In a Reiki session (called a healing), the practitioner passes healing energy into the seven major energy points (chakras, pronounced shock-rahs) in the body. These points are located at the top of the head, the face, throat, heart, sternum, naval, and the pubic bone. While passing the energies, the practitioner's hands become very warm. During the process, the practitioner wi ll lightly place their hands on each of these areas so that the healing energies may be sent to each chakra directly. The practitioner will also place their hands on the knees and the feet for additional healing. A complete Reiki session involves passling the healing energies first into the head and then to each chakra, the knees, and the feet, moving down the front of the body and back up, repeating the procedure on the back of the body. For special "trouble" areas, the practitioner may directly address them by placing their hands on these spots for the purpose of passling additional energy where it is most needed. This is always at the discretion of the person being healed. When complete, the person receiving the healing usually feels rested and refreshed.
Reiki energy will pass through clothing so it is not necessary to undress for a session unless you are also receiving massage.
A normal session may take anywhere from 40 minutes to an hour. For subjects with special problems, a healing session can take longer.


La Hacienda Taqueria and Golden Wok China Buffet will not reopen for business because of the recent Wildcat Creek flood, which displaced 300 residents, as reported by The Manhattan Mercury.
La Hacienda confirmed Henderson's statement to the Mercury on Wednesday morning, attributing the closing to the company's insurance not covering flood losses. The taco shop was opened in February of 2010.
La Hacienda and Golden Wok are located in within the strip mall shown above.
Powercat Sports Grill, Goblin Games, Via Christi Therapy Center and Legends Sports Bar and Grill will remain closed until damage is assessed and the businesses move forward with a reopening plan.
Shannon Lewis is the owner of Debonaire's Haircuts in the same strip of businesses that had feet of water standing in them. He is now located in Candlewood next to Little Apple Pilates off of Kimball Avenue and Seth Child's Road.
Genesis Health Clubs managed to reopen on Wednesday after more than 60 employees, volunteers and disaster restoration workers cleaned the facility, as reported online via their Facebook page.
Manhattan Running Company, located along Anderson Avenue and Garden Way, began to take water during the surge as well. After the owners had the water under control, they bought a half dozen pizzas for the Riley County Police Department and Firefighters who were rescuing over 50 tenants on the same street.
"The fine folks at Manhattan Running Company also fed the first responders so they could continue to make rescues and get people and their animals to dry land. All this while tending to their own flooding issues in their store. I'm sure there are many examples of other businesses doing the similar things today. Needless to say, I was quickly reminded how fortunate I am to live in such an amazing little town where people pull together to help one another in hard times," Amee continued.
Schwab Eaton, CSL Plasma and The Midwest Dream Car Collection all were affected by the flood along Anderson and Seth Child Road, among several hundred homes in the area.
As a community full of small businesses, we encourage our readers to support the damaged businesses once they reopen.
In response to the recent flooding in Manhattan, Kansas and the surrounding area, the Greater Manhattan Community Foundation has created the 2018 Manhattan Flood Recovery Fund. This fund is now active and accepting donations for relief and recovery efforts for the flooding that began on September 1, 2018.


There's nothing like watching the Bruins dominate the ice at TD Garden. Thanks to a partnership with Eversource, that experience has gotten even better. Over the past five years, Eversource has empowered the Bruins and TD Garden with a hat trick of energy efficiency improvements - LED lighting, advanced controls and an improved HVAC system - enhancing the fan experience and saving enough energy a year to power all of the homes of a sold-out crowd (17,565 people) for 19 days!


Chicago: "Rock and Roll; Respect; Interview with Al Bell [Part 3 of 3]," WGBH Media Library & Archives, accessed April 20, 2019, http://openvault.wgbh.org/catalog/V_B2A2996A84314A8DB66990E1CB7B226F.
MLA: "Rock and Roll; Respect; Interview with Al Bell [Part 3 of 3]." WGBH Media Library & Archives. Web. April 20, 2019. <http://openvault.wgbh.org/catalog/V_B2A2996A84314A8DB66990E1CB7B226F>.


The Egliana company was founded in 1992 by A. Drasutavicius. We began providing road haulage services in 1995. We care for every new customer, so from the very beginning of our activities we have focused our attention on meeting the requirements of our customers by the services we provide. Ensuring our customers of our reliability is the basis for our growth. Our company started with one person and two trucks, and today we can boast that we are a medium sized Lithuanian road haulage company. The company is and has been a member of the Linava Lithuanian National Road Carriers' Association since 1999. The company owns a vehicle fleet of 20 trucks (120 m3) meeting EURO 3 or EURO 5 standards. All cargo transported by us is insured according to the CMR convention. Because of our concern on how to best satisfy the requirements of our customers, we established the subsidiary UAB Egliana ir Ko in 1999, which is a member of the Lithuanian National Freight Forwarders Association LINEKA. UAB Egliana ir Ko managers, having vast experience, co-operate with their partners – carriers from Lithuania, Poland, Latvia, and Russia. This enables our company to manage a fleet of over 150 vehicles in Western and Eastern Europe, and Russia.
We serve you, saving your time and always striving for the utmost efficient co-operation in the future. Even if you contact us for the first time, we will serve you with the same level of excellence and quality that we apply to our loyal customers. Our motto: ALWAYS ON TIME, ALWAYS IN THE RIGHT PLACE.


text:
Q: Matplotlib Scatter Plot Color One Point Given the following data frame:
import pandas as pd
df = pd.DataFrame({'X':[1,2,3],
                   'Y':[4,5,6],
                   'Site':['foo','bar','baz']
                   })
df

    Site    X   Y
0   foo     1   4
1   bar     2   5
2   baz     3   6

I want to iterate through rows in the data frame to produce 3 scatter plots (in this case, though a general solution for n rows is needed):
One in which the dot for "foo" is red and the rest are blue,
another in which the dot for "bar" is red and the rest are blue,
and a third in which the dot for "baz" is red and the rest are blue.
Here's a sample for "foo" done manually:
import matplotlib.pyplot as plt
%matplotlib inline
color=['r','b','b']
x=df['X']
y=df['Y']
plt.scatter(x, y, c=color, alpha=1,s=234)
plt.show()

Thanks in advance!

A: You have two options:

*

*Create two "views" from the data, one with the to-be-red elements, and other with the remaining elements. You would apply conditional slicing for that, for example. Then, you plot one set in red, and the other in blue. That would be two scatter commands in the same figure. Repeat for each set.

*Quite conveniently, the default jet colormap is blue and red in its extremes. You can then just call scatter once for all the data, but have the c argument of scatter set to a boolean array taken from the original data via conditional slicing. That would make the colors for the desired items be mapped to "1", while the other, false items would be "0", and colormapped accordingly.
Note: when I talk about conditional slicing, its like:
interesting_items = array[array == interesting_value]

or some equivalent in Pandas.

redpajama_set_name: RedPajamaStackExchange


text:
import javax.servlet.http.HttpServlet;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
import java.io.IOException;

import com.twilio.twiml.Body;
import com.twilio.twiml.Message;
import com.twilio.twiml.MessagingResponse;
import com.twilio.twiml.TwiMLException;

public class TwilioServlet extends HttpServlet {

  // service() responds to both GET and POST requests.
  // You can also use doGet() or doPost()
  public void service(HttpServletRequest request, HttpServletResponse response) throws IOException {
    Message sms =
      new Message.Builder().body(new Body("The Robots are coming! Head for the hills!")).build();

    MessagingResponse twiml = new MessagingResponse.Builder().message(sms).build();

    response.setContentType("application/xml");

    try {
      response.getWriter().print(twiml.toXml());
    } catch (TwiMLException e) {
      e.printStackTrace();
    }
  }
}

redpajama_set_name: RedPajamaGithub


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Built with stability in mind and little else, the Walk N Work still suffers from flaws inherent to desks paired with running treadmills. It poses both an inconvenience and a safety hazard to users, and its incompatibility with desking peripherals makes it an ergonomic dud. We caution deskers against the Walk N Work and its ilk, and encourage them to use dedicated walking workstations.
Not for use with ergonomic peripherals.
Impedes access to treadmill console.
The Walk N Work is an ill-fated attempt to convert a running treadmill to a treadmill desk. While it's certainly more stable than other similar offerings, it still creates a workspace that is unergonomic, unstable, and unsafe.
Every once in a while, we at the WorkWhileWalking labs encounter products that remind us just how uncommon it is to find an acceptable walking workstation. The treadmill desk industry is saturated with kluges that try to grab a piece of the rising trend without a clear understanding of user safety and ergonomics. Among them is the Walk N Work, a product with great intentions and poor execution.
The Walk N Work, which looks like a fusion between a bar stool and a sawhorse, is the latest on our list of shoddy workarounds meant to convert running treadmills to walking desks. We've already explained why a running treadmill is never a good substitute for a dedicated walking treadmill, but we nevertheless keep finding these platforms that sit between the walker and the treadmill console.
We say "desk" because of the myriad problems inherent in the Walk N Work – and all similar hack treadmill desks. For starters, the fact that this thing sits in front of the treadmill console already impedes its usability as a treadmill desk. Pictures on the Walk N Work website do show the desk paired with a repurposed running treadmill, but anyone who decides to walk on one of these should be aware of how their treadmill's side rails may obstruct the desk. Add to that the space separating the user from the treadmill console and you've got yourself a recipe for frustration, or worse.
The Walk N Work is not only inconvenient, it's downright unsafe. The distance you have to reach for the console means that you're less able to quickly adjust the speed of the treadmill or to stop it without using an emergency stop plug. Additionally, the Walk N Work takes up a significant amount of space on the treadmill. Judging by the product website's pictures, you lose half the walking space of the belt and risk falling off the back. Your natural response will be to walk as far forward as you can, in which case you risk slamming your shin into that crossbar.
In an effort to retain as much space as possible, the Walk N Work was made extremely slim. While the website does not offer specific dimensions for the table's depth, photos indicate that there is barely enough table depth to accommodate a laptop. You can forget about the monitor arms and keyboard trays that make a good ergonomic work station. Your neck, wrists and arms are in for a rough time on the Walk N Work. Even if paired with a walking treadmill, this desk's inability to accommodate ergonomic peripherals makes it impossible to recommend.
The Walk N Work does not currently have pricing or shipping published, and does not look like it's available on the market yet. Nevertheless, the Walk N Work gets a resounding pass from our experts. You're better off finding a dedicated treadmill desk for your workspace.
So I've rigged up a monitor on a pole behind my treadmill, but finding a stable platform for the keyboard has been a challenge. If you have monitors mounted separately, would this work better?
We do recommend full treadmill desks for an ergonomically sound workstation. And if you are looking for a keyboard tray, check out our blog on Selecting The Right Ergonomic Keyboard and Adjustable Keyboard Tray.


text:
"Baseball and insurance are the only industries exempt from antitrust laws."
— Americans United for Change on Monday, October 12th, 2009 in a television advertisement
Liberal group says health insurance, baseball are only industries exempt from antitrust laws
By Louis Jacobson on Tuesday, October 13th, 2009 at 3:59 p.m.
An ad from the liberal group Americans United for Change says baseball and insurance are the only two industries with antitrust exemptions.
Supporters of the Democratic health care plan have invoked baseball in their latest television ad that tries to demonize the health insurance industry.
In the 30-second ad, the liberal group Americans United for Change asks, "How are professional baseball and insurance companies alike? Baseball and insurance are the only industries exempt from antitrust laws. How are they different? Insurance industry executives are scared of competition. Baseball players aren't. When baseball players fix the games, they get in trouble. When health insurance executives fix the games, they get rich. Time for competition when it comes to health insurance. We need the choice of a public health insurance plan."
In this item, we'll focus on their opening claim, that "baseball and insurance are the only industries exempt from antitrust laws."
Let's first explain what "antitrust" means. Antitrust laws protect against anticompetitive conduct by cartels and monopolies. Federal antitrust laws target price-fixing, predatory pricing and mergers that reduce competition. Courts have consistently ruled that the federal government has the authority to pass laws that police competition in "interstate commerce" — that is, business activity that crosses borders and ripples through the national economy.
While federal antitrust laws do cover most industries, some are exempted, thanks either to the courts or Congress. The Americans United for Change ad cites what is probably the best-known exemption: baseball.
Baseball's sweeping exemption stems from a 1922 U.S. Supreme Court decision. The justices, presented with an upstart league's lawsuit against the well-established National League, ruled that teams' travel across state lines was not "essential" to the business. As a result, the justices ruled, the federal government had no antitrust power over baseball, since games were essentially events held in one state. Most notably, the exemption allows Major League Baseball to prevent teams from moving without the league's consent. In more recent challenges, the high court declined to overturn baseball's exemption, saying it was up to Congress to rescind it. Despite numerous bills, lawmakers have so far declined to do so.
So, the ad is correct that baseball has an antitrust exemption. Does insurance have one too?
It does. Insurance — in fact, all kinds of insurance, not just health coverage — is exempt from federal antitrust laws, though these protections are more limited than they are for baseball teams. A 1945 law exempts from federal antitrust law the "business of insurance" as long as it is "regulated by state law." However, in some contexts — such as if the conduct involves an agreement to "boycott, coerce or intimidate" — federal antitrust law does apply.
This is hardly an arcane issue. As Congress struggles with health care reform legislation, some lawmakers are seeking to lift health insurers' antitrust exemption. Sen. Patrick Leahy, D-Vt., has introduced the Health Insurance Industry Antitrust Enforcement Act, which would, among other things, "repeal the federal antitrust exemption for health insurance and medical malpractice insurance companies for flagrant antitrust violations, including price-fixing, bid rigging, and market allocations." Reps. Diana DeGette, D-Colo., and John Conyers, D-Mich., have introduced an equivalent measure in the House. Both measures are pending.
Even though baseball and insurance have somewhat different types of antitrust exemptions, we find they are similar enough to justify the ad's pairing of the two. But when the ad says that baseball and insurance are "the only industries exempt from antitrust laws," it's wrong.
For starters, three additional industries — agricultural cooperatives, fishing cooperatives and maritime shipping — have, like baseball and insurance, what the American Bar Association calls "general" antitrust exemptions. Each of these exemptions stem from a law passed by Congress. For example, they permit co-ops, from milk producers to cranberry growers, to jointly market their products, including setting prices and output. (Congress has also exempted labor unions from antitrust law, but unions aren't an "industry," so we won't include them in our calculations.)
Also, other industries benefit from more limited forms of antitrust exemptions, usually laws that protect specific practices rather than invoking a blanket exemption for business activity.
Studies by the ABA and a federal commission counted almost two dozen such partial exemptions. These govern a wide range of activities, including the actions by broadcasters to curb violence in television shows, efforts by airlines to ease airport congestion, attempts by financially troubled newspapers to merge some functions with competitors, and activities by soft drink producers to draw up exclusive sales territories.
The Americans United for Change ad is generally correct to equate the antitrust exemptions of baseball and health insurance, but the one for health insurance is more limited. And the ad is incorrect to say that these are the "only industries exempt from antitrust laws." Agricultural and fishing co-ops and maritime shippers have similar exemptions. And a host of other sectors, notably freight rail, have some pretty significant antitrust protections as well. We rate the ad's claim False.
About this statement:
Published: Tuesday, October 13th, 2009 at 3:59 p.m.
Researched by: Louis Jacobson
Edited by: Bill Adair
Subjects: Baseball, Health Care
Americans United for Change, " Baseball ," advertisement released Oct. 12, 2009
American Bar Association Section of Antitrust Law, Federal Statutory Exemptions from Antitrust Law , book published in 2007
Antitrust Modernization Commission, final report of the commission, April 2, 2007
Sen. Patrick Leahy, "Leahy Introduces Bill To Repeal Antitrust Exemption For Health, Medical Malpractice Insurance Companies" news release , Sept. 17, 2009
Rep. Diana DeGette, "DeGette Introduces Bill to Repeal Antitrust Exemption for Health, Medical Malpractice Insurance Companies" news release , Sept. 17, 2009
Dow Jones Newswires, " House Panel Passes Bill Stripping Rail Antitrust Exemptions ," Sept. 16, 2009
U.S. Supreme Court, Federal Club v. National League , decided May 29, 1922
ESPN.com, " Baseball's antitrust exemption: Q & A ," Dec. 5, 2001
Interview with Jonathan L. Rubin, partner with the law firm Patton Boggs, Oct. 13, 2009
Interview with Barry Nigro, partner with the law firm Fried, Frank, Harris, Shriver & Jacobson, Oct. 13, 2009
Interview with Jeremy Funk, spokesman for Americans United for Change, Oct. 13, 2009

redpajama_set_name: RedPajamaCommonCrawl


text:
John Tory's Raptors jacket makes noise
Staff The Canadian Press
Toronto Mayor John Tory has often worn his love of the Raptors on his sleeve.
He did that again, and this time literally, during Game 1 of the NBA Eastern Conference final between Toronto and Milwaukee Bucks on Wednesday night. Tory channelled his inner Don Cherry and wore a loud black jacket covered with gold Raptors logos — in the style of Drake's OVO brand — while mingling with fans watching the game in Jurassic Park outside Scotiabank Arena.
Tory's fashion statement made some noise, with the Sportsnet broadcast cutting away several times to show the Toronto mayor cheering along with fans as the Raptors took an early lead against the Bucks. A tweet featuring four pictures of Tory hobnobbing in his Raptors-themed sartorial splendour had over 1,000 likes as of Thursday morning.
Mayor John Tory wearing a Raptors jacket ahead of Game 1 against the Milwaukee Bucks.
Max Trotta/Global News
But perhaps a jacket that mimicked Drake's brand also brought the Toronto rapper's famous sports curse, as the Raptors blew a fourth-quarter lead en route to a 108-100 loss at Milwaukee's Fiserv Forum.
Tory has shown off his Raptors fandom before. He wore a jacket with the Raptors' popular "We The North" slogan to a meeting with Prince Harry and Prime Minister Justin Trudeau to promote the 2016 Invictus Games in Toronto. And he has joked that Raptors superstar Kawhi Leonard deserves to be Toronto's mayor after Leonard's buzzer-beating winning shot in Game 7 of Toronto's Eastern Conference semifinal with Philadelphia.
Game 2 of the East final is Friday night in Milwaukee. There has been no word yet on whether Tory plans another fashion statement.
© 2019 The Canadian Press


The Panel will discuss the implementation of the key actions under the Integrated SET-Plan with focus on renewable energy. Throughout 2015 the representatives of the Commission, Member States, Associated Countries part of the SET Plan, and relevant stakeholders have been working on translating the key actions into agreements on strategic targets and priorities in each of the action areas, as well as on implementation plans that will aim to deliver the agreed targets and priorities. The aim of the panel is to discuss the state of play in the area of renewable energy and the way forward.
The panel will discuss the implementation of key actions under the Integrated SET-Plan, focusing on energy efficiency. It will also consider the lessons member states learned from the implementation of the 2020 Framework targets on energy efficiency and R&I and what should be done to meet the ambitious targets of the 2030 Framework. In addition to the above issues, the panel discussion will consider the review of the directive on energy efficiency to be discussed in the EU Council during the Slovak Presidency.
The panel discussion will examine prospects for strengthening the role of the Agency for the Cooperation of Energy Regulators (ACER) in harmonizing member state regulatory frameworks, which is a fundamental precondition to the creation of a fully integrated energy market within the EU. Another central issue to be discussed by the panel concerns the electricity market design package that is expected to be discussed during the 2016 Slovak Presidency, including a review of the directives on energy efficiency and support for renewable sources of energy. In addition to key EU level topics, the panel will also reflect on the experiences of the Central European member states relating to the regional integration of energy markets.
A workshop presentation of the research findings produced by project CBC01014, supported by the Norwegian Financial Mechanism and co-funded from the Slovak state budget.
Representatives of gas transmission companies and experts from the member state energy ministries and the Energy Community Secretariat will be invited to comment on the major challenges facing the EU and member states in Central and South Eastern Europe relating to security of gas supplies and developing a strategic gas transmission infrastructure. The panelists will discuss the review of the EU directive on security of gas supply and the decision on transparency of intergovernmental agreements to be debated during the 2016 Slovak Presidency. Special attention will be paid to the implementation of the "Road Map towards the regional gas market among Visegrad 4 countries" adopted by the Visegrad Group Prime Ministers in Warsaw on 16 June 2013. They will also discuss the key challenges in the regional integration of V4 national gas markets.
The panel will assess the lessons learned in relation to the market-coupling in electricity between the Czech Republic, Slovakia (2009), Hungary (2012) and Romania (2014) that created the basis for building a regional electricity market in Central and South-Eastern Europe. They will consider the experiences of market-coupling from the point of view of the transmission network operators (ETSOs) and market operators (MOs) and the perspectives of other countries from the region on joining the integrated CZ-SK-HU-RO electricity market. Other issues include the main obstacles to expanding a regional electricity market and the prospects for market-coupling of regional electricity markets within the EU.


text:
Q: Checking to see if last 2 numbers in array both exist in 2D array using loops I have two arrays, one singular and the other 2 dimensional.
int[][] array1 = {
    new int [] {1, 22, 3, 44, 5, 66},
    new int [] {11, 22, 33, 44, 55, 66},
    new int [] {1, 2, 3, 4, 5, 6},
};

int[] array2 = new int[] {1, 2, 3, 5, 66}

I need to create a loop which searches the array1 for both the 2nd last digits in array2, so it would return how many times an array with array1 contains both 5 and 66, which is 1, as the other two only contain 1 of each number.
I already managed to write a function which returns how many times array2 as a whole exists in array1, this new function is effectively a refinement of that.
for (int a = 0; a < array1[i].Length; a++)
{
    for (int b = 0; b < array2.Length; b++)
    {
        if (array2[c] == array1[a][b])
            count++;

        temp[b] = array1[a][b];
    }
}

I feel all would be needed to search for just the last two digits is a slight change to this function, I tried to add in another loop but that didn't work either. How would I go about doing this? I'm using loops and not Contains for a reason since i'm still learning the basics.

A: The one thing is not clear in question that, does it matter which position the two digits occur in the 2D array?
If ithis is not the case, then you can use Intersect() which produces the set intersection of two sequences by using the default equality comparer to compare values:
var result = array1.Count(x => x.Intersect(array2.Reverse().Take(2)).Count() == 2);

If you have paid an attention we have used this line, for getting last two elements of array1:
array1.Reverse().Take(2);

.NET Fiddle
Additional:
If you want to find if last two elements of arrays in 2D array is equal to last two elements of array1, then you can try LINQ solution:
var result = array1.Count(x=> x.Reverse().Take(2).SequenceEqual(array2.Reverse().Take(2)));

Explanation of used extension methods:
Reverse() inverts the order of the elements in a sequence.

Take() returns a specified number of contiguous elements from the start of a sequence.

SequenceEqual() determines whether two sequences are equal by comparing the elements by using the default equality comparer for their type.
After getting last two elements of both arrays, we will use SequenceEqual() to determine if both arrays are equal.

A: var res = array1.Where((x) => (x.Contains(array2.Last()) && x.Contains(array2[array2.Length - 2]))).Count();

Explaination:

*
*array1.Where takes every subarray of array1 and filters the ones that
   meet a certain condition.
* The condition being every subarray of
   array1 contains the last && next-to-last element of array2.
*The
   Count() methods returns the number of subarrays that meet the
   conditions

A: You can create an array of target values and then count the number of times that the intersection of that array with each subarray in the 2D array contains all the items in the target array:
using System;
using System.Linq;

namespace ConsoleApplication2
{
    class Program
    {
        [STAThread]
        private static void Main()
        {
            int[][] array1 =
            {
                new [] {1, 22, 3, 44, 5, 66},
                new [] {11, 22, 33, 44, 55, 66},
                new [] {1, 2, 3, 4, 5, 6},
                new [] {1, 66, 3, 4, 5, 6} // This one has the target items out of order.
            };

            int[] array2 = {1, 2, 3, 5, 66};

            // Extract the targets like this; it avoids making a copy
            // of array2 which occurs if you use IEnumerable.Reverse().

            int[] targets = {array2[array2.Length - 2], array2[array2.Length - 1]};

            // Count the number of times that each subarray in array1 includes
            // all the items in targets:

            int count = array1.Count(array => array.Intersect(targets).Count() == targets.Length);

            Console.WriteLine(count);
        }
    }
}


text:
\section{Introduction}
As a standard cosmological model, the $\Lambda$CDM is widely
    accepted basing on some remarkable observations, including type Ia
    supernovae (SNe Ia) \citep{1998Riess, 1999Perlmutter}, cosmic
    microwave background (CMB)
    \citep{2011Bennett,2013Bennett,2014Planck,2016Planck}, baryon
    acoustic oscillations (BAOs) \citep{2005Eisenstein} and
    gamma-ray bursts \citep{2015Wang}. But many imperfections of
    $\Lambda$CDM are also needed to be faced, including the fine tuning
    problem and the cosmic coincidence problem \citep{1989Weinberg,
        1999Zlatev}. Additionally, the capability of using SNe Ia to prove
    cosmic acceleration is under doubt recently \citep{2016Nielsen,
        2016Shariff}.

    In a bunch of cosmological models, power-law cosmology was proposed
    with an assumption that the scale factor varies as $a(t)\propto
    t^{n}$ \citep{1997Dolgov, 2014Dolgov}. Many works have devoted into
    the study of power-law cosmology. \citet{2007Melia} and
    \citet{2012Melia} made a special situation of this model, where a
    non-accelerated cosmology was considered as $a(t)\propto t$. Namely,
    the cosmic horizon $R_{ h}$ equals to the light-travel time
    distance. By using different kinds of observations, this
    non-accelerated power-law cosmology was found to be preferred
    \citep{2013Melia,2015MeliaA,2015Melia, 2017Tutusaus}. However this
    model was also perceived to be against to SNe Ia and BAO data
    \citep{2012Bilicki,2014Dolgov,2015Shafer,2017Haridasu}. Progress has
    been made in probing power-law cosmology
    \citep{2005Sethi,2008Dev,2008ZhuA,2014Dolgov,2014Yu}. Nevertheless,
    many researches also questioned the possibility of replacing
    $\Lambda$CDM by power-law cosmology
    \citep{2012Kumar,2015Cardenas,2015Rani,2015Yuan,2016Tutu,2017Haridasu,2017Lin}.

    Treating SNe Ia as standard candles is broadly used in probing
    cosmology, and this method is required to be deliberately considered
    according to some literature recently. \citet{2017Tutusaus} found
    that SNe Ia are consistent with  a non-accelerated universe with
    assumption that supernovae intrinsic luminosity depends on the
    redshift. Considering the independence of supernovae intrinsic
    luminosity on redshift, \cite{2017Lin} got a contradictory
    conclusion with \citet{2017Tutusaus}. \citet{2016Nielsen} presented
    an improved maximum-likelihood procedure to reanalyze the SNe Ia
    dataset with improvement of precision and scale. They found the
    marginal evidence of an accelerated expansion cosmology which was
    widely accepted before. A new method called BAyesian HierArchical
    Modeling for the Analysis of Supernova cosmology (BAHAMAS) was
    introduced by \citet{2016Shariff}, and they found a sharp dropping
    of the color correction parameter value $\beta$ with redshift. Color
    correction parameter is roughly constrained over all redshift
    through empirical period-luminosity relation. However, some voices
    \citep{2016Rubin,2016Ringermacher} have grown to demonstrate an
    accelerated cosmology and pointed some inappropriatenesses in
    \citet{2016Nielsen}. While using SNe Ia, a set of complex parameters
    are involved to be constrained by empirical period-luminosity
    relation of Cepheid variables \citep{1993Phillips}. Several
    uncertainties of this relation are also needed to be prudently
    studied, e.g., the dependence of absolute B band magnitude $M_{
        B}$ on redshift \citep{2005Holz}, the effects of systematic errors
    \citep{2010Freedman,2012Ruiz}, and poor uniformity of SNe Ia in
    various galaxy environment \citep{2010Gilfanov}. When probing cosmic
    acceleration, all the considerations above trigger us to use other
    observations. We choose strong gravitational lensing systems which
    are purely geometrically effected and endorsed by certain theory.

\citet{1979Walsh} discovered the first strong gravitational lensing
    Q0957+561. Decades years later, strong gravitational lensing systems
    are widely used in cosmology
    \citep{2008Zhu,2011Wang,2012Cao,2014Wei,2016Liao,2018Leaf,2018aYu,2018WangY}. Basing
    on the Einstein radius formulation, the Hubble constant is
    eliminated through distance ratio. This may avoid some undiscovered
    relationship between Hubble constant and other observed values,
    e.g., the absolute magnitude $M_{ B}$ of SNe Ia. Considering that
    the strong gravitational lensing systems may show of lacking
    capability to constrain $\Omega_{ m }$ for $\Lambda$CDM
    \citep{2010Biesiada}, other kinds of data are combined to constrain
    parameters precisely in this paper.

    In our work, we focus on using strong gravitational lensing systems,
    Hubble parameters $H(z)$ and BAOs to compare cosmological
    models through Markov chain Monte Carlo (MCMC) method. We also pick a
    favorable cosmological model quantitatively through Bayesian evidence.
    \newline

    This paper is organized as follows. Two cosmological models will be
    briefly introduced in section \ref{sec:Model}. All kinds of data and
    methodology are given in section \ref{sec:samples}. The results of
    MCMC simulation are presented in section \ref{sec:result}.
    Conclusions are given in section
    \ref{sec:discuss}.

    \section{Cosmological Models}\label{sec:Model}
    In this section, we briefly present two cosmological models in our analysis, including
    $\Lambda$CDM and power-law model.

\subsection{$\Lambda$CDM model}
    With an assumption of isotropy and homogeneity of the universe, the Hubble parameter can be derived as
    \begin{equation}
    \label{equ:Hza}
    \left(\frac{H}{H_{0}}\right)^{2}=\Omega_{r}a^{-4}+\Omega_{m}a^{-3}+\Omega_{k}a^{-2}+\Omega_{\Lambda},
    \end{equation}
    %
    where $\Omega_{r}$, $\Omega_{\Lambda}$, $\Omega_{m}$ and $\Omega_{k}$ represent radiation, dark energy, matter and curvature of the universe, respectively. $\Omega_{r}$ is fixed as $\Omega_{r}=0$ in our analysis, basing on the radiation of universe is observed to be negligible in present day. $\Omega_{m}+\Omega_{k}+\Omega_{\Lambda}=1 $ represent the total density which is dimensionless.
    Using $a=(1+z)^{-1}$, eq.(\ref{equ:Hza}) can be derived into
    \begin{equation} \label{equ:HOM}
    \begin{aligned}
    H(z)=H_{ 0 }[\Omega _{ m }(1+z)^{ 3 }+\Omega _{ k }(1+z)^{ 2 }+\Omega _{ \Lambda  }]^{ 1/2 }.
    \end{aligned}
    \end{equation}
    %
    We consider a flat-$\Lambda$CDM model and a $\Lambda$CDM with curvature (denoted as curve-$
    \Lambda$CDM). Through fixing $\Omega_{k}=0$ for flat-$\Lambda$CDM, eq.(\ref{equ:HOM}) can be written as
    %
    \begin{equation}\label{equ:FLCDM}

    H(z)=H_{ 0 }[\Omega _{ m }(1+z)^{ 3 }+ \Omega _{ \Lambda  }]^{ 1/2 }.

    \end{equation}

\subsection{Power-law model}
    Power-law cosmology (denoted as PL) is derived from the power-law relation between the scale factor and proper time as
    %
    \begin{equation}
    \label{equ:PLscale}
    a(t)=\left( \frac{t}{t_0}\right)^{n}.
    \end{equation}
    %
    By using $H \equiv { \dot { a(t) }  } /{ a(t) }$ and $a=(1+z)^{-1}$, one can easily obtain Hubble parameter function as
    %
    \begin{equation}
    \label{equ:PLhubble}
    H(z)=H_{0}(1+z)^ {\frac {1}{n}},
    \end{equation}
    %
    where $H_{0}=n/t_{0}$.

    The $R_{ h}=ct$ can be considered as a unique circumstance of power-law model, in which
    $n=1$. The gravitational horizon scale is handled as $R_{ h}=ct$. Taking $n=1$ into eq.(\ref{equ:PLhubble}),
    we can obtain the Hubble parameter given as
    %
    \begin{equation}
    \label{equ:RHCThubble}
    H(z)=H_{0}(1+z).
    \end{equation}
    %
    The deceleration parameter of $R_{ h}=ct$ model is $q=0$, which expresses a universe expanding steadily. $n>1$ and $n<1$ represent an accelerated and a decelerated universe respectively, according to the relation $q=1/n- 1$.

    After reviewing these two cosmological models, one can derive the comoving distance for each model as below \citep{1999Hogg}.
    The comoving distance for flat-$\Lambda$CDM is written as
    %
    \begin{equation}
    \label{equ:FCMDcomovingdistance}
    D_{ C }=\frac { c }{ H_{0} } \int _{ 0 }^{ z }{ \frac { 1 }{ \sqrt { \Omega _{ m }(1+z)^{ 3 }+\Omega _{ \Lambda  } }  }  } dz.
    \end{equation}
    %
    For curve-$\Lambda$CDM the comoving distance is based on curvature ${ \Omega  }_{ k }$,
    %
    \begin{equation}
    \label{equ:KCMDcomovingdistance}
    D_{C}=\left\{ \begin{array}{ll}
    \frac { c }{ \sqrt {  { \Omega  }_{ k }  }  } \sinh { \left( \int _{ 0 }^{ z }{ \frac { 1 }{ H(z) }  } dz\cdot \sqrt {  { \Omega  }_{ k }   }  \right)  } & { \Omega  }_{ k }>0\\
    \\
    { c }\int _{ 0 }^{ z }{ \frac { 1 }{ H(z) }  } dz\quad & { \Omega  }_{ k }=0 \\
    \\
    \frac { c }{ \sqrt { \left| { \Omega  }_{ k } \right|  }  } \sin { \left( \int _{ 0 }^{ z }{ \frac { 1 }{ H(z) }  } dz\cdot \sqrt { \left|{ \Omega  }_{ k }\right| }  \right)  } & { \Omega  }_{ k }<0
    \end{array} \right . ,
    \end{equation}
    %
    where $H(z)$ is from eq.(\ref{equ:HOM}).
    For power-law model $(n\neq 1)$ we have
    %
    \begin{equation}
    \label{equ:PLcomovingdistance}
    D_{ C }=\frac { c }{ H_{ 0 } } \frac { \left( 1+z \right) ^{ 1-\frac { 1 }{ n }  }-1 }{ 1-\frac { 1 }{ n }  } .
    \end{equation}
    %
    When $n=1$ namely $R_{ h}=ct$ model, the function can be derived as
    %
    \begin{equation}\label{equ:RHCTcomovingdistance}
    D_{ C }=\frac { c }{ H_{ 0 } } \ln \left(1+z\right) .
    \end{equation}
    %
    The angular diameter distance for each model can be written as
    \begin{equation}\label{equ:DaDc}
    D_{ A }=\frac { D_{ C } }{ \left(1+z\right) } .
    \end{equation}

\section{Data and Methodology}\label{sec:samples}
    In this section, we present data including strong gravitational lensing systems, $H(z)$, and BAO. The methods which we treat to various data will be illustrated here.
\subsection{Strong lensing systems}
    Strong gravitational lensing system has become a useful and vital tool in probing cosmology. From the first lensing system has been discovered, there are abundant projects searching for lensing systems, including Sloan Lens ACS (SLACS), BOSS Emission-Line Lens Survey (BELLS), etc. Approximated by singular isothermal sphere (SIS) model or singular isothermal ellipsoid (SIE) model, the Einstein radius can be obtained by measuring the foreground image of Einstein rings and can be expressed through the formula as

\begin{equation}
    \label{equ:SIS}
    \frac{D^{ls}_{A}}{D^{s}_{A}}=\frac{\theta_{ E}\; c^2}{4 \pi \sigma^2_{SIS}}=\mathcal{D}^{obs},
\end{equation}
    %
    where $c$ is the speed of light and $\theta_{ E}$ represents Einstein radius. $D^{ls}_{A}$ and $D^{s}_{A}$ are angular diameter distances from lensing to source and observer to source respectively.

\citet{1996White} found that the dynamical temperature of dark matter halos is larger than measured stellar
velocity dispersion, which hints that the velocity dispersion
$\sigma_{SIS}$ in eq.(\ref{equ:SIS}) may not be equal to
observed stellar velocity dispersion $\sigma_{ap}$.
        \citet{2015Cao} assumed that the mass of strong lensing systems is
        distributed spherically and symmetrically. In their work power-law
        index $\gamma$ of massive elliptical galaxies is treated as a free
        parameter, and $\mathcal{D}^{obs}$ can be derived as
        \begin{equation}
        \label{equ:SIS_cao}
        \mathcal{D}^{obs}=\frac{\theta_{ E}\; c^2}{4 \pi \sigma^2_{ap}} f \left( \theta_{ E}, \theta_{ap},\gamma \right).
        \end{equation}
        $f \left( \theta_{ E}, \theta_{ap}, \gamma \right)$ is a
        complex function related to Einstein radius $\theta_{E}$,
        aperture of certain lensing surveys $\theta_{ap}$, and power-law
        index $\gamma$. But this method may show
        poor sensitivity to cosmological parameters \citep{2016Jie}.

        Another simple method is replacing $\sigma_{SIS}$ of eq.(\ref{equ:SIS})
        by $\sigma_{SIS} = f_e\sigma_{ap}$
        \citep{1992Kochanek,2003Ofek}. As a phenomenological free parameter,
        $f_e$ accounts the systematic errors caused by taking
        $\sigma_{ap}$ as $\sigma_{SIS}$. Unlike \cite{2018Leaf}
        have done recently, free parameter $f_e$ is introduced to calculate
        $\mathcal{D}^{obs}$. Therefore, $\mathcal{D}^{obs}>1$ can not be
        used to exclude unphysical observed lensing systems, which has been
        used in \cite{2018Leaf}.

Moreover, in order to correct observed stellar velocity
dispersion into a circular aperture of radius, $\sigma_0 =
\sigma_{ap}\left(\theta_{eff}/\left(2\theta_{ap}\right)\right)^{-0.04}$
can be used \citep{1995JorgensenA,1995JorgensenB}. $\theta_{eff}$
represents the effective radius, which is achieved by fitting de
Vaucouleurs model \citep{1948Vaucouleurs}. \cite{2015Cao} replaced
$\sigma_{ap}$ of eq.(\ref{equ:SIS_cao}) by $\sigma_0$. Replacing
$\sigma_{SIS}$  directly by $\sigma_{0}$ in eq.(\ref{equ:SIS}) may
not be a proper treatment, which has been used by \cite{2018Leaf}.
Because $\sigma_{0}$ just changes slightly from $\sigma_{ap}$
\citep{2015Cao}.

In order to exclude other systematic errors and unknown
uncertainties introduced from lensing model fitting effect, we use
$\sigma_{ SIS} = f_e\sigma_{ap}$ in this paper, which has been
widely used \citep{2012Cao,2016Liao,2017Li,2017Xia}.

From eq.(\ref{equ:SIS}), we can obtain the angular diameter
distance ratio observed from lensing surveys $\mathcal{D}^{obs}$.
The uncertainty of $\mathcal{D}^{obs}$ can be written as
\begin{equation}\label{equ:ratio uncertainty}
\sigma_{\mathcal{D}^{obs}} =\mathcal{D}^{obs} \sqrt
{\left(\frac{\sigma_{\theta_{E}}}{\theta_{
E}}\right)^{2}+4\left(\frac{\sigma_{ \sigma_{
SIS}}}{\sigma_{SIS}}\right)^{2} }.
\end{equation}

    %
    Following the approach taken by \citet{2008Grillo}, we take uncertainties of Einstein radius as $\sigma_{\theta_{ E}}=0.05\theta_{ E}$.
    The theoretical angular diameter distance ratio $\mathcal{D}^{th}$ can be derived from eqs.(\ref{equ:FCMDcomovingdistance})
    $\sim$ (\ref{equ:DaDc}). The angular diameter distance is written as
    %
    \begin{equation}\label{equ:Dals}
    D_{A}^{ls}=\frac{D_{C}^{ls}}{1+z_{s}}.
    \end{equation}
    %
    Easily,  $\mathcal{D}^{th}$ has the relation
    %
    \begin{equation}\label{equ:ratio theo}
    \mathcal{D}^{th}=\frac{D_{C}^{ls}}{D_{C}^{s}},
    \end{equation}
    %
    where $D_{C}^{ls}=D_{C}^{s}-D_{C}^{l}$ for flat-$\Lambda$CDM,  PL model and $R_{ h}=ct$ model. For curve-$\Lambda$CDM, it is unnecessary to derive an equation relating
    $D_{C}^{ls}$, $D_{C}^{l}$, and $D_{C}^{s}$, but to substitute the range of integration in eq.(\ref{equ:KCMDcomovingdistance}) from $0$ to $z$ into $z_l$ to $z_s$ \citep{2015Syksy}.

    $f_{e}$ as a free parameter in eq.(\ref{equ:SIS}) is required to be fitted simultaneously. Naturally, the mean values
    of parameters can be obtained by minimizing
    %
    \begin{equation}\label{equ:chiSL}
    \chi^{2}_{ SL}=\sum _{ i=1 }^{ n }{ \frac { \left( \mathcal{D}^{th}-\mathcal{D}^{obs} \right) ^{ 2 } }{ \sigma^{2} _{ \mathcal{D}^{obs} } }  } .
    \end{equation}
    %
    The likelihood is $\mathcal{L}_{ SL}\propto \exp(-\chi^{2}_{ SL}/2)$.

    The idea of reducing systematic errors requires a dataset comprehending as much high-quality  data as possible. We utilize 152 strong gravitational lensing systems in our analysis. 118 strong gravitational lensing systems are taken from catalog of \citet{2015Cao}. The catalog was assembled from the Sloan Lens ACS Survey (SLACS), BOSS emission-line lens survey (BELLS), Lens Structure and Dynamics (LSD), and Strong Lensing Legacy Survey (SL2S). Further more, 34 new strong gravitational lensing systems are carefully selected and used in this work. 7 reliable BELLS data with much higher source redshifts are selected cautiously from \citet{2016Shu}. Actually, there are 17 grade-A lenses listed in \citet{2016Shu}. To be specific, five systems require special model-fitting treatments, four systems show significantly larger relative deviations of the Einstein radius, and one system do not meet the selection thresholds. These 10 systems are excluded in order to get rid of some unknown systematic errors imported by any model fitting effect.
    27 SLACS data are chosen from 40 grade-A lenses listed in \citet{2017Shu}. In their work, a parameter $\chi^{2}/dof$ is achieved, which represents the goodness of fitting for SIE model. 27 lenses are filtrated carefully, whose $\chi^{2}/dof$ is within the interval of $1\sigma$ around the constrained value $\chi^{2}/dof=1$. Apart from 118 strong gravitational lensing systems, the new 34 data are listed in Table \ref{newSL}.

\subsection{Hubble parameter H(z)}
By using \textit{cosmic chronometers} approach \citep{2002Jimenez}, the Hubble parameter is measured independently of cosmological models. Through this approach one can directly constrain the expansion history of the universe, and avoid any integrated distance measurements over redshift like SNe Ia and BAOs.

In our work we take 30 $H(z)$ data from \citet{2016Moresco} over 25
    data listed in \citet{2015MeliaA}. Note that all 30 $H(z)$ data are
    cosmological-model independent. The $\chi_{ H(z)}^{2}$ for Hubble
    parameters is given by
    %
    \begin{equation}\label{equ:chiHZ}
    \chi^{2}_{ H(z)}=\sum _{ i=1 }^{ n }{ \frac { \left( {H(z)}^{th}-{H(z)}^{obs} \right) ^{ 2 } }{ \sigma ^{2}_{ {H(z)}^{obs} } }  } ,
    \end{equation}
    %
    where $H(z)^{th}$ is the theoretical value of Hubble parameter. The likelihood is $\mathcal{L}_{H(z)}\propto \exp(-\chi^{2}_{ H(z)}/2)$.

\subsection{Baryon acoustic oscillations}\label{sec:BAO}
As a model-independent standard ruler, BAO is a practical tool in
probing cosmology. Through measuring the comoving sound horizon of
the baryon drag epoch at different redshifts \citep{2005Eisenstein},
the sound horizon size at the end of the drag era $z_d$ is written
as
    %
    \begin{equation}\label{equ:rd}
    { r }_{ d }=r_{s}(z_{d})=\int _{ { z }_{ d } }^{ \infty  }{ \frac { { c }_{  s }(z)dz }{ H(z) }  } ,
    \end{equation}
    %
where $c_{s}$ is the speed of sound. $r_d$ may relate more to early
universe, from which we can't get enough information. Besides
$\Lambda$CDM, other cosmological models may not have a compatible
function of $r_d$ \citep{2017Verdea}. Considering our work focus on
different cosmological models, we regard $r_d$ as a free parameter
following. BAO measures the ratio of comoving sound horizon and the
distance scale \citep{2005Eisenstein} given as
    %
    \begin{equation}\label{equ:BAOratio}
    R(z)=\frac{r_{d}}{D_{V}},
    \end{equation}
    %
    and $D_{V}$ is defined as
    %
    \begin{equation}\label{equ:DV}
    { D }_{ V }(z)\equiv \left[ D_{ C }^{ 2 }(z)\frac { cz }{ H(z) }  \right]^{\frac{1}{3}},
    \end{equation}
    %
    where comoving distance $D_{C}$ and Hubble parameter $H(z)$ are both defined in Section \ref{sec:Model}.

We use \textbf{11} BAO measurements from different surveys, which are
listed in Table \ref{tab:BAO}. In order to avoid importing BAO data
at same redshifts repeatedly, we use the latest measurements of each
redshift. Also we avoid importing BAOs with correlated surveys as far as possible \citep{2018Yu}.
To be specific, BAOs from 6dFGS, SDSS DR7, BOSS DR12, BOSS DR14 and Ly-$\alpha$ are
uncorrelated with each other. Actually, there are two methods of Ly$\alpha$-forest. One method is Ly$\alpha$ auto-correlation, and the other is Ly$\alpha$ cross-correlation. Here, we use the
 BAO of combining both these two methods from \cite{2017Mas}, who have combined
 their measurement by cross-correlation at redshift 2.4 and auto-correlation at redshift 2.33 \citep{2017Bautista} together.

Basically, there are two main analytical methods of
measuring BAOs. One is anisotropic galaxy clustering measurement
which constrains comoving distance $D_{M}(z)$ in the transverse direction
 and Hubble parameter $H(z)$ along line-of-sight. In this work,
  $D_M$ equals to $D_C$ which has been defined for different cosmological
   models in section \ref{sec:Model}.
This method is also known as an application of Alcock-Paczynski
effect \citep{1979Alcock}. The other is spherically averaged
clustering which constrains volume-averaged distance $D_V$
\citep{2005Eisenstein}.

Results of both measurements are all used in this work.
The original data of each BAO are listed in Table \ref{tab:BAO}.
Specially, for
different BAO measurements at $z = 0.38, 0.51, 0.61$, measurements in the transverse direction and along line-of-sight are both included \citep[following e.g.][]{2017Wojtak, 2018Lemos, 2018Ryan}. So we take covariance matrix from
  \citet{2017Alam} into our calculation. For BAO at $z=2.4$ \citep{2017Mas}, we also take a small covariance matrix.

The $\chi^{2}_{BAO}$ is given by
\begin{equation}\label{equ:chiBAO}
\chi^{2}_{ BAO}=  ({\bm{V}^{obs}-\bm{V}^{th}})\bm{C}^{-1}(\bm {V}^{obs}-\bm{V}^{th})^{T},
\end{equation}
where ${\bm{V}^{obs}}$ and ${\bm{V}^{th}}$ are observed measurements
and theoretical values corresponding to second column of Table \ref{tab:BAO}.
$\bm{C}^{-1}$ is inverse covariance matrix of the observed variables. For BAOs at $z = 0.38, 0.51, 0.61$, the corresponding elements of inverse covariance matrix in eq.(\ref{equ:chiBAO}) are:
$$\begin{array}{lll}
c_{4 4}=2.88, & c_{4 5}=-1.24,& c_{4 6}=0.16,\\
c_{4 7}=-6.76, & c_{4 8}=3.61,& c_{4 9}= -0.58,\\
c_{5 5}=2.49, & c_{5 6}=-0.90,& c_{5 7}=2.01,\\
c_{5 8}=-7.14, & c_{5 9}=3.21,& c_{6 6}=1.40,\\
c_{6 7}=-0.66, & c_{6 8}=2.28,& c_{6 9}= -4.82,\\
c_{7 7}=380.85, & c_{7 8}=-192.93,& c_{7 9}= 18.60,\\
c_{8 8}=510.88,& c_{8 9}= -210.83,& c_{9 9}= 339.81.
\end{array}$$
For BAO at $z=2.4$, the inverse covariance matrix is:
$$\begin{array}{lll}
c_{10 10}=799.17, & c_{10 11}=1578.
\end{array}$$
These elements should be multiplied by $10^{-3}$. Here, $c_{ij}=c_{ji} \; \left( i\neq j \right)$. For the rest of elements, we have $c_{ii}=1/\sigma_{i}^{2}$ and $c_{ij}=c_{ji}=0 \; \left( i\neq j \right)$, where $\sigma_{i}^{2}$ is error for BAO measurements.

The likelihood is $\mathcal{L}_{BAO}\propto \exp(-\chi^{2}_{BAO}/2)$.
\\

In our work, we constrain the parameters for each cosmological model
by using different combinations of these three kinds of data. The
free parameters $f_e$ and $r_d$ are also needed to be constrained
simultaneously. The three different datasets and corresponding total
likelihoods are listed as below.
    \begin{itemize}
        \item Strong gravitational lensing system only (hereafter SL): $\mathcal{L}_{ SL}$
        \item Strong gravitational lensing system and $H(z)$ (hereafter SL+$ H(z)$): $\mathcal{L}_{ SL}\cdot \mathcal{L}_{ H(z)}$
        \item Strong gravitational lensing system, $ H(z)$ and BAO (hereafter SL+$ H(z)$+BAO) $\mathcal{L}_{ SL}\cdot \mathcal{L}_{ H(z)}\cdot \mathcal{L}_{ BAO}$
    \end{itemize}

It should be noted that the maximum likelihood method can be achieved by
Bayesian approach \citep[e.g.][]{2005DAgostini,2010Hogg} or
frequentist approach \citep[e.g.][]{2016bPlanck}. In this work, we use maximum likelihood method basing on Bayesian approach.
    Using information criteria may not be an excellent choice,
    because the information criteria derived from Bayesian approach
    may be a little different from
     the true values of comparison criteria. Also, the information criteria do not include the
     prior probability distributions into comparison \citep{2007Liddel}. So, we then introduce Bayesian
      evidence \citep{2007Liddel,2008Trotta} as model comparison criteria. The Bayesian evidence is defined as
\begin{equation}
\label{equ:BE}
E\equiv \int { \mathcal{L}(\theta ) } P(\theta) \rm d\theta,
\end{equation}
where $\theta$ represents parameters of models. $\mathcal{L}(\theta)$ is likelihood function,
and $P(\theta)$ gives priors distribution of parameters. The Bayes factor in natural logarithm $\ln B$ can
be derived as
\begin{equation}
\label{equ:Bfactor}
\ln B = \ln E_{fid} - \ln E_{\alpha},
\end{equation}
where $fid$ represents flat-$\Lambda$CDM which we fix as the fiducial model, and ${\alpha}$ represent other models in one-on-one comparison.
The $\ln E$ represents Bayesian evidence (eq.\ref{equ:BE}) in natural logarithm.
The preference strength for flat-$\Lambda$CDM  can be described as weak, moderate or strong,
according to $\ln B > 1.0,$ $2.5$ or $5.0$ \citep{2008Trotta}.
Naturally, a negative $\ln B$ value represents flat-$\Lambda$CDM is not favored.

\section{Results}\label{sec:result}
We use an open source python package {emcee} \citep{2013Foreman} to
constrain cosmological parameters through Markov chain Monte Carlo
method. The python package {nestle}\footnote{https://github.com/kbarbary/nestle}
is used to calculate Bayesian evidence through nested sampling algorithm \citep{2004Skilling}.
The Hubble constant $H_{0}$ and the comoving sound horizon
$r_{d}$ are replaced by $h_0=H_{0}/100$ and $r_{*}=r_{d}/100$ in our
numeration. Uniform distributions of prior probabilities for the
parameters are assumed: $P(\Omega_{ m })=U[0,1]$, $P(\Omega_{ k
})=U[-1,1]$, $P(n)=U[0,2]$, $P(f_{e})=U[0.5,1.5]$, and
$P(h_{0})=U[0.5,1]$. When we constrain
parameters of curve-$\Lambda$CDM, we add another prior $P(\Omega_{
    \Lambda })=U[0.6,0.8]$ to constrain $\Omega_{ k }$ more precisely.

\cite{2017Verdeb} constrained the early cosmology from
current CMB observations without any assumptions of late-time
cosmology. They model-independently measured the value of $r_d$ as $r_d=147.4\pm 0.7$ Mpc.
Because BAOs are sensitive to $r_{d}$ and $H_{0}$, BAOs may not be able to constrain both $r_{d}$ and $H_{0}$ at same time. So,
we set uniform prior of $r_{*}$ as $P(r_{*})=U[1,2]$ or Gaussian prios $r_{*} = 1.474 \pm 0.007$ when importing BAO measurements, respectively.
Meanwhile, we set $\Omega_{ \Lambda  }$ as a free parameter in curve-$\Lambda$CDM by only setting uniform priors on $\Omega_{ k }$ and $\Omega_{ m }$.

Due to the poor quality of SL data, it may not properly constrain cosmological parameters. In Table \ref{tab:parameters}, we only list the mean value and 1$\sigma$ limits of each parameter. According to Bayes factors listed in Table
\ref{tab:IC}, flat-$\Lambda$CDM is
slightly favored rather than $R_h=ct$, according to $\ln B > 2.5$.
However, \citet{2018Leaf} found $R_{ h}=ct$ model is preferred over
$\Lambda$CDM model. The reason is that they excluded some SL
systems, as we discuss in section \ref{sec:samples}.

Then another dataset SL+$ H(z)$ is imported in our analysis. The
fitting results are listed in the second four rows of Table
\ref{tab:parameters}. By comparing the result only fitted by SL, one
can easily find that the accuracies of $\Omega_{ m }$ and $n$ are
both improved dramatically. There is no significant variation of the
free parameter $f_e$ for different models. Till now, we believe that
through combination of different datasets, the accuracy of fitting
will be enhanced significantly. By comparing Bayes factors in Table
\ref{tab:IC}, it is impossible to rule out some models from
flat-$\Lambda$CDM. Only PL can be
ruled out, according to $\ln B > 2.5$.

Next, the last dataset SL+$ H(z)$+BAO is applied to our work.
Firstly, we use a flat prior of $r_{d}$ , and our calculation
    gives optimized fitting results, which are listed in table \ref{tab:parameters} (called case 1). To be specific,
    the top-left panel of Figure \ref{fig:prior_rd} reveals the results of MCMC simulation
for curve-$\Lambda$CDM. The mean values are $\Omega_{ m
}=0.30\pm 0.02$, $\Omega_{ k }=0.03\pm 0.09$,
$h_{0}= 0.68\pm 0.02$, and $r_{*}=1.47\pm 0.04$. The value of
$\Omega_{ k }$ is consistent with zero at $1\sigma$ confidence
interval. The fitting results of flat-$\Lambda$CDM are shown in top-right panel of Figure
\ref{fig:prior_rd}, where $\Omega_{ m }=0.30\pm 0.02$, $h_{0}= 0.69\pm 0.02$, and $r_{*}=1.46\pm
0.04$. For these two models, $r_{*}$ and $h_{0}$ are
consistent. In the bottom-left panel of Figure \ref{fig:prior_rd}, constraints on PL model are
$n=0.93\pm 0.02$, $h_{0}= 0.60\pm 0.01$, and
$r_{*}=1.50\pm0.04$. For $R_{h}=ct$ model, the bottom-right panel of Figure
\ref{fig:prior_rd} reveals the mean values as
$h_{0}= 0.62\pm 0.01$, and $r_{*}=1.49\pm0.04$.
Values of $r_{d}=100r_{*}$ for these two models are a little bit larger than $r_d$ measurement as
$r_{d}=147.4\pm 0.7 {\rm Mpc}$ \citep{2017Verdeb}.
 Table \ref{tab:IC} shows a
 large improvement of fitting by adding BAO data. It is possible to
rule out some models. We get the Bayes factors of flat-$\Lambda$CDM
versus PL model is 7.33, and versus $R_{ h}=ct$ is 10.18. So the dataset prefers
the flat-$\Lambda$CDM.
But Bayes factor is not large enough to compare flat-$\Lambda$CDM and
 curve-$\Lambda$CDM.

We then only set a Gaussian prior $r_{*} = 1.474 \pm 0.007$ to apply SL+$ H(z)$+BAO. In contrast to
flat prior of $r_{*}$,
we denote the results as case 2 in Tables \ref{tab:parameters} and \ref{tab:IC}.
We also set red density contours in Figure \ref{fig:gau_rd}.
The mean value of $\Omega_{ m }$ and $\Omega_{ k }$ for flat-$\Lambda$CDM and
curve-$\Lambda$CDM are slightly changed.
For flat-$\Lambda$CDM, $\Omega_{ m} = 0.30\pm 0.02$.
For curve-$\Lambda$CDM, $\Omega_{ m} = 0.29\pm 0.02$ and $\Omega_{ k }=0.04\pm 0.09$.
And the values of $r_{d} = 100r_{*}$ for these four models basically equal to  $r_{d}=147.4\pm 0.7\, {\rm Mpc}$ \citep{2017Verdeb}. In Figure \ref{fig:gau_rd}, as what we expected, setting Gaussian prior of $r_d$ breaks the degeneracy between $r_{d}$ and $H_{0}$. It slightly increases the value of Hubble parameter for power-law and $R_{h}=ct$ models from Table \ref{tab:parameters}. But the model preference is not enhanced significantly from case 2 in Table \ref{tab:IC}.
According to Bayes factors in Table \ref{tab:IC}, flat-$\Lambda$CDM is still the data-favorable model rather than PL and $R_h=ct$ models.

One may see the degeneracy between $r_{d}$ and $H_{0}$ in Figure \ref{fig:prior_rd}. If we only set a large Gaussian prior on $H_{0}$, the $r_{d}$ will be reduced significantly. We have certified this idea. Because the value of $r_{d}$ is not properly constrained, we do not list the result here. As shown in Table \ref{tab:parameters}, the case 2 also shows lower values of $H_{0}$ for power-law and $R_{h}=ct$ models than $\Lambda$CDM model. So, we set Gaussian priors not only on $r_{d}$, but also on $H_{0}$. The main reason for setting these two Gaussian priors is that we try to properly constrain $r_{*}$ and $h_{0}$ for power-law and $R_{h}=ct$ models, and to improve the preferences of models. The results are listed in Table \ref{tab:parameters}, and Bayes factors in Table \ref{tab:IC}. Except the same Gaussian prior of $r_{d}$ is set both for case 3 and case 4, case 3 represents the Gaussian prior on $H_{0}$ as $H_{0} = 73.52 \pm 1.62\, \rm{km\,s^{-1}\,Mpc^{-1}}$ from \citet{2018Riess}, and case 4 represents the Gaussian prior $H_{0} = 67.80 \pm 0.09\,\rm{km\,s^{-1}\,Mpc^{-1}}$ from \citet{2016Planck}. In Table \ref{tab:IC}, we can see that the model preferences are increased. The power-law and $R_{h}=ct$ models are penalized more by the additional Gaussian priors on $H_{0}$. However, it can not give a strong evidence to support flat-$\Lambda$CDM over curve-$\Lambda$CDM.

\section{Conclusions}\label{sec:discuss}
In this work, we use 152 strong gravitational lensing systems, 30
    $ H(z)$ and \textbf{11} BAO data to compare cosmological models. In all cases, we find that the flat-$\Lambda$CDM is strongly preferred over the power-law and $R_{h}=ct$ models.
    The corresponding probability of data-favorable model at $\ln B >5$ is greater than $99.3\%$ \citep{2008Trotta},

     The flat-$\Lambda$CDM is not obviously preferred over the
    curve-$\Lambda$CDM according to that the Bayes factors
    give weak evidence to distinguish them.
    The value of $n$ for power-law cosmology become close to $1$ as more datasets are
    considered.

    By using strong gravitational lensing systems only, the capability
    of discriminating cosmological models may not be reliable. This may due to the
    absence of accuracy in measuring Einstein radius and stellar
    velocity dispersion. We roughly give a correction $f_e$ to all
    lensing systems from different surveys, as what has been done
    \citep{2012Cao,2016Liao}. It is important to consider an
    effective method targeting at correction of velocity dispersion
    like the work done by \citet{2015Cao}. This task should
    consider of systematic errors imported from different lensing
    surveys. Strong gravitational lensing systems are equipped with
    intrinsic goodness. We still look forward to probe cosmological models
    using strong gravitational lensing systems only. Because of the
    limitation of lacking enormous database, combining
    other kinds of data seems like an efficient and
    straightforward way to probe cosmic acceleration.

\section*{Acknowledgements}
We thank an anonymous referee for useful suggestions and comments.
We would like to thank G.Q. Zhang, Z.Q. Sun, Y.Y. Wang, and Hai
Yu for helpful discussion. This work is supported by the National Natural Science Foundation of China
(grant U1831207).

redpajama_set_name: RedPajamaArXiv


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Home > Unlabelled > Washington Capitals' Adorable Labrador Puppy Does Its First Interview - Video
Washington Capitals' Adorable Labrador Puppy Does Its First Interview - Video
The National Hockey League (NHL) club has adopted a ten-week-old Labrador puppy named Captain for training.
The puppy was presented to fans of the club by the team captain of the Washington Capitals, Alexander Ovechkin.
Captain's debut took place during the match between the Washington Capitals and the Carolina Hurricanes (2-3), on the night of October 5th at 11 p.m. GMT.
Meanwhile, the team's new service dog got its own special Twitter account so that fans can follow the pup's life.
Within 14-16 months, the Labrador will undergo specialised training and socialisation. Hockey players, fans and employees of the Washington Capitals will help him in this.
The Washington Capitals won the Stanley Cup last year for the first time in history, and Ovechkin became the first Russian with the rank of a team captain to ever win the cup. The Washington Capitals claimed a 4-3 victory in the final playoff match over the Vegas Golden Knights ice hockey team.
Besides Ovechkin, two more Russian players play for the Capitals, Evgeny Kuznetsov and Dmitry Orlov.


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Jacopo Fazzini (Massa, 16 de marzo de 2003) es un futbolista italiano que juega en la demarcación de centrocampista para el Empoli FC de la Serie A.

Biografía
Tras formarse en las filas inferiores del Viareggio 2014, Capezzano y Empoli FC, finalmente debutó con el primer equipo el 19 de enero de 2022 en un encuentro de la Copa de Italia contra el Inter de Milán. Siete meses después debutó con el equipo azzurri en la Serie A, el 14 de agosto de 2022, contra el Spezia Calcio.

Clubes

Referencias

Enlaces externos
 Ficha del jugador en footballdatabase
 Ficha del jugador en soccerway

Futbolistas de la selección de fútbol sub-17 de Italia
Futbolistas de la selección de fútbol sub-18 de Italia
Futbolistas de la selección de fútbol sub-19 de Italia
Futbolistas del Empoli Football Club

redpajama_set_name: RedPajamaWikipedia


Moscow, Russia (BBN)-Vladimir Putin has said Russia is using "far from everything we are capable of" in its military operations in Syria.
"We also have other things as well and will use them if necessary," the Russian president said, reports BBC.
Putin was speaking a day after the UN Security Council endorsed a peace plan for the war-torn nation, including calls for a ceasefire.
The Syrian war, heading into its fifth year, has killed more than 250,000 people and displaced millions more.
However, the resolution makes no mention of the future role of Syrian President Bashar al-Assad.
Western countries have called for his departure, but Russia and China say he should not be required to leave power as a precondition for peace talks.
Russia – a key ally of the Syrian president – has previously blocked resolutions critical of Assad at the UN Security Council and has continued to supply weapons to the Syrian military despite international criticism.
In September Russian forces began launching air strikes against rebels, saying the so-called Islamic State (IS) and "all terrorists" were targets. However, Western-backed groups were reported to have been hit.
The resolution passed at the UN in New York on Friday foresees talks between the Syrian government and opposition in early January.
The plan sets out a timetable for UN-supervised elections within 18 months, and stresses that the Syrian people will decide the future of their country.
The plan also calls for a ceasefire, but there is also disagreement over which armed groups should be designated as terrorists and consequently excluded from any talks or ceasefire.
Actions against groups considered terrorist organisations would not be affected, allowing Russian, French and US air strikes against Islamic State to continue.
The agreement demands that all parties cease attacks against civilians.


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Hands on with the new iPad
Readers of this publication will know that the Catalyst reviewed the new iPad, released by Apple on Mar. 16, in somewhat less than glowing terms after viewing Apple's keynote presentation on the device. After our write-up, which admittedly was done without the ability of getting first-hand experience with the device (since it had not been released yet), the Catalyst was given the opportunity to give the device a test drive alongside models of the original iPad and the iPad 2, courtesy of Educational Technology Services Coordinator Allen Goldberg.
On first look, the new iPad's screen is quite impressive — colors are much brighter and the display looks very crisp, especially when held up next to an original iPad or an iPad 2. By itself, though, the new iPad's screen looks almost like any other computer screen one would expect to find. The more robust screen requires a faster processor that theoretically would eat away at the tablet's battery life, but the new iPad features a battery Goldberg said is 70 percent larger than that of the previous iPads, ensuring the same amount of battery life for a far more powerful device, something he described as an impressive feat of engineering.
Goldberg's iPad also featured cellular connectivity via AT&T's long-term evolution (LTE) network, which was recently introduced to Sarasota and boasts faster mobile Internet browsing speeds than previous iPads. The Catalyst noted how quickly its website loaded on the new iPad versus over AT&T's 3G network on the iPad 2 and over wifi on the original iPad — while the new iPad loaded the site in under 10 seconds, the original iPad took about twice as long over wifi and iPad 2's connection timed out. These tests were being performed in the Jane Bancroft Cook Library, which has limited cellular service, may have played a role in the differences in load time.
Goldberg, who has done consulting work for Apple, argued that the company "didn't need to do a lot" with the new iPad, theorizing that because Apple already has cornered the market for so-called post-PC devices, the updates to the new iPad did not have to very revolutionary. He also suggested that owners of the original iPad — as well as anyone new to the tablet market — would be best served purchasing the new iPad, as the better screen and increased processor speed more than makes up for the additional $100 cost over an iPad 2.


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Penny's Postcards
Indian Lake Park
Shimek Forest
Early History of Farmington
Farmington was settled in 1833, following the Blackhawk War and over a dozen years before Iowa's statehood. The town was platted by Henry Bateman in 1839 and was incorporated in 1841. Farmington is the oldest village in Van Buren County, was the first county seat, and was a major center for milling, manufacturing, and trading.
By 1878, Farmington supported one printing office, four dry goods stores, two drug stores, three grocery stores, two agencies, three hardware stores, one harness shop, three wagon shops, two blacksmith shops, one cigar manufactory, two shoe shops, two furniture houses, one grist mill, and one saw mill. Also present, at the time, were three lawyers, five physicians, and two Justices of the Peace serving 1,000 citizens.
See more historic photos of Farmington - Here
1909 Farmington Chautauqua Program -
farmingtonchautauqua.pdf
Photographs of Farmington **1898** -
Cover.pdf
Page 2.pdf
End.pdf
In addition to Farmington's enchanting and colorful history, the town is surrounded by thousands of acres of natural beauty. Shimek Forest, to the east, covers over 8,000 acres of woodland. And, Indian Lake Park, to the west, is a 177-acre City owned park, ideal for camping, fishing, hunting, canoeing, hiking, biking, and more.
Milestones in Farmington's history include the following:
Home of the first Congregational Church west of the Mississippi, in 1848.
Home of the Farmington Wagon and Carriage Works, owned by Lewis Burg.
The birth of the first white child on January 17, 1836 - Jacob Alfrey, son of James and Maggie Alfrey.
The first Postmaster - Dr. R. D. Barton, keeping his post office in his hat.
Home of the first cheese factory in the State, and the first steam flour mill in the county, in Abner Kneeland's colony of Salubria, south of Farmington.
The burial site of Rebecca Pollard, who had opened a private school and developed a series of books.
Provided citizens who were active participants and onlookers in the Civil War Battle of Croton and Athens.
Was home to the only Catholic Church in Van Buren County at the time.
Was the location of the Annie Wittenmeyer Home for Orphans before it was moved to Davenport.
Home of Stirling Woolen Mills and Company.
Site of the George Stillwell murder case.
Site of the Chautauquas, which were held in Anderson Park, and which boasted such famous orators as Williams Jennings Bryan, Billy Sunday, and Champ Clark.
Was home to a wooden covered bridge, which was the longest railroad bride in the world at the time of its construction.
Site of the famous "Tar and Feather" case of a newspaper editor.
Was one of the centers for Iowa's cucumber industry.
Gold and Mercury were discovered in the gravel pit south of Farmington.
Home of Dr. Lonnie A. Coffin, who in 1958 was awarded the American Medical Association General Practitioner of the Year award by the American Medical Association.
This website is maintained by a city employee, if anything is out of place please let me know by contacting me the Web Admin


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16 September 2018 / Home & Energy
Which goods do we return most often?
Melissa Massey	Consumer Rights Deputy Editor
There's nothing quite as frustrating as making a new purchase, eagerly getting it out of the box and discovering it doesn't work. But what goods are most often faulty?
We've been analysing the data from our free faulty items claim tool, and we can now reveal which faulty goods people most commonly try to return.
While cars and furniture come out on top, half the items reported are technology goods.
Here are the top 10 items people used our faulty goods tool for in the last three months. The top categories were:
Troublesome tech
The results raise some interesting questions about product reliability and lifespan. For example, how long should tech products like laptops and mobile phones reasonably last for?
I recently bought a new phone after my old phone (purchased in 2014) started misbehaving and freezing more than I had patience left to deal with it – a four year lifespan.
As tech leaps forward each year, the interplay between new software releases and depreciating hardware is an interesting one.
How long do you think a phone should reasonably operate without problems that curb its ability to do the job? What about a computer?
Your faulty goods rights
Under the Consumer Rights Act, you have an early right to reject faulty goods that are of unsatisfactory quality, unfit for purpose or not as described, and get a full refund.
You have the right to reject your item and get a refund within 30 days from the date you took ownership of the goods. You can still ask for a repair or replacement after the first 30 days and within the first six months.
Guide: What to do if you have a faulty product
Your rights against the retailer can last for up to six years (five years in Scotland), but after the first six months the onus is on you to prove a fault was present at the time you took ownership of the goods.
Our faulty goods claim tool asks some simple questions about the problem and will send you a ready-to-go letter you can send to the retailer.
Our Managing Director of Home Products and Services, Alex Neill, will be discussing our faulty goods findings tonight on LBC's Consumer Hour from 20:00. Be sure to tune in.
Have you had trouble with any of the items on our top 10 list? How long to do you expect your tech to last for?
The faulty goods data runs from April to June 2018.
faulty goods 6
How much does sustainability influence your clothes purchases?
Sustainability is my main consideration
I consider sustainability in most of my clothes purchases
I consider sustainability in the more expensive items I buy
I consider sustainability in the basic items I buy
Sustainability is not a consideration in my clothes purchases
malcolm r says:
The Consumer Rights Act also requires products to be "durable", that is to last a reasonable time without fault (considering such things as price and use). You have a legal right to redress if a product you buy does not last as long as it should.
This is an important aspect of the CRA that Which? seems unwilling to get to grips with and yet is, from reports in other Convos, something consumers have difficulty with, often from an unhelpful or intransigent retailer. It is particularly frustrating when a product fails just out of warranty.
When we buy a product we should be entitled to expect it to work properly, not just for 6 months or the length of the warranty but, in many cases, for several years. If it does not, and it's been properly used and looked after, it may be down to poor design, poor quality components, defective assembly or simply be a rogue machine that got through the net. If so, this is down to the manufacturer. The unlucky purchaser should not be expected to bear the cost.
Durability is good for the consumer and for our resources. I hope sometime Which? will help us use CRA by providing durability benchmark lives for appropriate products, beginning with domestic appliances and others from the "top ten" list above, that we can use to press a claim with the retailer when things go wrong.
Andrew Winton says:
Technology is advancing most aspects of reliability. However durability is NOT a priority for manufacturers or government.
Technically there is no real reason why any manufactured product should not last much longer than they do. However – if say an electric kettle was designed to last 20 years and did last 20 years – then the manufacturer would complain of limited prduct sales and the government would complain of limited production and corresponding tax revenue.
Our whole society is based around fast turn over and quick returns – money, money money – really sad.
John Ward says:
The Intro says – "Your rights against the retailer can last for up to six years (five years in Scotland), but after the first six months the onus is on you to prove a fault was present at the time you took ownership of the goods.".
Is it not the case that in England, Wales and Northern Ireland the period from which the consumer rights start applying is the date of purchase, whereas in Scotland it is the date from which the problem manifested? I have asked this several times in Which? Conversation without ever getting a response; now that we have the benefit of members of the Which? Legal team in attendance on our comments, could we please have an opinion on this question, or even a definitive answer if possible? Thank you.
I was hoping we might have had an explanation by now from someone in the Which? legal team on the point I raised above about the difference between Scotland and the rest of the UK in the period during which consumers can exercise their rights.
I increasingly get the impression that, despite assurances recently received to the contrary,.the comments received in Which? Conversation are not all being read by a Which? colleague, nor even by the author of the article.
Chirag Khetiya says:
Hi John, Sorry about the delay on this. We are looking at this for you and will get back too you with an answer as soon as possible.
Thanks very much, Chirag.
It's of general interest as people have been perplexed why the rules in Scotland are so different and it prompts the question why the timescales cannot be uniform throughout the UK.
I look forward to seeing your comments in due course.
I am glad you are on the case.
Hello John ,
Thank you so much for your patience on this. I have referred your question to our legal team, and they have provided the following response which I hope answers your question:
In England and Wales the time limits for different types of claim are set out in the Limitation Act 1980 which states that a breach of contract claim must be commenced within 6 years of the date of the breach.
For claims relating to faulty goods, the time starts from the date of purchase/delivery as the allegation is that the goods were inherently defective, however for services it may not always be from the date the contract is made.
For example if on the 01st of January you enter an agreement with a builder to build you a porch that is the date the contract is made. However, if a defective window is installed on the 20th, the time limit to start a claim is from the 20th when it was installed, not when the contract was made on the 1st.
In Scotland the rules are different, and the law that governs the time limit to bring a breach of contract claim is the Prescription and Limitation (Scotland) Act 1973. Under this law there are two broad provisions – limitation and prescription.
Limitation acknowledges that rights may exist, however once the limitation period has expired they are no longer enforceable in the courts. It does not have much relevance to your query. Prescription on the other hand does.,It is where a right or obligation is extinguished – eg through the passage of time. Section 6(1) of the 1973 Act states that an obligation is extinguished if no claim has been made within the time allowed – 5 years. The five-year period will usually start on delivery of the goods when the defect is obvious. Some faults do not show up for some time and here the five-year period runs from when the consumer becomes aware, or could with reasonable diligence have become aware, that loss, injury or damage had occurred. It should be remembered that where defective goods cause personal injury or death a three-year prescription applies.
Using the builder example above, let's say the problem is that the window doesn't open because the handle is defective, a diligent person would inspect the work shortly after completion and such an obvious defect would be pretty much immediately noticeable. If a claimant attempted to bring a claim 7 years later because they simply didn't inspect the work, a court is highly unlikely to accept the claim as they should have noticed sooner, and it would therefore be deemed to be out of time.
Thank you, Chirag
The Legal Team's statement confirms what I thought was the case, i.e. that in Scotland the five-year claim period can start with the date of discovery of the problem rather than from the date of delivery [as in England & Wales with a six-year claim period] so long as reasonable diligence was exercised at the outset.
Looking at the Consumer Rights Act 2015 (which applies generally to England, Wales, Scotland and Northern Ireland) Section22 the relevant times stated are:
" the first 6 months means 6 months beginning with the first day after these have all happened—
(a)ownership or (in the case of a contract for the hire of goods, a hire-purchase agreement or a conditional sales contract) possession of the goods has been transferred to the consumer,
(b)the goods have been delivered, and
(c)where the contract requires the trader to install the goods or take other action to enable the consumer to use them, the trader has notified the consumer that the action has been taken.".
Although specifics for Scotland are given 40 times in the document. there is no qualification given for the relevant time.
Thanks, Malcolm – frustratingly I had noted that previously in trying to find an explanation so assumed that it was covered by a Scottish statute of limitations that gave a different definition from the E,W & NI versions. The Which? legal team will surely know for certain, however, so I await their comments with interest.
So do I. Incidentally I could find no mention in the CRA of 5 or 6 years.
wavechange says:
The Act gives references to other legislation specifying the time period and I believe this is why there is a difference 5/6 year between Scotland and England:
"(2) Where this subsection applies—
(a) in the case of proceedings in England and Wales, the
Limitation Act 1980 applies as if the claim were an action in a court of law;
(b) in the case of proceedings in Scotland, the Prescription and Limitation (Scotland) Act 1973 applies as if the claim related to an obligation to which section 6 of that Act applies;
(c) in the case of proceedings in Northern Ireland, the Limitation (Northern Ireland) Order 1989 applies as if the claim were an action in a court established by law."
Thanks for this information. If I've read the correct bits:
5Time limit for actions founded on simple contract.
An action founded on simple contract shall not be brought after the expiration of six years from the date on which the cause of action accrued.
6Extinction of obligations by prescriptive periods of five years.
(1)If, after the appropriate date, an obligation to which this section applies has subsisted for a continuous period of five years—
(a)without any relevant claim having been made in relation to the obligation, and
(b)without the subsistence of the obligation having been relevantly acknowledged,
then as from the expiration of that period the obligation shall be extinguished:
Provided that in its application to an obligation under a bill of exchange or a promissory note this subsection shall have effect as if paragraph (b) thereof were omitted.
If a claim is made before the end of 6 (5) years but after the expiration date the remedy was found not to have been effective then it looks as though further action could be taken?
Patrick Taylor says:
A misleading title as actually it refers to the number of uses of a letter which is not the same thing as what do we return most often in the UK. My suspicion would be those things we can hand carry such as clothing and problematic food.
Also we are not given the overall figures which would have been interesting to see, particularly on cars where the names of the manufacturers would have seemed relevant.
I wonder if the charity the Citizens Advice letter app. is also analysed.
Can we experiment with the faulty claims tool without information being recorded? I'd like to explore the advice given but would not want to contribute any spurious information to statistics.
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