC while speaking at Ramlila Maidan in Delhi.
Amit Shah on NPR, NRC and CAA protest
The Home Minister said that CAA was about giving citizenship to people belonging to certain class and that it couldn't deprive citizens of their citizenship. He further said that NPR was a register of population residing in India. It would help in framing schemes.
He said that in NRC every individual would be asked to prove his basis for becoming a citizen of this country. He assured that there was no similarity between NRP and NRC and that these two are different laws and couldn't be used to supplement each-other.
Amit Shah criticized opposition
The Union Home Minister accused the opposition of trying to misleading public on NPR because they couldn't do so on CAA. He said that people had understood what CAA was and what its advantages were. He gave example of … Read the rest
China Sees Hong Kong Boiling In Support Of Uighurs
Pro-democracy protestors rallied in Hong Kong streets to show solidarity with Uighur minorities in China. They said that their condition was no different than that of Uighurs in mainland China.
But a protestor went ahead and pulled a Chinese flag hoisting over a government building during the rally. This short incident of violence was enough for the riot control police to swing into action to disperse the protestors.
Uighurs in China
China is facing flak from the world community for keeping over 10 lack Uighurs out of whom most are Muslims in captivity in north-west province Xinjiang. Earlier Beijing used to deny having any Uighur camps but it now says that these camps are vocational training centers for fighting against terrorism.
Hong Kong with Uighur
Hong Kong has kept a close watch over the Uighurs camps in Xinjiang and for this reason, people protesting against the illegal detention of Uighurs have become a common sight in Hong Kong. Sunday rally was also dedicated to support the cause of Uighur Muslims.
Sunday rally in Hong Kong
More than 1000 people gathered … Read the rest
BJP To Start Poll Campaigns For Delhi Elections From PM Modi's Rally
Weeks after the parliament passing the National Capital Territory of Delhi (Recognition of Property Rights of Residents in Unauthorised Colonies) Bill, Prime Minister Narendra Modi will receive a total of 11 lack signatures by residents of those colonies as a gesture of gratitude at a mega rally in Delhi.
PM Modi's Delhi rally is going to be mega
BJP would start its election campaign for the assembly elections next year with the mega rally of PM Modi where he will address 2 lack people and apprise the Delhi residents about the milestones achieved by the centre including the bill for unauthorized colonies that grants ownership rights to the residents of unauthorized colonies.
According to senior BJP leader Vijay Goel, the rally was organized to thank PM Modi for regularizing the unauthorized colonies. He said that over 40 lakh residents of 1,731 colonies would be benefitted with this legislation. He further said that the BJP was in full-swing to win assembly election after winning all 7 Lok Sabha seats of Delhi. It will be PM Modi's first election rally in Delhi after winning a landslide victory in general election last year. … Read the rest
News & Politics / Today's Special
July 1, 1987 Is The New Cut Off For Citizenship In India
The centre went on an overdrive to dispel fears regarding CAA and the proposed nationwide implementation of National Register of Citizens (NRC). Muslims fear that NRC will strip them of their citizenship and leave stateless.
Ministry of Home Affairs dispelled the fear of NRC
The MHA announced that no individual who was born or whose parents were born in India on or before July 1, 1987 would be considered an illegal immigrant. A senior office from MHA said that people born on or before the prescribed date would be considered Indians under naturalization as per the law.
There was no comment on nationwide implementation of NRC but the official said that there was no similarity between CAA and NRC in Assam because the cut-off date in NRC was 1971. The official said that there was no discussion on nationwide implementation of NRC.
2004 Citizenship Act Amendments
The amendments laid certain conditions for awarding citizenship. People that fulfil the following conditions are considered natural citizens of India.
• Born in the country on or after January 1, 1950 but before July 1, 1987
IPL 2020 Auction: Australian Players Dominated The Auction With Pat Cummins Getting Rs. 15.50 Crore
Australian players received highest bids in the Indian Premier League (IPL) auction 2020. The fast bowler Pat Cummins got the highest bid of Rs. 15.50 crore by Kolkata Knight Riders (KKR).
IPL auction 2020
A total of 62 players were auctioned and Pat Cummins was the most expensive player of the auction. He was followed by Glenn Maxwell who was bought by Kings XI Punjab for Rs. 10.75 crore. Piyush Chawla, a leg spinner, was bought by three-time IPL Champions Chennai Super Kings in a surprise buy. He got Rs. 6.75 crore.
Here's the complete list of auction
CSK retained its core squad but added four bowling options including the leg spinner Piyush Chawla and English all-rounder Sam Curran to the team.
This season, DC invested heavily on big-hitters. They spent Rs. 7.75 crore on ShimronHetmyer and bought Marcus Stoinis for Rs. 4.80 crore.
In addition to spending Rs. 10.75 crore on Glenn Maxwell, Punjab also invested on the West Indies fast bowler Sheldon Cottrell. He was paid Rs. 8.50 crore.
Imran Khan Speaks On Citizenship Amendment Bill And Receives A Fitting Reply Fitting Reply
India categorically rejects Imran Khan's opinion on the Citizenship (Amendment) Bill and said that his thoughts were inspired by anti-India mindset. India also advised Imran Khan to work for his country.
Pakistan President Imran Khan in Geneva
Imran Khan said that India's CAB was creating a major refugee problem in South Asia. But India replied that his thinking shows prejudice and hatred towards India. Also, that Imran Khan should be more worried about his country.
India's Permanent Representative to UN, Rajiv K Chander further said that India strictly condemn the baseless comment of Imran Khan. Pakistan presented itself as a self-proclaimed champion of human right but little did it know that the minority population had shrunk from 23% in 1947 to 3% today maintained Rajiv K Chander. The draconian blasphemy laws and blatant use of forced conversions reduced the size of minorities in Pakistan.
Imran Khan should take care of his country
Rajiv K Chander: Pakistan is a self-proclaimed champion of human rights that has shrunk the size of its own minority community, 23% in 1947 to 3% today, by subjecting them to draconian


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Home Press ReleasesJoint Statement between the Kingdom of Saudi Arabia and the Islamic Republic of Pakistan
Joint Statement between the Kingdom of Saudi Arabia and the Islamic Republic of Pakistan
May 2, 2022| Press Releases|
H.E. Mr. Muhammad Shehbaz Sharif, Prime Minister of the Islamic Republic of Pakistan paid an official visit to the Kingdom of Saudi Arabia at the invitation of His Royal Highness Prince Mohammed bin Salman bin Abdulaziz Al Saud, Crown Prince & Deputy Prime Minister from 27 – 29/09/1443H corresponding to 28-30 April 2022.
An official meeting was held between both sides, during which they reviewed the historical relations between the two countries & the close cooperation in various fields, as well as discussed ways to strengthen relations in all areas.
The text of the following joint statement was released on the occasion.
The Text: Joint Statement between the Kingdom of Saudi Arabia and the Islamic Republic of Pakistan


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Natural Resources Grants
Browse 12224 Federal Natural Resources Grants below, sorted by the deadline to apply. The United States Government agency or department offering the grant is also listed.
Select a specific Natural Resources grant to read the full description of the opportunity. The full description contains the grant type, total award amount, eligible applicants, important dates, and official contact details. If you wish to search for a specific keyword or view grants sorted by governmental agency, use the links on the menu bar.
Close Date Grant Title Agency
Apr 15, 2011 BLM-UT NLCS GSENM Nipple Lake Pollen Analysis Project Bureau of Land Management
Apr 15, 2011 Restore America's Estuaries Fish and Wildlife Service
Apr 15, 2011 Development, Management, and Protection of Indian Tribal Water Resources Bureau of Reclamation Pacific Northwest Region
Apr 15, 2011 Coastal and Estuarine Land Conservation Program - FY 2012 Competition Department of Commerce
Apr 15, 2011 Intent to Single Source Award two Bear Interns National Park Service
Apr 15, 2011 FA-BLM AZ Interpretive Association for the AZ Strip District Bureau of Land Management
Apr 15, 2011 Conservation Innovation Grants - Wyoming State Component Wyoming State Office
Apr 15, 2011 Henry Hagg Accessibility -- WACO Bureau of Reclamation Pacific Northwest Region
Apr 14, 2011 INtent to Single Source Award for Bird Monitoring National Park Service
Apr 14, 2011 Finding the Next Generation of Land Ethic Leaders Fish and Wildlife Service
Apr 13, 2011 Clear Creek Environmental Water Program: Implementation Development Fish and Wildlife Service
Apr 12, 2011 BLM OR-WA: Peterson Road - Juniper Dunes Recreation Area Access Bureau of Land Management
Apr 10, 2011 Upper Arkansas River NRDAR: Native Plant Propagation at Hayden Ranch Fish and Wildlife Service
Apr 10, 2011 Punchline Mountain Bike Trail and two Dog Reroute Bureau of Land Management
Apr 09, 2011 Restoration of Trumpeter Swans in Pacific Flyway Fish and Wildlife Service
Apr 08, 2011 Migratory Bird Coordinator Fish and Wildlife Service
Apr 08, 2011 Walker Basin Restoration Program - Water Rights Acquisition Bureau of Reclamation Mid Pacific Region
Apr 08, 2011 BLM CA Moreno Shale Formation Rare Earth Element Project Bureau of Land Management
Apr 08, 2011 Interpretive programs and volunteer coordination National Park Service
Apr 08, 2011 Great Lakes Climate Extension Capacity Building Department of Commerce
Apr 08, 2011 Englebright Dam Reach/Narrows Reach Channel Habitat Restoration, Yuba River, Ca Fish and Wildlife Service
Apr 07, 2011 Fund Arizona Fish and Game Department to Study Long Nosed Bats National Park Service
Apr 07, 2011 Competitive Faculty Development Program Fish and Wildlife Service
Apr 06, 2011 Western Alaska Landscape Conservation Cooperative Projects 2011 Fish and Wildlife Service
Apr 05, 2011 Vermont Conservation Innovation Grant (Cig) Vermont State Office
Apr 04, 2011 Montana/Dakota Youth Assistance Program Utilizing Youth Groups Bureau of Land Management
Apr 01, 2011 Lahontan Cutthroat Trout - Pyramid Lake Fish and Wildlife Service
Apr 01, 2011 Landbird Inventory & Monitoring North Coast & Cascades Network National Park Service
Apr 01, 2011 Owyhee Canyonlands Wilderness Education and Outreach, Boise ID Bureau of Land Management
Apr 01, 2011 Scion and Seed Collection and Processing National Park Service
Apr 01, 2011 Oklahoma Texas Area Office Water Conservation Field Services Program Bureau of Reclamation Great Plains Region
Apr 01, 2011 2012 National Sea Grant College Program Dean John A. Knauss Marine Policy Fellowship Department of Commerce
Apr 01, 2011 Opportunity FWS-JVGLRI-2011 Fish and Wildlife Service
Apr 01, 2011 Conservation Innovation Grants - FY2011 Colorado State Component Colorado State Office
Apr 01, 2011 A Cooperative Agreement to advance our understanding of and ability to anticipate changes in the Earth's environment Department of Commerce
Apr 01, 2011 Interior Black Rail Literature Compilation Fish and Wildlife Service
Mar 31, 2011 BLM-UT Inventory of Mineral Resources including Energy Minerals in the BLM Cedar City Field Office Bureau of Land Management
Mar 31, 2011 Diagnostic, field, and training assistance for avian health and disease monitoring Migratory Birds
Natural Resources Grants 5201-5240 of 12224
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Bainbridge Island may see some long-awaited rain this weekend.
That's the latest forecast for the island from the National Weather Service in Seattle.
Saturday will see a 30 percent chance of showers, mainly after 11 a.m. It will stay mostly cloudy, with the high temperature reaching near 70 degrees.
Saturday night, the threat of rain continues (20 percent chance of showers). It will remain mostly cloudy, with a low around 54.
On Sunday, raindrops may keep falling after 11 a.m., as a 20 percent chance of showers remains. It will be mostly cloudy, with a high near 71, and stay cloudy overnight, with a low around 54.
The sunshine returns on Monday, with mostly sunny skies and a high near 74.
Sunny weather is expected to stick around until midweek.