text stringlengths 8 5.77M |
|---|
Sony pros take the A7R III on exciting adventures across the world
While we have plenty of sample images from the new Sony A7R III for you to peruse in our Gallery, Sony has also been publishing some very neat videos about the new camera.
Below we have shared a pair of Sony A7R III videos from time lapse professional Drew Geraci and adventure photographer Chris Burkard respectively.
The video from Geraci was captured in New Zealand and is a stunning display of time lapse skill and technical prowess. There are beautiful mountain vistas, still lakes and the Milky Way shown off below. Be sure to watch it at a high quality setting.
Chris Burkard and Renan Ozturk took the Sony A7R III to the American Southwest, both on the ground and in the air. It's a pretty wild adventure they took their A7R III cameras on. Check it out below. |
We hope your experience with the ClickAtHome ordering web site and vendors
has been exciting and fun for you! We need your feedback to determine the
success of the program and how we can further improve the program for future
participants. Your feedback is greatly appreciated. Please take 5 minutes
to complete the following survey by Wednesday, April 11.
http://etcsurvey.corp.enron.com/wi/p0503555/i.asp?r=1048&s=FOGSZNQK&l=9
Thanks,
ClickAtHome Project Team |
/**
* This script is intended to be used in conjunction with the CameraLabs.bsh
* script. See https://micro-manager.org/wiki/Measuring_camera_specifications
* for more information.
*/
import org.jfree.data.xy.XYSeries;
import ij.measure.ResultsTable;
img = ij.IJ.getImage();
ij.ImageStack stack = img.getImageStack();
sqrt2 = Math.sqrt(2);
ij.plugin.ImageCalculator calc = new ij.plugin.ImageCalculator();
XYSeries data = new XYSeries("");
ResultsTable rt = new ResultsTable();
rt.reset();
for (int i=0; i <stack.getSize()/2; i++) {
ip = stack.getProcessor(2*i + 1);
ip2 = stack.getProcessor(2*i + 2);
ij.process.ImageStatistics stats = ip.getStatistics();
ipDiff = calc.run("Subtract create 32-bit", new ij.ImagePlus("1", ip), new ij.ImagePlus("2",ip2) );
ij.process.ImageStatistics statsDiff = ipDiff.getStatistics();
stdDev = statsDiff.stdDev/sqrt2;
rt.incrementCounter();
rt.addValue("Signal DN", stats.mean);
rt.addValue("Noise DN", stdDev);
rt.addValue("Diff in signal", statsDiff.mean);
if (i>0) {
rt.addValue("Slope of Log", ( (Math.log(stdDev) - Math.log(data.getY(i-1))) / (Math.log(stats.mean) - Math.log(data.getX(i-1)))));
rt.addValue("PCF", stats.mean/(stdDev*stdDev));
}
gui.message("Processing: " + i);
data.add(stats.mean, stdDev);
}
t = "Photon Transfer Data -" + img.getTitle();
rt.show(t);
plotData("Photon Transfer Curve -" + img.getTitle(), data, "Signal (DN)", "Noise (DN)", 100, 100, true, true);
|
Syracuse edges Cincinnati on late basket
C.J. Fair played the role of hero, tipping the ball in for the go-ahead basket in the waning seconds that lifted the No. 3 Syracuse Orange to a 57-55 victory over 21st-ranked Cincinnati.
Michael Carter-Williams scored 16 points, including a game-tying 3-pointer, for the Orange (18-1, 6-0 Big East), who were coming off their fourth win in program history against the nation's top-ranked team. Syracuse edged then-No. 1 Louisville on Saturday.
Fair and Brandon Triche had 13 points apiece for Syracuse, which extended its school-record home winning streak to 35 games.
Sean Kilpatrick hit six 3-pointers and finished with 21 points for the Bearcats (16-4, 4-3), who lost for the first time in eight games away from home this season.
Cincinnati led 49-42 on a Cheikh Mbodj layup with six minutes remaining, but the Orange fought back and pulled even at 55-55 on Carter-Williams' trey heading into the final minute.
Cashmere Wright, who missed Cincinnati's last game with a sprained right knee, misfired on a 3-pointer. Syracuse's Jerami Grant then attacked the basket on a drive but didn't score. Fair, though, bailed out his teammate and put the Orange on top with 13 seconds left.
Wright missed another shot from beyond the arc before Triche missed the front end of a 1-and-1 at the foul line with 2.5 seconds remaining.
The Bearcats secured the rebound and JaQuon Parker missed a 3-pointer as the horn sounded.
"As a team we came together at the end...and we had confidence in ourselves and our teammates, and that helped us pull out the victory," Grant said.
The Orange held Cincinnati to 20.7 percent shooting in the first half and led 22-18 at the break.
Game Notes
Carter-Williams had seven assists and five rebounds ... Kilpatrick shot 6- of-15 from 3-point range. He attempted only one field goal from inside the arc ... Parker compiled 11 points ... Cincinnati fell to 2-2 against ranked opponents this season. |
Graft versus host disease (GVHD) remains a major complication of bone marrow transplantation. Inflammatory cytokines are thought to play an important role during GVHD. We have used a murine model of GVHD after allogenic bone marrow transplantation to examine cytokine dysregulation, and we have demonstrated that Interleukin-1 (IL-1) is increased during GVHD. We have shown the importance of IL-1 in GVHD pathophysiology in this model by administering an IL-1 receptor antagonist (IL-1ra) to mice after transplant and reducing both the mortality and the immunosuppression associated with GVHD. We now propose to investigate the relationships between inflammatory cytokines, IL-1ra and GVHD in this murine model, and to extend these findings to other murine models of GVHD. We also propose to investigate the production of inflammatory cytokines during clinical transplantation and to evaluate the effects of IL-1ra in patients with steroid-resistant GVHD. Our specific aims are: 1) To analyze inflammatory cytokine dysregulation in GVHD target organs in murine models of GVHD to both minor and major histocompatibility antigens. 2) To characterize the effect of IL-1ra administration on both the production of inflammatory cytokines and on the clinical course of GVHD in these murine models. 3) To analyze the production of inflammatory cytokines after clinical bone marrow transplantation, both before and during treatment for acute GVHD. 4) To evaluate the safety and efficiency of IL-1ra for steroid-resistant acute GVHD and to evaluate its effect on the production of inflammatory cytokines. |
Q:
Smallest group containing two given elements
Given two elements of a finite group a, b Ԑ G, what is the smallest group containing both these elements?
Is it {axby| x = 0, 1,...., m & y = 0, 1,...., n} ? OR
Is it the Union, {axby| x = 0, 1,...., m & y = 0, 1,...., n} U {byax| x = 0, 1,...., m & y = 0, 1,...., n}?
where m and n are the orders of a and b respectively..
What exactly do we mean when we talk of a subgroup generated by a given subset S ⊂ G?
A:
Neither of these needs to be a subgroup. For example, if $a,b$ are generators of the free group $F_2$, then neither of these sets contain $aba$.
The smallest subgroup of $G$ containing $a$ and $b$ (called the subgroup generated by $a$ and $b$) is
$$\langle a,b\rangle = \left\{a^{m_1}b^{n_1}\cdots a^{m_k}b^{n_k} : m_i,n_i\in \mathbb Z, k\in\mathbb N\right\}$$
Note that in general elements an element of $\langle a,b\rangle$ can be written in the form $a^{m_1}b^{n_1}\cdots a^{m_k}b^{n_k}$ in more than one way. The subgroup generated by a set $S\subseteq G$ is defined similarly, i.e.
$$\langle S\rangle=\left\{s_1^{n_1}\cdots s_k^{n_k} : s_i\in S, n_i\in \mathbb Z, k\in\mathbb N\right\}$$
|
target "4.6-neon" with source configurePhase
location "https://download.eclipse.org/releases/neon/201705151400/" {
// Eclipse platform
org.eclipse.sdk.ide lazy
org.eclipse.emf.sdk.feature.group lazy
org.eclipse.ecf.core.feature.feature.group lazy
org.eclipse.ecf.filetransfer.feature.feature.group lazy
// Mylyn integration
org.eclipse.mylyn.commons.sdk.feature.group lazy
org.eclipse.mylyn.ide_feature.feature.group lazy
org.eclipse.mylyn.team_feature.feature.group lazy
org.eclipse.mylyn_feature.feature.group lazy
org.eclipse.mylyn.context_feature.feature.group lazy
org.eclipse.mylyn.sdk_feature.feature.group lazy
// SWT layout spy not available
}
|
Q:
Python Plotnine - Create a stacked bar chart
I've been trying to draw a stacked bar chart using plotnine. This graphic represents the end of month inventory within the same "Category". The "SubCategory" its what should get stacked.
I've built a pandas dataframe from a query to a database. The query retrieves the sum(inventory) for each "subcategory" within a "category" in a date range.
This is the format of the DataFrame:
SubCategory1 SubCategory2 SubCategory3 .... Dates
0 1450.0 130.5 430.2 .... 2019/Jan
1 1233.2 1000.0 13.6 .... 2019/Feb
2 1150.8 567.2 200.3 .... 2019/Mar
Dates should be in the X axis, and Y should be determined by the sum of "SubCategory1" + "SubCategory2" + "SubCategory3" and being color distinguishable.
I tried this because I thought it made sense but had no luck:
g = ggplot(df)
for key in subcategories:
g = g + geom_bar(aes(x='Dates', y=key), stat='identity', position='stack')
Where subcategories is a dictionary with the SubCategories name.
Maybe the format of the dataframe is not ideal. Or I don't know how to properly use it with plotnine/ggplot.
Thanks for the help.
A:
You need the data in tidy format
from io import StringIO
import pandas as pd
from plotnine import *
from mizani.breaks import date_breaks
io = StringIO("""
SubCategory1 SubCategory2 SubCategory3 Dates
1450.0 130.5 430.2 2019/Jan
1233.2 1000.0 13.6 2019/Feb
1150.8 567.2 200.3 2019/Mar
""")
data = pd.read_csv(io, sep='\s+', parse_dates=[3])
# Make the data tidy
df = pd.melt(data, id_vars=['Dates'], var_name='categories')
"""
Dates categories value
0 2019-01-01 SubCategory1 1450.0
1 2019-02-01 SubCategory1 1233.2
2 2019-03-01 SubCategory1 1150.8
3 2019-01-01 SubCategory2 130.5
4 2019-02-01 SubCategory2 1000.0
5 2019-03-01 SubCategory2 567.2
6 2019-01-01 SubCategory3 430.2
7 2019-02-01 SubCategory3 13.6
8 2019-03-01 SubCategory3 200.3
"""
(ggplot(df, aes('Dates', 'value', fill='categories'))
+ geom_col()
+ scale_x_datetime(breaks=date_breaks('1 month'))
)
|
/*
* Legal Notice
*
* This document and associated source code (the "Work") is a part of a
* benchmark specification maintained by the TPC.
*
* The TPC reserves all right, title, and interest to the Work as provided
* under U.S. and international laws, including without limitation all patent
* and trademark rights therein.
*
* No Warranty
*
* 1.1 TO THE MAXIMUM EXTENT PERMITTED BY APPLICABLE LAW, THE INFORMATION
* CONTAINED HEREIN IS PROVIDED "AS IS" AND WITH ALL FAULTS, AND THE
* AUTHORS AND DEVELOPERS OF THE WORK HEREBY DISCLAIM ALL OTHER
* WARRANTIES AND CONDITIONS, EITHER EXPRESS, IMPLIED OR STATUTORY,
* INCLUDING, BUT NOT LIMITED TO, ANY (IF ANY) IMPLIED WARRANTIES,
* DUTIES OR CONDITIONS OF MERCHANTABILITY, OF FITNESS FOR A PARTICULAR
* PURPOSE, OF ACCURACY OR COMPLETENESS OF RESPONSES, OF RESULTS, OF
* WORKMANLIKE EFFORT, OF LACK OF VIRUSES, AND OF LACK OF NEGLIGENCE.
* ALSO, THERE IS NO WARRANTY OR CONDITION OF TITLE, QUIET ENJOYMENT,
* QUIET POSSESSION, CORRESPONDENCE TO DESCRIPTION OR NON-INFRINGEMENT
* WITH REGARD TO THE WORK.
* 1.2 IN NO EVENT WILL ANY AUTHOR OR DEVELOPER OF THE WORK BE LIABLE TO
* ANY OTHER PARTY FOR ANY DAMAGES, INCLUDING BUT NOT LIMITED TO THE
* COST OF PROCURING SUBSTITUTE GOODS OR SERVICES, LOST PROFITS, LOSS
* OF USE, LOSS OF DATA, OR ANY INCIDENTAL, CONSEQUENTIAL, DIRECT,
* INDIRECT, OR SPECIAL DAMAGES WHETHER UNDER CONTRACT, TORT, WARRANTY,
* OR OTHERWISE, ARISING IN ANY WAY OUT OF THIS OR ANY OTHER AGREEMENT
* RELATING TO THE WORK, WHETHER OR NOT SUCH AUTHOR OR DEVELOPER HAD
* ADVANCE NOTICE OF THE POSSIBILITY OF SUCH DAMAGES.
*
* Contributors
* - Sergey Vasilevskiy
* - Doug Johnson
*/
/******************************************************************************
* Description: Implementation of the Company Competitor input file
* that scales with the database size.
******************************************************************************/
#ifndef COMPANY_COMPETITOR_FILE_H
#define COMPANY_COMPETITOR_FILE_H
#include <string>
#include "utilities/EGenStandardTypes.h"
#include "DataFileTypes.h"
namespace TPCE {
class CCompanyCompetitorFile {
CompanyCompetitorDataFile_t const *m_dataFile;
// Configured and active number of companies in the database.
// Depends on the configured and active number of customers.
//
TIdent m_iConfiguredCompanyCompetitorCount;
TIdent m_iActiveCompanyCompetitorCount;
// Number of base companies (=rows in Company.txt input file).
//
UINT m_iBaseCompanyCount;
public:
/*
* Constructor.
*
* PARAMETERS:
* IN dataFile - CompanyCompetitorDataFile
* IN iConfiguredCustomerCount - total configured number of
* customers in the database IN iActiveCustomerCount - active number
* of customers in the database (provided for engineering purposes)
*
* RETURNS:
* not applicable.
*/
CCompanyCompetitorFile(const CompanyCompetitorDataFile_t &dataFile, TIdent iConfiguredCustomerCount,
TIdent iActiveCustomerCount, UINT baseCompanyCount);
/*
* Calculate company competitor count for the specified number of
* customers. Sort of a static method. Used in parallel generation of
* company related tables.
*
* PARAMETERS:
* IN iCustomerCount - number of customers
*
* RETURNS:
* number of company competitors.
*/
TIdent CalculateCompanyCompetitorCount(TIdent iCustomerCount) const;
/*
* Calculate the first company competitor id (0-based) for the specified
* customer id.
*
* PARAMETERS:
* IN iStartFromCustomer - customer id
*
* RETURNS:
* company competitor id.
*/
TIdent CalculateStartFromCompanyCompetitor(TIdent iStartFromCustomer) const;
/*
* Return company id for the specified row.
* Index can exceed the size of the Company Competitor input file.
*
* PARAMETERS:
* IN iIndex - row number in the Company Competitor file
* (0-based)
*
* RETURNS:
* company id.
*/
TIdent GetCompanyId(TIdent iIndex) const;
/*
* Return company competitor id for the specified row.
* Index can exceed the size of the Company Competitor input file.
*
* PARAMETERS:
* IN iIndex - row number in the Company Competitor file
* (0-based)
*
* RETURNS:
* company competitor id.
*/
TIdent GetCompanyCompetitorId(TIdent iIndex) const;
/*
* Return industry id for the specified row.
* Index can exceed the size of the Company Competitor input file.
*
* PARAMETERS:
* IN iIndex - row number in the Company Competitor file
* (0-based)
*
* RETURNS:
* industry id.
*/
const std::string &GetIndustryId(TIdent iIndex) const;
const char *GetIndustryIdCSTR(TIdent iIndex) const;
/*
* Return the number of company competitors in the database for
* the configured number of customers.
*
* PARAMETERS:
* none.
*
* RETURNS:
* configured company competitor count.
*/
TIdent GetConfiguredCompanyCompetitorCount() const;
/*
* Return the number of company competitors in the database for
* the active number of customers.
*
* PARAMETERS:
* none.
*
* RETURNS:
* active company competitor count.
*/
TIdent GetActiveCompanyCompetitorCount() const;
/*
* Overload GetRecord to wrap around indices that
* are larger than the flat file
*
* PARAMETERS:
* IN iIndex - row number in the Company Competitor file
* (0-based)
*
* RETURNS:
* reference to the row structure in the Company Competitor file.
*/
const CompanyCompetitorDataFileRecord &GetRecord(TIdent index) const;
};
} // namespace TPCE
#endif // COMPANY_COMPETITOR_FILE_H
|
Q:
iPhone - custom UIImagePickerController
I am showing a UIImagePickerController in an app that just works with videos. So, it is nonsense to show pictures to users.
I have changed all properties I see on the controller but the picker shows like the next picture.
Two questions:
How do I get rid of this choice and show just the Photo Library, without having to tap first to get there.
As far as I know, all videos shot with iPhone end on camera roll. Suppose the iPad gets a camera in the future. Does this Photo Library option include the camera roll or what?
thanks in advance.
A:
You can probably use this and customize to fit your needs.
http://www.icodeblog.com/cloning-uiimagepickercontroller-using-the-assets-library-framework/
I found some issues with it, mostly that it takes a while to load on a device when there are 200+ images. I have not dug into to much, but this might be a start for you.
|
On the twelfth day of the blessed Ramadan month, a group of students and representatives from university student associations, across the nation, met with Ayatollah Khamenei.
At this meeting Ayatollah Khamenei held, "The Iranian people are moving forward, and today’s fumbling with firecrackers will not affect the will-power of the people. Everyone must realize this, the terrorists are too small to affect the will of the Iranian people and the authorities'. This also reveals that if the Islamic Republic had not resisted, at the center of all this conspiracy, we would have had much more trouble of this sort in the country. God willing, they will "bite the dust."
The Leader of the Revolution today, while meeting a group of university students stated regarding the controversial 2030 agenda that: The question of independence is extremely important. UNESCO's 2030 document fits this category. Some say they showed reservation, or they said that they did not agree on some parts: No, this is not the matter. Even if, we assume that there is no example of evident contradiction to Islam, which is not the case... I still say the country’s educational framework should not be written outside of this country.
This evening, for the first time, an Iraqi student represented foreign students in Iran and took the podium to speak.
To read the full text of the speech click here. |
1. Field of the Invention
The present invention relates to a holder and, more particularly, to a socket holder for supporting and positioning a socket.
2. Description of the Related Art
A conventional socket holder in accordance with the prior art shown in FIGS. 13 and 14 comprises a holder body 50 having a through hole 51, two steel balls “R” mounted in the through hole 51 of the holder body 50, and a spring “S” mounted in the through hole 51 of the holder body 50 and biased between the steel balls “R” to push the steel balls “R” outward from the through hole 51 of the holder body 50. When a socket is mounted on the holder body 50, the steel balls “R” press the inner wall of the socket to position the socket onto the holder body 50. However, the steel balls “R” increase the cost of fabrication of the conventional socket holder. In addition, it is inconvenient to assemble the steel balls “R” in the through hole 51 of the holder body 50. Further, the steel balls “R” and the spring “S” easily produce rust due to moisture. Further, the spring “S” produces an elastic fatigue during a long-term utilization, thereby failing the conventional socket holder. |
Trudeau declared a climate emergency. And then approved a pipeline.
Trudeau Liberals are ignoring their own warnings about climate dangers, that they spoke of last night.
Emergencies require immediate, serious action.
Elizabeth will do everything in her power to stop this pipeline. She’s already been arrested protesting Trans Mountain, alongside Indigenous leaders, environmentalists and scientists. But for the next phase, she and Green MP Paul Manly will need all the support they can get to fight this reckless pipeline in the House of Commons.
We can’t let this go unchecked.
Will you add your name now to send Trudeau a clear message that we can’t build more pipelines in the middle of a climate emergency, before these bonuses go through? |
5 Common Ft . Accidents You Must Know About
The feet are a vital component of the body, as anyone with ft . soreness or even a ft . damage currently knows. In fact, a quarter from the bone fragments within your body are placed with your ft. Every feet and leg has 26 bone fragments, 33 joints and over 100 muscle tissue, ligaments and tendons.
Your toes are accountable for numerous functions, providing you with stability, versatility and freedom to navigate during your entire day. It's sometimes an easy task to take the feet for granted, until you expertise some form of foot soreness or damage.
There are many different points that can cause ft . ache such as something as simple as the shoes that you opt to put on. Here's an overview of 5 medical ailments that may trigger feet soreness.
1. Gouty arthritis: This particular arthritis is likely to looking for morning blend milwaukee trigger sudden assaults of soreness and soreness, generally round the foundation part of the large toe. If heat, inflammation and swelling, quite often an invasion of gout symptoms is associated with. Normally this condition is triggered from uric crystals that increase inside your blood flow. You ought to seek competent medical assistance in order to get a precise prognosis and treatment methods if you believe you could have gout symptoms in your foot.
2. Bunions: While this distressing situation is frequently linked to putting on shoes or boots that happen to be way too small, additionally, it may run in families and stay linked to genetics. After having a long period of strain between the 2nd and very first toe, bunions may start to formulate. Bunions are bony protrusions made up of gentle bone fragments and tissue. They are generally together with irritation and ache. And if they continue, it can result in other types of foot and toe soreness.
3. Morton's Neuroma: If you suffer from Morton's neuroma it may http://query.nytimes.com/gst/abstract.html?res=980CE4D9153EE53ABC4950DFB566838E649EDE seem like a taking pictures soreness inside your ft . or just like you are sitting on a compact pebble. This uncomfortable neurological situation leads to a build-up of cells and neural system around your toes and in some cases the tennis ball of your respective ft .. The pain sensation could leave your ft . stinging and even sensing numb. If left unattended, wandering can be challenging as it is increasingly unpleasant to use any stress in your ft ., with time.
4. Plantar Fasciitis: This typical issue is usually described as extreme heel pain. The pain sensation is commonly most apparent first thing in the morning and it can also work up after resting or getting non-active for long periods of your energy. The thicker music band of tissue, called the plantar fascia, gets to be swollen and makes uneasy pain along your hindfoot and midfoot. If needed, fortunately, this condition can normally be taken care of through regular extending, appropriate footwear along with other medical solutions.
5. Bursitis: It is a situation that could arise all over the physique which includes spots much like your trendy and feet. Bursitis is definitely an excessively use situation that takes place about as well as in joint parts. Liquid filled sacs named bursa tend to come to be infected soon after performing recurring motions and also have been known to trigger significant ache across the big toe. Treatment for bursitis usually calls for sufficient sleep as well as a change to different types of activities that supply comfort on the influenced entire body aspect.
Exercising good foot health insurance and taking care of your ft is something that rewards folks for each age group. Deciding on excellent boots that offers enough assistance and luxury for your feet is obviously significant. You ought to seek healthcare assist if you are suffering from foot discomfort that can not vanish entirely. A professional medical doctor will examine you and then identify the reason behind your feet soreness as well as treatments. Overlooking constant ft . discomfort will more than likely only intensify the condition and may even cause other ft . problems. |
Videos - click to view
Wednesday, February 25, 2009
Sandi Kohlen and Pamela Waterfield win ladies darts doubles
Well I am not sure if it has been said before, but was it Too Much For the Money?
Eleven pairs played off in the "Doubles Event" at the Comox Legion Ladies Darts Tournament on Sunday, Feb. 15; it had to be their longest day.
The top 8 went to the best of three knock-out round; the outcome had Sandi Kohlen and Pamela Waterfield taking first place, Milly Davies and Ruby Ross placed second followed by Brenda Durant and Wendy Jackson, Moe Felhouser and Carol Merkley came in fourth. (full article...)
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We use third-party advertising companies to serve ads when you visit our website. These companies may use information (not including your name, address, email address, or telephone number) about your visits to this and other websites in order to provide advertisements about goods and services of interest to you. If you would like more information about this practice and to know your choices about not having this information used by these companies, click here. |
WASHINGTON (NBC News) — Senate Republicans have unveiled a draft of their legislation to revamp the government's role in the nation's health care system, a proposal that includes big reductions to Medicaid spending, tax cuts and the elimination of the mandate for individuals to purchase insurance.
The bill winds down the expanded Medicaid program under Obamacare after 2020 — a longer timeline than the House health care bill that was passed in May. But it also makes deeper cuts to the program in the long run by changing the federal funding allocation formula for states to receive fewer federal dollars for Medicaid recipients. It's an attempt at a compromise to appease those Medicaid advocates like Sens. Rob Portman of Ohio and Susan Collins of Maine as well as conservatives like Sens. Mike Lee of Utah and Ted Cruz of Texas.
The measure also helps people who purchase insurance out of pocket, known as the individual marketplace, afford the insurance through tax credits based on income, combining the ideas behind Obamacare and the House bill. The House bill gave people tax credits based on age, severely impacting older Americans who would see premiums rise by more than 700 percent, according to analysis of the bill.
By basing tax credits on income, the Senate is aiming to ensure older Americans are not penalized. But unlike Obamacare, which gives a subsidy upfront, the Senate bill would provide a tax credit, to be received after the fact.
The details of the bill had been tightly held by Republican leaders as Senate Majority Leader Mitch McConnell wrote a bill that aims to appeal to his most conservative members and the most moderate in his 52-member conference. With no Democrats expected to support a repeal of the Affordable Care Act, McConnell can only afford to lose two votes for the measure to pass.
McConnell: "I'm pleased we were able to arrive at a draft that incorporates input from so many different members" https://t.co/2vAEAGC5gt
Republican senators filed into a room in the U.S. Capitol Thursday morning, sat in chairs lined up in rows to listen to a presentation of a "discussion draft" of the legislation that could be voted on as early as next week.
Drafts of the bill circulated among Washington lobbyists in the days leading up to its reveal even as Republican Senators remained unaware of its contents.
According to Senate rules, the Senate can vote on this bill only after it is scored by the non-partisan Congressional Budget Office. Senators expect that analysis to be done as early as Friday or perhaps Monday.
The CBO analysis of the House bill says that 23 million people would lose insurance in the next decade under their bill, which President Donald Trump called "mean" in a meeting with senators earlier this month. |
Six months later and his near-decade stay at Wolves is over, sold to Reading for £1million.
When footballers are concerned you normally take quotes like the above with a pinch of salt, as an empty platitude, a tired cliché.
But with Dave the words came with substance. One of the most articulate and moral-centred footballers you could meet really gave a damn.
Edwards doesn’t act like a ‘normal’ footballer. This is a man who recently said “I’d love to get to a point where I literally just did charity work – what a great life to have.”
Wolves were lucky to have him and indeed with their player ins and out having a higher turnover than the staff roster at Poundland, (25 players in and 22 out since Fosun took charge) it’s increasingly likely that, academy products aside, a spell of anything approaching 10 years at Molineux will be very rare indeed.
When the chips were down, it was Edwards who would stand tall, encourage his team mates and never shirk his responsibilities. He didn’t bask in glory or attention but when it came to facing up after a defeat, he'd be the one clapping the fans at full time and was often the player who’d try and justify Wolves’ performance to the press. Those qualities will be missed.
Supporters generally like their players to be wear their heart on their sleeve, give 100 per cent every single time they cross that white line, respect the club's traditions and fans, play with passion and get every ounce out of their ability. Edwards did all that. He also rescued Wolves a number of times and provided some unforgettable memories, the winner in the 4-3 against Leeds and the injury time goal in the 4-4 thriller with Fulham last season standing out among many.
Edwards celebrates after his late winner in a 4-3 victory over Leeds (© AMA / Dave Bagnall)
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For all the stinging and wildly unnecessary criticism he received from people who were unable to ignore what he couldn’t do on a football field, instead of appreciating what he could do, the reaction to his exit was mostly one of sadness. As it should have been – Edwards was a fine representative of Wolverhampton Wanderers. Dependable, reliable, the archetypal model professional who left an indelible mark on those he afforded his time to – and that, with Dave, was everyone who requested it. That sadness has been reflected in the dressing room where Edwards was a role model for many.
The reaction has been similar with Nouha Dicko. He loved Wolves too – the striker was reportedly in tears after Saturday’s draw at Brentford, knowing it would be the last time he turned out in gold and black (or light blue).
One third of the Dicko, Afobe, Sako triumvate whose thrilling 'partnership' burned so brightly but too briefly, Dicko was a prolific and at times electrifying goalscorer in his first 18 months, notching 28 in 59 appearances and displaying the drive and passion that the club had been so sorely lacking in the couple of years before he joined.
A devastating cruciate knee ligament injury sullied his Wolves career but he deserves the utmost respect for the way he battled back to full health and never cowered during that horrible goal drought he endured last season. Ironically he was just started to look like his old self again.
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Again the memories are numerous...a hat-trick in the 6-4 Rotherham madness, two more in the aforementioned Leeds victory and winners in 1-0 victories against Forest and Leeds (again) towards the end of last season at the forefront, as was a confrontation with a Walsall fan on the Banks's pitch when Dicko stood his ground. "He's one of our own," they sing.
Dicko was confronted on the pitch at Walsall (© AMA / Sam Bagnall)
So two loyal and likeable servants have departed in a summer that has very much felt like the end of an era.
Edwards and Dicko’s time at Molineux adds to a combined total of 13 years. Add in the departures of long-serving staff Pat Mountain, Tony Daley and Rob Edwards, the latter pair having also played for Wolves, and you’re talking 43 years’ service.
But despite sadness within the club at losing affable and popular players and staff, the feeling among the fanbase is that a clean sweep was necessary.
There is sound logic to that. Wolves' last two seasons had been mediocre and apathetic.
"I think the club definitely needs shaking up," Paul Lambert said in May.
"I think there's been an acceptance here for too long, for too many years. We have to try and shake it up."
Fosun have certainly done that and sentiment is an alien concept to Jeff Shi, to Nuno and certainly to the increasingly influential Jorge Mendes.
While Edwards was being pushed out the door at 2.20pm on Saturday, Shi was in the pub buying drinks for fans. The coincidental timing was unfortunate but the imagery felt apt. This club is moving on in a hurry.
And if the chairman is to be getting a celebratory round of Champagne in at the Hogshead in May, this is what he and the hierarchy feel is necessary.
Thank you for the memories... pic.twitter.com/ybk4AqUOsx — Dave Edwards (@_DaveEdwards) August 29, 2017
After two seasons of going nowhere changes had to be made. "The secret of change is to focus all of your energy not on fighting the old, but on building the new," Socrates philosophised 2,400 years ago, and it's a motto Wolves have adapted, led by the trump card that is Nuno whose opening weeks have been deeply impressive.
It's ruthless, perhaps cold...but in 12 months this has become a very, very different club to the one run by Steve Morgan – a club which spectacularly failed with successive relegations to League One in one of the low points of Wolves' modern history, either side of their longest stay in the top flight for 30 years and a pride-restoring couple of years under Kenny Jackett.
The 'cosy club', as many fans came to term it, has now been disbanded.
In its place is a carousel of mostly overseas recruits who see the club as a stepping stone to the Premier League, with or without Wolves, and whether success is forthcoming or not won't hang around long enough to be heroes in the mould of Wright, Richards or Bull. Those days are long gone.
Do fans care? While the team is winning, it appears not. Heck, Ruben Neves admitted he saw the club as a path to the top flight and no one batted an eyelid. Should they care? The game has moved on and now, rightly or wrongly, Wolves are catching up. Whatever the rights and wrongs of leaning so heavily on an agent, whose primary motivation is to make money, Mendes has attracted players to Molineux that wouldn't even consider talking to Wolves in normal circumstances. The concern isn't of Wolves using Mendes...it's of Mendes using Wolves.
But this is an exciting new era and the Molineux hordes are daring to dream – that is a wondrous thing. Football is nothing without hope. Losing the likes of Edwards and Dicko and sacrificing loyalty and players that the fans can more readily associate with for a perceived increase in quality seems to be collateral damage if the Premier League dream is to be realised.
Dicko and Edwards during pre-season (© AMA / James Baylis)
Wolves tried the hard-working plucky underdog route under Mick McCarthy which took them to giddy yet too-brief heights, then the youthful and loyal approach under Kenny Jackett which, when extra funds weren't forthcoming, had its limitations. Now it's the superstar mercenaries era.
As is increasingly common at Wolves these days the methods may leave a sour taste but the destination supersedes everything and everyone.
Losing its soul? Maybe. Reinvention, revolution and a dispensing with tradition? Certainly. A brighter future? We can but hope...that's what these fans crave and deserve. |
A golden beer with a fluffy white head. The aroma is sweet with notes of corn, besides light notes of malt. The flavor is sweet with primary notes of straw, on a boring malty background. Towards the end I pick up light notes of corn, before a dry end sets in. A boring beer.
[Canned] Pale golden, airy head. Very vague citric nose. Sweetish with rounded mouthfeel. Completely void of any sort of character. Though it has medium body and some light bitterness there is hardly any flavour whatsoever.
(on can) Funny name and what´s the thing with the mink with a hat on the label? Pale yellow, disapearing head. vague aroma, but I got both vanilla, barley and grass. carbonated like a sodapop. Nice, rounded taste of the pale malts actually,. But a fizzu and metallic finish.
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Your basic membership is free and allows you to read all beer ratings.
Click here to create your account... and give your opinion! |
A GREAT comedy sketch by Katocha and Kenchan (from the band/comedy group Dorifu). It is about a disciple trying to be taught in the sword arts, but his master does not consent. Any resemblance to actual facts, people and events is purely coincidental. English subbed. Enjoy! |
Q:
C++ How to access Collection member variable from Iterator (inner class) - and does it make sense?
I'm trying to write class similar to std::vector, which would contain an Iterator as inner class. For some member functions of Iterator I would like to access variables from my Vector class. For example when overloading operator++ I would like to check if index of Iterator doesn't exceed size of Vector (and if so throw std::out_of_range()). I've implemented this access to outer class variable based on this topic. But for some reason compiler throws following error at me:
error C2440: '': cannot convert from 'initializer list' to 'Vector::Iterator'
Here is minimal version of my code replicating the issue:
template <typename Type>
class Vector
{
public:
class Iterator;
Vector() : size(0), capacity(0), data(nullptr) {}
Iterator begin()
{
return Iterator(this, 0);
}
private:
size_t size, capacity;
Type* data;
};
template <typename Type>
class Vector<Type>::Iterator
{
public:
Iterator(Vector& vectorRef, size_t index) : vectorRef(vectorRef), index(index) {}
private:
size_t index;
Vector& vectorRef;
};
int main()
{
Vector<int> vec;
vec.begin();
return 0;
}
What would be the cause of this? And does it make sense to pass reference to Vector class like that? Or is there a better way?
A:
That's because this has type Vector* or const Vector* but your constructor is accepting a Vector& so no matching constructor is found.
Try with Vector(*this, 0).
|
Village uproar over festival
Councillor Keith Sowden.
Tension is growing ahead of a religious festival which could see 2,500 members of the travelling community and 700 vehicles descend on Overton.
Around 100 people crammed into a village meeting about the planned Light and Life Festival this July – with much of the anger directed at Lancaster City Council.
Councillor Keith Sowden, who represents Overton on the city council, said villagers feel the council has “washed its hands of them”.
This is because the festival will be held on private land and the city council says it has “no role to play”.
But residents are worried thousands of people and hundreds of vehicles will bring congestion and nuisance to the peaceful village.
An Overton resident, who wished to remain anonymous, said: “Villagers are scared and worried and it’s made much much worse by the lack of information given.
“I must admit to being disappointed with the response from Lancaster City Council.
“One of the major issues will be the volume of traffic. To put in context, if one towed caravan joined Morecambe Road at the Asda roundabout per minute it would take up to 11 hours for 700. The traffic along that area is already a nightmare.”
Coun Sowden said: “Where are they going to put all these people? There are no parking places.
“Everyone is terrified about it. I’m locking my house and going abroad. Life will be impossible during that week.”
Danny Maddox, chairman of Overton Parish Council, said: “We are not saying anything about who is coming to the festival – the vast majority realise that is a religious festival. We can’t do anything to stop it so we’re trying to manage it. The police and Lancashire County Council have been really positive on our behalf.”
The event is expected to take place on privately-owned fields between Kevin Grove and Overton Saint Helen’s CE Primary School.
The four-day Light and Life Gypsy Church festival centres on a large big-top tent featuring bible classes, prayer meetings and gospel sessions. Last year’s event was held at Hewish, Somerset, when fields were taken over by 700 caravans and around 3,000 travellers and police dealt with calls about antisocial behaviour, people fouling and litter being tossed into hedgerows.
Mark Cullinan, chief executive of Lancaster City Council, said: “With the information the council has, there are no planning or licensing issues, so as things stand, the council does not currently have a role to play. We are aware that local people are in direct contact with the county council and police.” |
Q:
Sorting 1 before 10 in bash
I'm sorting numerically on a specific column of a ; separated file with:
sort -k3n file
But numbers 10 and 11 are sorted before 1. How do I fix this?
A:
If your fields are separated with something else than a blank, you can use the --field-separator or -t option, like so:
sort -k3n -t\; file
|
---
abstract: 'We compute the isospin asymmetries in $B \to (K^*,\rho) \gamma$ and $B\to (K,K^*,\rho) l^+l^-$ for low lepton pair invariant mass $q^2$, within the Standard Model (SM) and beyond the SM (BSM) in a generic dimension six operator basis. Within the SM the CP-averaged isospin asymmetries for $B \to (K,K^*,\rho) ll$, between $1{\,{\rm GeV}}^2 \leq q^2 \leq 4m_c^2$, are predicted to be small (below 1.5%) though with significant cancellation. In the SM the non-CP averaged asymmetries for $B \to \rho ll$ deviate by $\approx \pm 5\%$ from the CP-averaged ones. We provide physical arguments, based on resonances, of why isospin asymmetries have to decrease for large $q^2$ (towards the endpoint). Two types of isospin violating effects are computed: ultraviolet (UV) isospin violation due to differences between operators coupling to up and down quarks, and infrared (IR) isospin violation where a photon is emitted from the spectator quark and is hence proportional to the difference between the up- and down-quark charges. These isospin violating processes may be subdivided into weak annihilation (WA), quark loop spectator scattering (QLSS) and a chromomagnetic contribution. Furthermore we discuss generic selection rules based on parity and angular momentum for the $B \to Kll$ transition as well as specific selection rules valid for WA at leading order in the strong coupling constant. We clarify that the relation between the $K$ and the longitudinal part of the $K^*$ only holds for leading twist and for left-handed currents. In general the $B \to \rho ll$ and $B \to K^*ll$ isospin asymmetries are structurally different yet the closeness of $\alpha_{\rm CKM}$ to ninety degrees allows us to construct a (quasi) null test for the SM out of the respective isospin symmetries. We provide and discuss an update on ${\cal B}(B^0 \to K^{*0}\gamma)/{\cal B}(B_s \to \phi \gamma)$ which is sensitive to WA.'
bibliography:
- 'references.bib'
---
Edinburgh/13/05\
CP3-Origins-2013-007 DNRF90\
DIAS-2013-7
[**Isospin asymmetries in $B\to (K^*,\rho) \gamma/ l^+ l^-$ and $B \to K l^+ l^-$ in and beyond the Standard Model**]{} 1.3cm [ James Lyon$^{a,}\footnote{J.D.Lyon@sms.ed.ac.uk} $ & Roman Zwicky$^{a,}$[^1] 0.5cm [*$^a$ [*School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland*]{}*]{}]{}
Introduction
============
The isospin asymmetry in $B \to K^* ll$ gave, in recent years, some indication of being of opposite sign to the Standard Model (SM) prediction [@Aubert:2008ps; @Wei:2009zv]. This trend has not been confirmed by the new LHCb data in the year of 2012 [@Aaij:2012cq], yet in $B \to K ll$ a negative deviation from zero has been measured at the level of $4\sigma$ taking into account the entire $q^2$-spectrum. The isospin-asymmetry in $B \to Kll$ is expected to be small in the SM and therefore it is important to assess this observable. Isospin asymmetries of the $B \to K^* \gamma$ and $B \to \rho \gamma$ [@Amhis:2012bh] are found to agree and deviate by two standard deviations from the SM giving rise to constraints and curiosity for future measurements respectively.
Independent of any signs of deviation, the isospin asymmetry contributes to the microscopic investigation of flavour changing neutral currents (FCNCs). It is sensitive to a large number of four Fermi operators of the $\Delta F = 1$-type and complements the constraints from non-leptonic decays.
In this paper we consider two types of isospin violating effects: *ultraviolet (UV) isospin violation* due to unequal coupling of up and down quarks to Fermi operators as well as *infrared (IR) isospin violation from spectator emission* of the intermediate photon which is therefore proportional to the charge difference of up and down quark. The latter mainly result from processes for which the large energy release of the $b$-quark is transferred to the spectator quark which then emits an energetic photon as the external kinematics require. The processes are depicted in Fig. \[fig:isoSM\] and are from left to right: weak annihilation (WA), quark loop spectator scattering (QLSS) and the contribution from the chromomagnetic operator which we shall simply denote by ${\cal O}_8$ hereafter. Isospin effects in quantum chromodynamical (QCD) quantities such as masses and decay constants are known to be just below the sub-percent level, to be discussed later on, and therefore small in comparison to the precision accessible to near future experiments.
In this paper we have computed WA in LCSR, extending earlier results for $q^2 = 0$ [@Ali:1995uy; @Khodjamirian:1995uc], QLSS within QCD factorisation (QCDF) and ${\cal O}_8$ we take from our recent computation [@DLZ12]. Furthermore we include a complete set of dimension six operators relevant at leading order of the strong coupling constant $\alpha_s = g_s^2/4\pi$. By mapping a specific model into an operator basis, such as the family model considered in [@Ishida:2013sya], one can get the effects with our estimates.
Various aspects of the isospin asymmetry in $B\to K,K^* l^+l^-$ decay have been calculated previously. The closely related decay $B\to V\gamma$ has been computed using QCD factorisation (QCDF) in [@Kagan:2001zk] and using a mixture of QCDF and light-cone sum rules (LCSR) in [@Ball:2006eu]. A program computing the isospin asymmetry $B \to K^* \gamma$ in the minimal supersymmetric SM has been reported in [@Mahmoudi:2007vz]. $B\to K,K^* l^+l^-$ was computed using QCDF in [@Feldmann:2002iw], and a mixed approach was recently employed for $B \to Kll$ in [@Khodjamirian:2012rm]. In this paper we improve on these works by including a complete basis of dimension six operators for WA and QLSS, our recent ${\cal O}_8$-computation [@DLZ12], and the complete set of twist-3 terms for WA.
Essential results of the paper are that the isospin asymmetries of $B \to K,K^*,\rho ll$ are small in the SM; especially and systematically for high $q^2$. The isospin asymmetries of the $K^*$- and $\rho$-mesons turn out to be very similar at small $q^2$ up to form factor ratios due to the, presumably, accidental closeness of the Cabibbo-Kobayashi-Maskawa (CKM) angle $\alpha_{\rm CKM}$ to ninety degrees. This prompts us to define a quantity $\delta_{a_I}$ which serves as a (quasi) null test of the SM. The results of the generic dimension six operators are given in form of tables and complement constraints from non-leptonic decays and $B \to (K^*,\rho) \gamma$ decays, which we discuss.
This work is written in the language of $B \to K/K^*$-transition. Adaptation to other light vector mesons is generally straightforward, with the exception of WA for $B^0 \to \rho^0$- and $B_s \to \phi$-transitions which we discuss in the corresponding section in some detail. The paper is organised as follows: in section \[sec:rates\] we present formulae for pseudoscalar and vector meson decay rates in terms of helicity amplitudes, the relation of the latter to form factors and quark loop functions and finally formulae for the isospin asymmetries in a linear approximation. In section \[sec:weak-annihilation\] the complete operator basis of dimension six operators contributing at ${\cal O}(\alpha_s^0)$ to the WA subprocess is given; with results in subsection \[sec:WAresults\] and detailed formulae in appendix \[app:wa-formulae\]. In section \[sec:quark-loop-spectator\] we present the complete dimension six operator basis contributing to QLSS at order ${\cal O}(\alpha_s)$ along with results computed in QCDF. In section \[sec:iso\] we present the $B \to K^*ll$ and $B \to K^*\gamma$ isospin asymmetries. In subsection \[sec:selection\] we discuss selection rules: those applicable to any scalar $\to$ scalar $ll$ decay in \[sec:Ksel\], those particular to WA in the factorisation approximation \[sec:WAsel\] and we also discuss to what extent the $K$ distribution amplitude (DA) does or does not correspond to the $K^*_\parallel$ in \[sec:non-relation\]. In subsection \[sec:q2-dependence\] we discuss $q^2$ dependence of the isospin asymmetries, and in subsection \[sec:isospinSM\] we discuss the kaon isospin asymmetries in the SM respectively. In section \[sec:rho-meson\] we present the isospin asymmetry of $B \to \rho \gamma/ll$ as well as an extension of the operator basis for $\rho^0$-channel. In section \[sec:isospinBSM\] we cover aspects of isospin BSM: in \[sec:constraints\] we (briefly) discuss constraints and in \[sec:dai\] we propose the ratio of the $K^* \gamma$- and $\rho \gamma$-asymmetries as a (quasi) null test of the SM. We end the paper with a summary and conclusions in section \[sec:discussion\].
We give an updated prediction for ${\cal B}(B^0 \to K^{*0}\gamma)/{\cal B}(B_s \to \phi \gamma)$ in appendix \[app:update\], which was recently measured by LHCb. Various explicit results can be found in appendix \[app:results\], such as numbers for the generic dimension six operator basis for all isospin asymmetries discussed in this paper in \[app:tables\]. Aspects of gauge invariance of the WA and QLSS computations, which turn out to be rather intricate, can be found in appendix \[app:gauge-invariance\].
Decay rate and form factors {#sec:rates}
===========================
The effective Hamiltonian in the SM, to be extended in upcoming sections, is parametrised by $$\mathcal H_{\mathrm{eff}} = \frac{G_F}{\sqrt 2}\left( \sum_{i=1}^2
(\lambda_u C_i \mathcal O_i^u + \lambda_c C_i \mathcal O_i^c ) -\lambda_t \sum_{i=3}^{10} C_i \mathcal O_i \right) \;, \qquad
\lambda_i \equiv V_{is}^*V_{ib} \;,
\label{eq:effective-ew-hamiltonian}$$ where the $b \to s$ unitarity relation reads $\lambda_u + \lambda_c + \lambda_t = 0$. The basis is given by [@Buchalla:1995vs]: $$\begin{aligned}
\label{eq:SMbasis}
\mathcal O_1^q &= (\bar s_i q_j)_{V-A}(\bar q_j b_i)_{V-A} &
\mathcal O_2^q &= (\bar s_i q_i)_{V-A}(\bar q_j b_j)_{V-A} \nonumber \\
\mathcal O_3 &= (\bar s_i b_i)_{V-A} \sum_q (\bar q_j q_j)_{V-A} &
\mathcal O_4 &= (\bar s_i b_j)_{V-A} \sum_q (\bar q_j q_i)_{V-A} \nonumber \\
\mathcal O_5 &= (\bar s_i b_i)_{V-A} \sum_q (\bar q_j q_j)_{V+A} &
\mathcal O_6 &= (\bar s_i b_j)_{V-A} \sum_q (\bar q_j q_i)_{V+A} \nonumber \\
\mathcal O_7 &= -\frac{e m_b}{8\pi^2}\bar s \sigma\cdot F (1+\gamma_5)b &
\mathcal O_8 &= -\frac{g_s m_b}{8\pi^2}\bar s \sigma\cdot G (1+\gamma_5) b \nonumber \\
\mathcal O_9 &= \frac{\alpha}{2\pi}(\bar l\gamma^\mu l)(\bar s \gamma_\mu (1-\gamma_5) b) &
\mathcal O_{10} &= \frac{\alpha}{2\pi}(\bar l\gamma^\mu\gamma_5 l)(\bar s \gamma_\mu (1-\gamma_5) b) \;, & \end{aligned}$$ where $i,j$ are colour indices, $(\bar s b)_{V\pm A}=\bar s \gamma^\mu (1\pm\gamma_5) b$ and ${{\cal O}}'_{7-10}$ will denote the operators with opposite chirality as usual, and we have taken the opposite sign of $\mathcal O_{7,8}$[^2]. These are the same conventions as in [@Beneke:2001at]. Details of the calculation of the Wilson coefficients $C_{1-10}$ are given in appendix \[app:wilson-coefficients\]. Furthermore, $e = \sqrt{4 \pi \alpha} > 0 $ where $\alpha$ is the fine structure constant and $G_F$ is the Fermi constant.
We parameterise the amplitude as follows: $$\begin{split}
&_{\rm out}\left\langle M(p) l^+(l_1) l^-(l_2)\mid B(p+q)\right\rangle_{\rm in} \\
&= \frac{G_F}{\sqrt 2}\lambda_t \frac{\alpha m_b}{q^2\pi}
\left(\bar u(l_1)\gamma_\mu v(l_2)\sum_i\mathcal {\mathcal{T}}^V_i P^\mu_i + \bar u(l_1)\gamma_\mu\gamma_5 v(l_2)\sum_i{\mathcal{T}}^A_i P^\mu_i\right)\delta^{(4)}(q-l_1-l_2) \;,
\label{eq:amplitude-definition}
\end{split}$$ where M stands, throughout this work, for a light vector ($K^*$,$\rho$) or pseudoscalar ($K$) meson. The symbols $u,v$ correspond to lepton polarisation spinors of mass dimension $1/2$ and $q=l_1+l_2$ is the total momentum of the lepton pair. For lepton coupling we only allow $V$ and $A$-couplings as present in the SM. The isospin violating contributions all proceed through a photon and thus have a vectorial coupling. The axial coupling is included as it originates through $Z$-penguins and box diagrams which are significant in the SM. In this work we do not include non-SM lepton couplings. The basis tensors $P_i^\mu$ [@DLZ12] are the standard choice for penguin form factors $$\begin{aligned}
{2}
& K^*: \quad & P_1^\mu =& 2\epsilon^{\mu\nu\rho\sigma}\eta^*_\nu p_\sigma q_\rho \;,\nonumber \\
& & P_2^\mu =& i\left[(m_B^2-m_{K^*}^2)\eta^{*\mu} - (\eta^* \cdot q)(2p+q)^\mu\right] \;,\nonumber \\
& &P_3^\mu =& i(\eta^* \cdot q)\left[q_\mu - \frac{q^2}{m_B^2-m_{K^*}^2}(2p+q)^\mu\right] \;, \nonumber \\
& K: &P_T^\mu =& \frac{1}{m_B+m_K}\left[(m_B^2-m_K^2)q^\mu - q^2 (2p+q)^\mu\right] \;,\end{aligned}$$ in the sense that ${\mathcal{T}}^V_i=C_7 T_i(q^2)+\text{corrections}$[^3]. The basis for pseudoscalar and vector meson decays are $P_{T}^\mu$ and $P_{1,2,3}^\mu$ respectively. Note we have implicitly assumed $m_l =0$ as otherwise there is additional direction proportional to $q^\mu$ which vanishes for the $V$ but is proportional to $m_l$ for $A$. The four vector $\eta$ denotes the vector meson polarisation. We use the Bjorken & Drell convention for the Levi-Civita tensor $\epsilon_{0123}=+1$. In discussing physical quantities and problems it will prove advantageous to go over to the so-called *helicity basis*: $$\label{eq:Btrafo}
\begin{pmatrix}
{h}_0 \\
{h}_+ \\
{h}_-
\end{pmatrix} =
\underbrace{
\begin{pmatrix}
0 & a & b \\
1/\sqrt{2} &-c/\sqrt{2} & 0 \\
1/\sqrt{2} & +c/\sqrt{2} & 0
\end{pmatrix} }_{\equiv B}
\begin{pmatrix}
{\mathcal{T}}_1 \\
{\mathcal{T}}_2 \\
{\mathcal{T}}_3
\end{pmatrix} \;.$$ which corresponds to $0,\pm$[^4] polarisation of the vector meson. Basis tensors corresponding to $h_{0,\pm}$ are given in appendix \[app:decay-width-tensors\]. The variables $a,b,c$ in the basis transformation matrix are given by: $$\label{eq:abc}
(a,b) \equiv \sqrt{\frac{\hat q^2}{8}} \frac{1}{\hat m_V} \left( \frac{1+3 \hat m_V^2- \hat q^2}{\sqrt{\lambda_V}},\frac{ -\sqrt{\lambda_V}}{1-\hat m_V^2}\right) \;, \quad c \equiv \frac{1-\hat m_V^2}{\sqrt{\lambda_V}} = 1 +{\cal O}(\hat q^2) \nonumber \;,$$ where here and below hatted quantities are normalised with respect to the $B$-meson mass, $\hat q^2 \equiv q^2/m_B^2$, $\hat m_V^2 \equiv m_V^2/m_B^2$ and $ \lambda_V$ is the Källén-function with normalised entries: $$\label{eq:Kallen}
\lambda_{V} \equiv \lambda_V(1, \hat m_V^2, \hat q^2) = ((1 + \hat m_V)^2 - \hat q^2)((1 - \hat m_V)^2 - \hat q^2)\;.$$ For the $K$-meson there is no polarisation and no freedom in choosing a basis.
The decay rates are given by[^5] $$\begin{aligned}
\frac{d\Gamma}{dq^2}[B\to K^*l^+l^-] &= \left[\frac{\lambda_V^{3/2}}{ q^2}\right] \left(\frac{\alpha}{4\pi}\right)^2 \, c_F c_L \sum_{i=V,A} \left[\left|{h}^i_+\right|^2 + \left|{h}^i_-\right|^2 + |h^i_0|^2\right] \;,
\label{eq:vector-decay-rate} \\[0.1cm]
\frac{d\Gamma}{dq^2}[B\to K l^+l^-] &= \left[ \frac{\lambda_{P}^{3/2}}{2 (m_B+m_K)^2 } \right] \left(\frac{\alpha}{4\pi}\right)^2 \, c_F c_L \sum_{i=V,A} |{h}^i_T|^2 \;,
\label{eq:scalar-decay-rate}
\\[0.1cm]
\Gamma[B\to K^*\gamma] &= \left[ \frac{3}{4} \lambda_V^{3/2} \right] \left(\frac{\alpha}{4\pi}\right) \, c_F
\left[|{h}^V_+|^2 + |{h}^V_-|^2 \right]|_{q^2 = 0} \;,
\label{eq:photon_rate}\end{aligned}$$ where $c_F \equiv (G_F^2 |\lambda_t|^2 m_b^2 m_B^3/12\pi^3)$, ${h}_T^i \equiv {\mathcal{T}}_T^i$ and $c_L=(1+2m_l^2/q^2)\sqrt{1-4m_l^2/q^2}$ accounts for nonzero lepton mass. An important observation is that for $m_V \to 0$ the rate remains bounded[^6] provided that $$\label{eq:X2X3general}
{h}^i_0 = {\cal O}(m_V^0) \quad \Rightarrow \quad {\mathcal{T}}^i_2 = \frac{\lambda_V}{(1- \hat m_V^2)(1+3\hat m_V^2-\hat q^2)} {\mathcal{T}}^i_3 + {\cal O}(m_V) \;.$$ This expression reduces to the form we have given in our previous work [@DLZ12] in the appendix in the $m_V \to 0$ limit. In essence the relation between ${{\mathcal{T}}}_2$ and ${{\mathcal{T}}}_3$ cancels the explicit $1/m_V$ in $h_0$ which appears through and . Note in the SM $h_+ \ll h_-$ by virtue of the [$V$-$A$]{}-interactions. In [@Beneke:2001at], which operates in the heavy quark limit, $h_+ \to 0$. In our work $h_+$ is vital as we allow for right-handed structures that violate isospin.
The axial lepton amplitudes ${\mathcal{T}}^A_i$ arise only from the $\mathcal O_{10}$ operator and are given in terms of standard form factors by: $$\begin{aligned}
{\mathcal{T}}^A_1 &= \frac{C_{10} q^2 V(q^2) }{2m_b(m_B+m_{K^*})} \;,
&{\mathcal{T}}^A_3 &= -C_{10} \frac{m_{K^*}}{m_b} A_3(q^2) \;, \nonumber \\
{\mathcal{T}}^A_2 &= \frac{C_{10} q^2 A_1(q^2)}{2m_b(m_B-m_{K^*})} \;,
& {\mathcal{T}}^A_T &= C_{10} \frac{m_B+m_K}{2m_b} f_+(q^2) \;.
\label{eq:lepton-axial-ff}\end{aligned}$$ We will split the vector lepton amplitudes into isospin sensitive and insensitive parts denoted by ${\mathcal{T}}^q$ and ${\mathcal{T}}^{0}$ respectively with $q$ being the light flavour of the $B$-meson: $$\begin{aligned}
\label{eq:Tdec}
{\mathcal{T}}^V_i &= {\mathcal{T}}^{V,0}_i + {\mathcal{T}}^{V,q}_i \;,
& {\mathcal{T}}^{V,q}_i &= C_8^{\mathrm{eff}} G^q_i(q^2) + W^q_i(q^2) + S^q_i(q^2) \;.\end{aligned}$$ Note, we have absorbed the Wilson coefficient (WC) for WA and QLSS into the functions $W^q_i(q^2)$ and $S^q_i(q^2)$ respectively as there are quite a few of them. The WC $C^{\rm eff}_{7,8,9}$ correspond to scheme and basis independent WCs which include quark loop contributions and will be defined further below. The symmetric part is approximated throughout this work by the $C^{\rm eff}_{7,9}$ contributions, which in terms of standard form factors is given by: $$\begin{aligned}
{\mathcal{T}}^{V,0}_1(q^2) &= \frac{C_9^{\mathrm{eff}}(q^2) q^2 V(q^2)}{2m_b(m_B+m_{K^*})} + C_7^{\mathrm{eff}} T_1(q^2) \;, &
{\mathcal{T}}^{V,0}_3(q^2) &= -C_9^{\mathrm{eff}}(q^2) \frac{m_{K^*}}{m_b} A_3(q^2) + C_7^{\mathrm{eff}} T_3(q^2) \nonumber \\
{\mathcal{T}}^{V,0}_2(q^2) &= \frac{C_9^{\mathrm{eff}}(q^2) q^2 A_1(q^2) }{2m_b(m_B-m_{K^*})} + C_7^{\mathrm{eff}} T_2(q^2) \;, &
{\mathcal{T}}^{V,0}_T(q^2) &= C_9^{\mathrm{eff}}(q^2)\frac{m_B+m_K}{2m_b} f_+(q^2) + C_7^{\mathrm{eff}} f_T(q^2)
\label{eq:lepton-vector-sym-ff}\end{aligned}$$
![Isospin violating processes included in our calculation. Crosses indicate possible photon emission points. Throughout this paper double lines stand for the $b$-quark flavour. (left) Weak annihilation (WA) (middle) Quark loops with spectator scattering (QLSS) (right) Chromomagnetic operator ${\cal O}_8$. Note that in WA we have indicated photon emission from quarks with $Q_b$-charge as well as WA is sensitive to UV isospin violation where the four Fermi operator with spectator quark $u$ and $d$ appear in unequal proportion.[]{data-label="fig:isoSM"}](all-contributions){width="\textwidth"}
The isospin sensitive diagrams are shown in Fig. \[fig:isoSM\]. The weak annihilation amplitude, denoted $W^q_i(q^2)$, (Fig. \[fig:isoSM\],left) originates from $\mathcal O_{1-6}$ and is computed using LCSR in section \[sec:weak-annihilation\]. Spectator scattering with a quark loop, denoted $S^q_i(q^2)$, (Fig. \[fig:isoSM\],middle) arises from $\mathcal O_{1-6}$ as well and is computed using QCD factorisation in section \[sec:quark-loop-spectator\]. The spectator contributions due to $\mathcal O_8$ (Fig. \[fig:isoSM\],right) are denoted by $G_i^q(q^2)$ and are taken from our recent work [@DLZ12]. For the short distance form factors in and we use the fits in [@Ball:2004rg; @Ball:2004ye], recomputed with updated hadronic inputs as in [@DLZ12]. Quark loop contributions, other than the ones with a gluon connecting to the spectator, are absorbed into the effective WCs. The structures proportional to the $m_b$-mass are independent of $q^2$ and described by: $$\begin{aligned}
C_7^{\mathrm{eff}} &= C_7 - \frac{4}{9}{C}_3 - \frac{4}{3}{C}_4 + \frac{1}{9}{C}_5 + \frac{1}{3}{C}_6 \;, &
C_8^{\mathrm{eff}} &= C_8 + \frac{4}{3}{C}_3 - \frac{1}{3}{C}_5 \;.\end{aligned}$$ The other contributions are taken care off by $ C_9^{\mathrm{eff}}(q^2)$ [@Grinstein:1988me], $$C_9^{\mathrm{eff}}(q^2) = C_9 + Y(q^2) \;,$$ where $$\begin{split}
Y(q^2) =& h(q^2,m_c)\left(-\frac{\lambda_c}{\lambda_t}\left(3{C}_1 + {C}_2\right) + 3{C}_3 + {C}_4 + 3{C}_5 + {C}_6\right) \\
& - \frac{h(q^2,m_b)}{2}\left(4{C}_3 + 4{C}_4 + 3{C}_5 + {C}_6\right) \\
& - h(q^2,0)\left(\frac{\lambda_u}{\lambda_t}\left(3{C}_1+{C}_2\right) + \frac{1}{2}\left({C}_3 + 3{C}_4\right)\right) + \frac{4}{27}\left({C}_3 + 3{C}_4 + 8{C}_5\right) \;,
\end{split}$$ with $h(s,m_q)$ being photon vacuum polarisation which we quote in section \[sec:QLSS\], and we restored the factors $\lambda_u$ and $\lambda_c$ factors explicitly especially in view of the fact that for the $b \to d$ transition the hierarchies differ from the $b \to s$ transitions.
Definition of isospin asymmetries
---------------------------------
The experimentally accessible isospin asymmetry $a_I(q^2)$ and its CP-average $\bar{a}_I$[^7], which are functions of the lepton pair invariant mass $q^2$, are defined as follows: $$\begin{aligned}
a_I^{\bar 0 -}(q^2) &\equiv& \frac{d A_I^{\bar 0 -}}{dq^2} \equiv \frac{c_M^2 d\Gamma[\overline B^0\to \overline M^0 l^+l^-]/dq^2 - d\Gamma[B^-\to M^- l^+ l^-]/dq^2}{c_M^2 d\Gamma[\overline B^0\to \overline M^0 l^+l^-]/dq^2 + d\Gamma[ B^-\to M^- l^+ l^-]/dq^2} \;, \nonumber \\[0.1cm]
\bar{a}_I(q^2) &\equiv& \frac{1}{2}\left( a_I^{\bar 0 -}(q^2) + a_I^{0 +}(q^2) \right) \;,
\label{eq:dai-def}\end{aligned}$$ where $a_I^{0 +}$ corresponds to the CP-conjugated process of $a_I^{\bar 0 -}$. The constant $c_M$ is given by $c_K=c_{K^*}=1$ and $c_\rho=\sqrt{2}\,$[^8]. A similar definition without differential applies for the $B \to K^*/ \rho \gamma$ transition. The definition above makes clear the meaning of isospin in this context: it is understood throughout this paper to mean a rotation between $u$ and $d$ quarks, with no corresponding rotation between $b$ and $t$ quarks, as is understood in the case of the electroweak precision parameter $\rho$ for instance.
Assuming that the decay rate is dominated by $C_{7,9,10}$, only taking linear terms into account as in [@Kagan:2001zk; @Feldmann:2002iw], we arrive at: $$\begin{aligned}
\label{eq:dai}
\frac{d A_I^{\bar 0 -}}{dq^2} [B\to K^* l^+l^-] &= \frac{{\displaystyle \sum_{i=\{0,\pm\}}} {\mathrm{Re}}\left[{h}^{V,0}_i(q^2) \Delta^{V,d-u}_i(q^2) \right]}{
{\displaystyle \sum_{i=\{0,\pm\}}} \left[|{h}^{V,0}_i(q^2)|^2 + \left|{h}^A_i(q^2)\right|^2\right]} + {\cal O}([\Delta^{V,d-u}_i(q^2)]^2) \;, \nonumber \\
\frac{d A_I^{\bar 0 -}}{dq^2}[B\to Kl^+l^-] &= \frac{{\mathrm{Re}}\left[{h}^{V,0}_T(q^2) \Delta^{V,d-u}_T(q^2) \right]}{|{h}^{V,0}_T(q^2)|^2 + \left|{h}^A_T(q^2)\right|^2} + {\cal O}([\Delta^{V,d-u}_T(q^2)]^2) \;, \nonumber \\
a_I^{\bar 0 -} [B\to K^* \gamma]&= \frac{{\displaystyle \sum_{i=\pm}} \, {\mathrm{Re}}\left[{h}^{V,0}_i(0) \Delta^{V,d-u}_i(0) \right]}{
{\displaystyle \sum_{i=\pm}} \left[|{h}^{V,0}_i(0)|^2 + \left|{h}^A_i(0)\right|^2\right]} + {\cal O}([\Delta^{V,d-u}_i(0)]^2) \;,\end{aligned}$$ where $ \Delta^{V,d-u}_\iota(q^2) \equiv \left({h}^{V,d}_\iota(q^2) - {h}^{V,u}_\iota(q^2)\right)$. It is worth mentioning that in the above formulae we have explicitly and implicitly neglected effects from phase space differences, isospin corrections to QCD quantities such as decay constants, and the light quark masses $m_q$. The latter are negligibly small and QCD corrections to isospin are known to be small: for example the pseudoscalar decay constant differs by roughly $0.5\%$ between the neutral and charged case; see e.g. [@isoOLD] for a computation in chiral perturbation theory. For the $B$-mesons isospin effects are even smaller as $m_{B^0} -m_{B^\pm} = 0.32(6) {\,{\rm MeV}}$[^9] [@Beringer:1900zz] , which is minuscule in comparison with the heavy quark scale $\bar \Lambda = m_B - m_b \simeq 600 {\,{\rm MeV}}$. Thus in summary it is expected that isospin violation arising from the form factors will not reach the one percent level and we shall therefore not discuss them any further.
Weak annihilation (WA) contribution {#sec:weak-annihilation}
===================================
The WA process $B^-\to W^-\to K^{(*)-}$ is described by the “tree-level” operators $\mathcal O_{1,2}$ in a process as shown in Fig. \[fig:isoSM\](left). By extension, the same name is also given to diagrams with the same arrangement of quark lines involving $\mathcal O_{3-6}$, though they arise from renormalisation running and short distance penguins.
The WA contribution to $B\to K^*\gamma/l^+l^-$ has previously been computed at ${\cal O}(\alpha_s)$ using LCSR at $q^2 = 0$ in [@Ali:1995uy; @Khodjamirian:1995uc] and in QCD factorisation at $q^2 = 0$ [@Bosch:2001gv] and for $q^2 > 0$ [@Beneke:2001at; @Feldmann:2002iw]. We extend the LCSR computation to higher $q^2$ including twist-3 corrections from the $h_\parallel$ DA relevant to the longitudinal $K^*$ component which were neglected in [@Beneke:2001at; @Feldmann:2002iw].
Complete WA-basis of dimension $6$ operators at ${{\cal O}}(\alpha_s^0)$
------------------------------------------------------------------------
We include all four quark operators $\bar q \Gamma_1 b\, \bar s \Gamma_2 q$ which potentially contribute at ${\cal O}(\alpha_s^0)$[^10]: $$\begin{aligned}
O^{{\rm WA}}_1 &\equiv \bar q b \, \bar sq &
O^{{\rm WA}}_2 &\equiv \bar q\gamma_5 b\,\bar sq &
O^{{\rm WA}}_3 &\equiv \bar qb\,\bar s\gamma_5 q &
O^{{\rm WA}}_4 &\equiv \bar q\gamma_5 b\,\bar s\gamma_5 q \nonumber \\
O^{{\rm WA}}_5 &\equiv \bar q\gamma_\mu b\,\bar s\gamma^\mu q &
O^{{\rm WA}}_6 &\equiv \bar q\gamma_\mu\gamma_5 b\,\bar s\gamma^\mu q &
O^{{\rm WA}}_7 &\equiv \bar q\gamma_\mu b\,\bar s\gamma^\mu\gamma_5 q &
O^{{\rm WA}}_8 &\equiv \bar q\gamma_\mu\gamma_5 b\,\bar s\gamma^\mu\gamma_5 q \label{eq:OWA} \\
&& O^{{\rm WA}}_9 &\equiv \bar q\sigma_{\mu\nu} b\,\bar s\sigma^{\mu\nu} q &
O^{{\rm WA}}_{10} &\equiv \bar q\sigma_{\mu\nu}\gamma_5 b\,\bar s\sigma^{\mu\nu} q \;,\nonumber\end{aligned}$$ parametrised by the effective Hamiltonian: $${\cal H}^{{\rm WA,q}} = -\frac{G_F}{\sqrt{2}} \lambda_t \sum^{10}_{i=1} a_i^q O_i^{{\rm WA}} \;,
\label{eq:h-effective-wa}$$ where we suppress the $q$ superscript on the operators $O_i^{\rm WA}$ throughout this work. Note that at ${\cal O}(\alpha_s)$, as well as for the $\rho^0$ for ${\cal O}(\alpha_s^0)$ to be discussed in section \[sec:Heffrho\], the size of the basis doubles as octet combinations of the type $ O_1^{{\rm WA},8} \equiv (1/4) \bar q \lambda^a b \, \bar s \lambda^a q$ contribute as well.
### Projection on SM-basis (WA in SM) {#sec:WASM}
In the SM the operators obey minimal flavour symmetry (MFV) [@MFV1; @MFV2; @MFV3; @MFVmicro1; @MFVmicro2] and may be expressed in the form $\bar q \Gamma P_L b \, \bar s P_R\Gamma q$ . Since WA fixes the quark flavours and couples to only a single colour structure, two independent combinations of SM WCs ($\Gamma \in \{ \mathbf{1},\gamma_\mu \}$) appear in each $B\rightarrow Mll$ process. For a $bq \to sq$ process, with $q = u,d$, the couplings are given by $$\begin{aligned}
\label{eq:aSM}
\text{SM: } \text{scalars: } a^q_1 &= -a^q_2 = a^q_3 = -a^q_4 = -2\left(\frac{{C}_5}{N_c} + {C}_6\right) \nonumber \\
\text{vectors: } a^q_5 &= -a^q_6 = -a^q_7 = a^q_8 = \left(\frac{{C}_3}{N_c} + {C}_4\right) - \delta_{qu}\frac{\lambda_u}{\lambda_t}\left(\frac{{C}_1}{N_c} + {C}_2\right) \nonumber \\
\text{tensors: } a^q_9 &= a^q_{10} = 0 \;,\end{aligned}$$ where $a_{5-8}$ are the only ones which are non-degenerate in $q$ and $N_c=3$ denotes the number of colours. The role of ${{\cal O}}_{1,2}^u$ in the SM is exceptional as there is no $\mathcal O_{1,2}^d$ counterpart. It corresponds to what we called UV isospin violation. In particular radiation from all quarks in Fig. \[fig:isoSM\](left) contributes to the isospin asymmetry. Therefore the isospin asymmetry in the SM is sensitive to three independent combinations of the four quark WCs ${C}_{1-6}$. Note, in the SM the effect is CKM suppressed in $b \to s$ contrary to $b \to d$. In the latter case the closeness of $\alpha_{\rm CKM}$ to ninety degrees leads to a suppression of the effect; to be discussed and exploited in further sections.
-- ----------------------------------------------------- --- --- --- --- ----- --- --------------- --- --------------- ---- ---
Twist
1 2 3 4 5 6 7 8 9 10
cov. ($\alpha_s^0$)
$\chi$-even ($\phi_K$) 2 I,F$_{\rm c}$
$\chi$-odd ($\phi_{P,\sigma}$) 3 I,F
cov. ($\alpha_s^n$, $n >0$)
cov. ($\alpha_s^0$)
$\chi$-even ($\phi_\parallel$) 2 I I,F$_{\rm c}$
$\chi$-even ($g_\perp^{(v)},g_\perp^{(a)} $) 3 I I,F$_{\rm c}$
$\chi$-odd ($\phi_\perp$) 2 F F I I
$\chi$-odd ($h_\parallel^{(t)},h_\parallel^{(s)} $) 3 F I
cov. ($\alpha_s^n$, $n >0$)
-- ----------------------------------------------------- --- --- --- --- ----- --- --------------- --- --------------- ---- ---
: Operators contributing to WA. The acronyms t. and cov. stand for twist and for covariance respectively and $\chi$-odd/even for odd/even chirality. Furthermore: a) (I,F) radiation from inital (I) and or final (F) state; (F$_{\rm c}$) corresponds solely to a (local) contact term contribution from final state radiation. The latter are then necessarily to all orders in the twist expansion. b) () contribution expected in initial and final state c) () no contribution due to parity invariance of strong interactions in the factorisation approximation ${\cal O}(\alpha_s^0)$ d) () no contribution, in any order of $\alpha_s$ and twist, as chirality necessitates a Levi-Civita tensor structure for which there are not enough independent vectors for contraction (relevant for pseudscalar final state). We should also note that $g_\perp^{(v,a)}$ and $h_\parallel^{(s,t)}$ are related to $\phi_\perp$ an $\phi_\parallel$ by Wandzura-Wilczek type relations [@Ball:1998sk]. At our level of approximation, $m_q = 0$ and no 3-particle DA, this corresponds to Eqs.(4.15/16) and (3.21/22)[@Ball:1998sk] respectively. See also appendix \[app:light-DA\] for further comments. This means that when $g_\perp^{(v,a)}$ and $h_\parallel^{(s,t)}$ are computed $\phi_\parallel$ and $\phi_\perp$ are needed to render the computation gauge invariant at the relevant ${\cal O}(m_V)$-level. Thus for (I,F$_{\rm c}$), contrary to (F) itself, it is not possible to properly distinguish between twist $2$ and $3$ which is reflected in the table. []{data-label="tab:OWA"}
WA at leading order ${\cal O}(\alpha_s^0)$ {#sec:wa-factorisation}
------------------------------------------
The WA matrix element with uncontracted photon polarisation tensor $\epsilon(q)_\rho$ reads $$\begin{aligned}
{\cal A}^{*\rho}|_{\text{WA}} &=& \langle X\gamma^*(\rho)| \bar q \Gamma_1 b\,\bar s \Gamma_2 q | B \rangle|_{\text{WA}} \nonumber \\[0.1cm]
&=&
\underbrace{\langle X|\bar s \Gamma_2 q|0\rangle \langle \gamma^*(\rho)|\bar q \Gamma_1 b | B \rangle}_{\text{initial state radiation (ISR)}}
+ \underbrace{\langle X \gamma^*(\rho) |\bar s \Gamma_2 q|0\rangle \langle 0|\bar q \Gamma_1 b | B \rangle}_{\text{final state radiation (FSR)}} +{\cal O}(\alpha_s) \;.
\label{eq:wa-factorisation}\end{aligned}$$ We shall call the first and second term initial (ISR) and final state radiation (FSR) respectively. The computation of these two contributions is performed, as previously stated, using LCSR and further details are deferred to section \[sec:lcsr\]. The computation is valid as long as $q^2$ is away from partonic and hadronic thresholds. This means that the $\rho,\omega$-resonance region has to be treated with care and that the computation is valid say $1$-$2{\,{\rm GeV}}^2$ below the $J/\Psi$-resonance region. For $B \to V \gamma$ (partial) effects of the $\rho,\omega$-mesons are included into the photon DA [@Khodjamirian:1995uc; @Ali:1995uy; @Ball:2002ps]. For $q^2 > 1 \,{\,{\rm GeV}}^2$ the corresponding leading twist effects effects are included in the quark condensate contributions and appear as ${\Braket{\bar q q}}/q^2$ in the results. We refrain from using our computations between $0$ and $1{\,{\rm GeV}}^2$. A salient feature due to the resonance region is the appearance of an imaginary part. In the partonic computation this results from the photon emitted from the light valence quark of the $B$-meson corresponding to the cross in the lower left of Fig.\[fig:wa-diagram-pert\]. In the hadronic picture this corresponds to the emission of $\rho,\omega,..$-mesons and conversion into the photon; the analogous ${{\cal O}}_8$-case can be found in reference [@DLZ12] figure 4(left). In Fig. \[fig:wak8\] we plot the $W(q^2)_T$ matrix element for $a_8$-contribution (with $a_8 = a_8^u = a_8^d$), which illustrates the point made above.
We restrict ourselves to leading twist-2 and twist-3 DAs c.f. appendix \[app:light-DA\]. We neglect 3-particle DAs and quark mass corrections and thus the twist-3 2-particle DAs for the $K^*$ may be written in terms of the twist-2 DAs via the so-called Wandzura-Wilczek relations [@Ball:1998sk]. We include the first two moments in the Gegenbauer expansion and thus have a total of four input parameters to the $K^*$ in addition to the decay constants. The $K$ DAs $\phi_P$ and $\phi_\sigma$ are also related [@Ball:2004ye], but here we use the asymptotic forms for reasons discussed in appendix \[app:DA\].
[0.45]{} ![ Weak annihilation Feynman diagrams for $B\to M l^+l^-$. The zigzag line is the $B$-meson current insertion. Crosses mark possible photon insertions, although the contribution from the insertion at the dashed cross is zero. []{data-label="fig:wa-diagrams"}](perturbative "fig:"){width="\textwidth"}
[0.45]{} ![ Weak annihilation Feynman diagrams for $B\to M l^+l^-$. The zigzag line is the $B$-meson current insertion. Crosses mark possible photon insertions, although the contribution from the insertion at the dashed cross is zero. []{data-label="fig:wa-diagrams"}](qq-condensate "fig:"){width="\textwidth"}
![ WA contribution to $B\to Kll$ for from the $O^{WA}_8$ operator as defined implicitly in . The imaginary part originates from the emission of $\rho,\omega,..$-meson and conversion into the photon, which is analogous to the ${{\cal O}}_8$ contribution c.f. Fig 4(right)[@DLZ12]. []{data-label="fig:wak8"}](wa_k_8.pdf){width="45.00000%"}
In Tab. \[tab:OWA\] the selection rules for the operators are depicted. It is apparent that selection rules are at work. We refer the reader to section \[sec:WAsel\] where the WA selection rules in the factorisation, c.f. Eq. approximation are discussed in some detail.
At this point, we wish to briefly discuss the issue of gauge invariance (GI) in the factorisation approximation . At the level of the amplitude electromagnetic GI, that is invariance under $\epsilon^*(q)_\mu \to \epsilon^*(q)_\mu + q_\mu$, implies: $$\label{eq:WIem}
q_\rho {\cal A}^{*\rho}|_{\text{WA}} = 0 \;.$$ When the mesons are neutral this equation is satisfied for ISR and FSR separately. When the mesons are charged the two terms cancel each other when they are treated at the same level of approximation. From Tab. \[tab:OWA\] we infer that for the $K$ and $K^*$ this is the case for ${\cal O}_{4,8}$ and ${\cal O}_{5,6}$ respectively. For the current-current operators $ {\cal O}_{5-8}$ the final state radiation is, by virtue of the (axial)vector WI, equal to a contact term. This was implicitly used in [@Khodjamirian:1995uc; @Ali:1995uy] and analysed in more clarity and detail in [@Khodjamirian:2001ga]. In the case ${\cal O}_{4}$ for the $K$ there is ISR and FSR and no Ward identity (WI) at hand which complicates the issue. More precisely this necessitates the same approximation scheme be used for both ISR and FSR as discussed and illustrated at length in appendix \[app:wa-gauge-invariance\].
Light cone sum rules {#sec:lcsr}
--------------------
We calculate initial state terms using the technique known as *light cone sum rules* [@Balitsky:1989ry; @Colangelo:2000dp] which originates from QCD sum rules [@Shifman:1978bx; @Shifman:1998rb] and the light-cone operator product expansion (LC-OPE). We extract the matrix elements required in from the correlation function $$\Pi(q^2,p_B^2) = i\int d^4x e^{-ip_B\cdot x} \langle \gamma^*(q) M(p)|T\{J_B(x) \mathcal O(0)\}|0\rangle \;,
\label{eq:wa-matrix-element}$$ where $$J_B = im_b\bar b\gamma_5 q, \qquad \langle\bar B|J_B(0)|0\rangle = m_B^2 f_B \;,$$ is the interpolating current for the $B$-meson. By application of Cauchy’s theorem we can express this matrix element as $$\Pi(q^2,p_B^2) = \frac{m_B^2 f_B}{m_B^2 - p_B^2}\langle \gamma^*(q) M(p)|\mathcal O(0)|B(p_B)\rangle
+ \frac{1}{2\pi i} \oint_{\Gamma_{\mathrm{NP}}} \frac{ds}{s-p_B^2} \Pi(q^2,s) \;,
\label{eq:disp-hadron}$$ where the integration contour $\Gamma_{\mathrm{NP}}$ separates the pole at $p_B^2=m_B^2$ of the desired matrix element $\langle \gamma^*(q) M(p)|\mathcal O(0)|B(p_B)\rangle$ from all other poles and branch cuts. The matrix element in may also be calculated within the LC-OPE, and after applying Cauchy’s theorem to the LC-OPE result we get that, at large spacelike $p_B^2$: $$\Pi(q^2,p_B^2) = \frac{1}{2\pi i} \oint_\Gamma \frac{ds}{s-p_B^2} \Pi^{\rm LC-OPE}(q^2,s) \;,
\label{eq:disp-pert}$$ where the contour $\Gamma$ encloses all poles and branch cuts of this function. The sum rule is obtained by equating the two representations and and making the approximation, known as semi-global quark-hadron duality, $\Pi(q^2,s) = \Pi^{\rm LC-OPE}(q^2,s)$ under the integral in . A Borel transformation is also applied to reduce the sensitivity to the duality threshold, which in this case only requires the relation $$B_{p_B^2\to M^2}\left[\frac{1}{x-p_B^2}\right] = \frac{e^{-x/M^2}}{M^2} \;,$$ yielding the final form of the sum rule $$\label{eq:final_SR}
\begin{split}
\langle \gamma^*(q) M(p)|\mathcal O(0)|B(p_B)\rangle &= \frac{1}{f_B m_B^2}\frac{1}{2\pi i}\int_{\Gamma\backslash\Gamma_{\mathrm{NP}}}ds \exp\left(\frac{m_B^2-s}{M^2}\right) \Pi_P(q^2,s) \\
&\equiv \frac{1}{f_B m_B^2}\int_{\text{cut}}^{s_0} ds \exp\left(\frac{m_B^2-s}{M^2}\right) \rho(q^2,s) \;,
\end{split}$$ where $\Gamma\backslash\Gamma_{\mathrm{NP}}$ is the difference between the integration contours in and . The resulting contour will lie along either side of the real line and thus the final sum rule may be expressed in terms of an integral over the density function $\rho$ on the real line from the lowest perturbative state mass ($m_b^2$ here) to the duality threshold $s_0$. In the full theory the lowest lying multi-particle state coupling to the current $J_B$ occurs at $(m_B+2m_\pi)^2$, and $s_0$ is an effective parameter which is adjusted so that the continuum contribution matches that of QCD. In practice this means that one expects $\sim(m_B+2m_\pi)^2 \simeq 30.9 {\,{\rm GeV}}^2 < s_0 < (m_B+m_\rho)^2 \simeq 36.6 {\,{\rm GeV}}^2 $ with $s_0$ somewhat closer to the upper boundary as the other case is $\alpha_s$ suppressed.
WA results {#sec:WAresults}
----------
Due to our choice of basis for the four quark operators, it is convenient to present our results for the $K^*$ in the following linear combinations, which is basically the helicity basis, $$\begin{aligned}
W^q_V(q^2) &= W^q_1(q^2) = \frac{1}{\sqrt{2}}(W_-(q^2)+W_+(q^2)) \;, \nonumber \\
W^q_A(q^2) &= c W^q_2(q^2) = \frac{1}{\sqrt{2}}(W_-(q^2)-W_+(q^2)) \;, \nonumber \\
W^q_0(q^2) &= a W^q_2(q^2) + b W^q_3(q^2) \;,\end{aligned}$$ where $V$ and $A$ are the PC and PV transverse decay modes, and the constants $a,b,c$ are defined in (\[eq:Btrafo\],\[eq:abc\]). The matrix elements $W_\iota^q(q^2)$, with $\iota \in \{T,V,A,0\}$, are decomposed as follows $$W^q_\iota(q^2) = \sum_{j=1}^{10} a^q_j\left[
F^q_{j,\iota}(q^2) + I^q_{j,\iota}(q^2) \right] \;.$$ The functions $I$ and $F$ stand for ISR and FSR and are further parametrised as $$\begin{aligned}
I^q_{j,\iota}(q^2) =& \frac{1}{f_B m_B^2}\left({\Braket{\bar qq}}\exp\left(\frac{m_B^2-m_b^2}{M^2_{\rm WA}}\right)V^q_{j,\iota}(q^2) + \int_{m_b^2}^{s_0} ds\, \exp\left(\frac{m_B^2-s}{M^2_{\rm WA}}\right)\rho^q_{j,\iota}(q^2,s) \right) \;, \nonumber \\[0.1cm]
F^q_{j,i}(q^2) =& f_{K^*}^\perp f_B \left(\frac{m_B}{m_b}\right)^2\int_0^1 f^q_{j,i}(q^2,u) \; du \;,\end{aligned}$$ for the $K^*$-meson with $i\in\{V,A,0\}$ and $$\begin{aligned}
F^q_{j,T}(q^2) =& \mu_K^2 f_B^{\mathrm{wti}} \left(\frac{m_B}{m_b}\right)^2 \int_0^1 f^{q}_{j,T}(q^2,u) \; du \;,
\label{eq:wa-if-split}\end{aligned}$$ for the $K$-meson. We take the Borel parameter $M^2_{\rm WA}=9(2){\,{\rm GeV}}$ to be the same for all WA processes, although this is not strictly necessary since in principle the results should be independent of it within a reasonable range, and a calculation involving higher twist and/or $\alpha_s$ corrections would usually extremise the result w.r.t. the Borel parameter. We take the duality threshold as $s_0=35(1){\,{\rm GeV}}^2$. The quoted uncertainty in the Borel parameter and the duality threshold are the ranges over which we vary them to provide an estimate of the error of the LCSR method. The use of $f_B^{\mathrm{wti}}$ in $F^q_{j,T}(q^2)$ arises because this is the only case where both physical initial and final state radiation contribute, and thus we must choose $f_B^{\mathrm{wti}}$ as the sum rule approximation of $f_B$ which corresponds to our approximation of the initial state radiation contribution in order to fulfil the Ward identity: $$f_B^{\mathrm{wti}} = \frac{m_b^2}{f_B m_B^4}\left[\frac{3}{8\pi^2}\int_{m_b^2}^{s_0} \exp\left(\frac{m_B^2-s}{M^2_{\rm WA}}\right) \frac{(s-m_b^2)^2}{s} ds - m_b{\Braket{\bar qq}}\exp\left(\frac{m_B^2-m_b^2}{M^2_{\rm WA}}\right)\right] \;.$$ This procedure is discussed further in appendix \[app:wa-gauge-invariance\]. The occurrence of $f_B$ in $I^q_{j,\iota}$ is evaluated using the leading order sum rule including the ${\Braket{\bar qq}}$ and ${\Braket{\bar qGq}}$ condensates [@Aliev:1983ra]
(m\_B\^2 f\_B)\^2 = m\_b\^2 () (\_[m\_b\^2]{}\^[s\_0]{} () ds -m\_b\_- (1 - ) \_) ,
where $M^2_{f_B}=5.0(5){\,{\rm GeV}}$ is used. Quark condensates are taken at $\mu=1{\,{\rm GeV}}$ to be ${\Braket{\bar qq}}=(-0.24(1){\,{\rm GeV}})^3$ and ${\Braket{\bar qGq}}=(0.8(1) {\,{\rm GeV}})^2 {\Braket{\bar qq}}$ which are the same values as in [@DLZ12]. The occurrence of $f_B$ in $F^q_{j,i}$ is taken from lattice data as $f_B=191(5){\,{\rm MeV}}$ [@Bazavov:2011aa; @Na:2012kp]. Formulae for DAs of the external light mesons are given in appendix \[app:light-DA\]. Formulae for all functions appearing on the RHS of are given in appendix \[app:wa-formulae\].
WA at $q^2 = 0$ — photon DA replaces some ${\Braket{\bar qq}}$-contributions {#sec:WAq2eq0}
----------------------------------------------------------------------------
 a fully gauge invariant result.[]{data-label="fig:wa-diagram-lcope"}](wa-lc-ope){width="\textwidth"}
The local OPE for $q^2 \neq 0$, used in diagrams like Fig. \[fig:wa-diagram-lcope\](left) for the light quark propagator originating from the $J_B$-current, results in terms like $Q_q{\Braket{\bar qq}}/q^2$ c.f. which cannot be a good description at $q^2 =0$. The resolution to this apparent paradox is to replace the this term by the photon DA[^11] as sketched in Fig. \[fig:wa-diagram-lcope\].
This type of computation has been completed in [@Khodjamirian:1995uc; @Ali:1995uy] for the vector-current operators ${\cal O}^{{\rm WA}}_{5-8}$. Our calculation, essentially, extends this to the complete four quark operator basis . Aspects of GI and contact terms as well as a difference in the $(Q_b-Q_q) {\Braket{\bar qq}}$ contribution with reference [@Khodjamirian:1995uc] are discussed in appendix \[app:qq-photonDA\]. We note that the latter are small and have not been included in [@Ali:1995uy].
Our results are given, such that $I^q_{j,i}(q^2) \to I^q_{j,i}|_\gamma$ in , $$I^q_{j,i}|_\gamma = \frac{1}{f_B m_B^2}\left({\Braket{\bar qq}}\exp\left(\frac{m_B^2-m_b^2}{M^2_{\rm WA}}\right)V^{q,\gamma}_{j,i} + \int_{m_b^2}^{s_0} ds\, \exp\left(\frac{m_B^2-s}{M^2_{\rm WA}}\right)\rho^{q,\gamma}_{j,i}(s) \right) \;, \\[0.1cm]
\label{eq:wa-if-split-0}$$ where we re-use our result from $q^2\neq 0$ for the density via $$\rho^{q,\gamma}_{j,i}(s) = \rho^{q}_{j,i}(0,s) + {\Braket{\bar qq}} \widetilde{\rho}^{q,\gamma}_{j,i}(s) \;,$$ and $V^{q,\gamma}_{j,i}$ and $\widetilde{\rho}^{q,\gamma}_{j,i}(s)$ are given in appendix \[app:q2eq0\].
Quark loop spectator scattering (QLSS) {#sec:quark-loop-spectator}
======================================
![Hard gluon scattering through a charm loop. Isospin symmetry violating photon insertions are indicated by crosses. The segment in the dashed box is computed first without the DAs attached to simplify the calculation.[]{data-label="fig:quark-loop-spectator"}](charm-loop){width="30.00000%"}
The QLSS topology parallels the ${\cal O}_8$-contribution as can be seen from Fig. \[fig:isoSM\]. We would expect an LCSR computation of this contribution to include some long distance (LD) contributions, in analogy with the ${\cal O}_8$ contribution (intermediate multiparticle states with quantum numbers $(\bar s q)_{J^P = 0^\pm}$ c.f. Fig. 4(left) in [@DLZ12]. On a computational level though spectator scattering differs from the analogous ${\cal O}_8$-computation by the additional nested quark loop which makes the computation rather involved; especially in view of the fact that we further expect a non-trivial analytic structure including anomalous thresholds [@DLZ12]. Thus the evaluation of this contribution with LCSR is beyond the scope of this paper. We therefore resort to QCDF where it would seem that these LD contributions are, at least at leading order in ${\cal O}(\alpha_s)$, absent. In QCDF QLSS has been computed previously for the $B\to K^*l^+l^-$ [@Feldmann:2002iw] and for the $B\to K^*\gamma$ case in [@Kagan:2001zk]. We extend these computations by including a complete basis of four quark operators. Elements of GI are discussed in appendix \[app:QL-GI\].
Complete QLSS-basis of dimension $6$ operators at ${{\cal O}}(\alpha_s)$
------------------------------------------------------------------------
We now turn to the discussion of the relevant operators contributing to QLSS. The vectorial coupling of the gluon in Fig.\[fig:quark-loop-spectator\] imposes efficient selection rules such that only four out of the ten operator types, as listed in Eq. , can contribute: $$\begin{aligned}
{2}
\label{eq:OQLSS}
Q^{4f}_{1 L(R) } \equiv \frac{1}{4}\bar f \lambda^a \gamma_\mu f\,\bar s_{L(R)} \lambda^a \gamma^\mu b \;, \quad
Q^{4f}_{2 L(R) } \equiv \frac{1}{4}\bar f \lambda^a \sigma_{\mu\nu} f\,\bar s_{L(R)} \lambda^a \sigma_{\mu\nu} b \;.\end{aligned}$$ Quark flavours and colour matrices are arranged, differently from Eq. , in a way that is convenient for the QLSS computation. Since we shall set the light quark masses to zero the light flavour $u,d,s$ are effectively degenerate and it proves economic to introduce the $SU(3)_F$ singlet operator $$Q^{4SU(3)_F}_{xL(R)} \equiv (Q^{4u}_{xL(R)}+ Q^{4d}_{xL(R)} + Q^{4s}_{xL(R)}) \;, \quad x = 1,2 \;.$$ Finally, the relevant effective Hamiltionian for QLSS becomes, $${\cal H}^{\rm QLSS} = -\frac{G_F}{\sqrt{2}} \lambda_t \sum_{x,\chi,f} s_{x\chi}^f Q^{4f}_{x\chi} \;, \quad x=1,2\;, \;\; \chi = L,R \;, \;\; f=SU(3)_F,c,b \;,
\label{eq:qlss-hamiltonian}$$ with $s^f_{x\chi}$ being WCs. The somewhat baroque sum over the indices $x,\chi,f$, which amounts to twelve operators at this stage, will prove economic in the end. We would like to stress that this basis in linearly independent, though not orthogonal, to the WA basis . This is the case as in WA the flavour $f$ is, modulo a few exceptions, fixed by the spectator flavour and since in QLSS $f$ is either $c,b$ or the sum of light flavours linear independence follows.
QLSS results {#sec:QLSS}
------------
The computation of QLSS may be broken up into two stages: first, the intermediate process shown in the dashed box of Fig. \[fig:quark-loop-spectator\] is computed, and second, the results of this computation are combined with the remainder of the diagram Fig. \[fig:quark-loop-spectator\].
To start, the intermediate process can be written, by virtue of Lorentz-covariance, as $${\emph a}^\mu = {\Braket{s g(r,\mu)|H_{\rm eff}|b}} = \sum_{i=L,R} \left[K_{1,i}^\mu F_{1,i}(r^2) + K_{2,i}^\mu F_{2,i}(r^2) \right] \;,$$ where $r$ is the gluon momentum and $\mu$ is the gluon polarisation index. The two tensor structures $$\begin{aligned}
K_{1,(L,R)}^\mu &= \frac{r^\mu \slashed r - r^2\gamma^\mu}{r^2} P_{L,R} \;, &
K_{2,(L,R)}^\mu &= \frac{r^\mu - \slashed r\gamma^\mu}{r^2} P_{L,R} \;,\end{aligned}$$ are the only ones allowed by gauge invariance $r \cdot {\emph a} = 0$.
In our parametrisation , the functions $F_{x,\chi}$ are given by $$F_{x,\chi} = s_{x,\chi}^{SU(3)} H_x(s,0) + s_{x,\chi}^{c} H_x(s,m_c) + s_{x,\chi}^{b} H_x(s,b) \;,$$ and it is clear that $F_2 \sim m_f$, where $f$ is the flavour of the quark running in the loop, by virtue of dimensional analysis. This means that $s_{2L(R)}^{SU(3)}$ is heavily suppressed and not present in our approximation where we set the light quark masses to zero and so only ten of the twelve operators in effectively contribute. The functions $H_x$ result from loop integrals for the vector and tensor currents and are given by $$\begin{aligned}
H_1(s,m) &= -\frac{1}{96\pi^2}\left[9h(s,m) + 4\right] \;, \nonumber \\
H_2(s,m) &= -\frac{m}{4\pi^2} B_0(s,m^2,m^2) \;,\end{aligned}$$ where the function $h(s,m_q)$ is the vacuum polarisation (this form from [@Feldmann:2002iw]), with $z\equiv\frac{4m_q^2}{s}$, $$\begin{aligned}
h(s,m_q) &= -\frac{4}{9}\left(\log\frac{m_q^2}{\mu^2} - \frac{2}{3} - z\right) - \frac{4}{9}(2+z)\sqrt{|z-1|}
\begin{cases}
\displaystyle\arctan\frac{1}{\sqrt{z-1}} & z > 1 \\[1em]
\displaystyle\log\frac{1+\sqrt{1-z}}{\sqrt{z}} - \frac{i\pi}{2} & z \leq 1
\end{cases} \nonumber \\
B_0(s,m_q^2,m_q^2) &= 2 - \log\frac{m_q^2}{\mu^2} + 2\frac{\frac{9}{4}h(s,m_q) + \log\frac{m_q^2}{\mu^2} - \frac{2}{3} - z}{2+z} \;,\end{aligned}$$ which can be found in any standard textbook on quantum field theory.
Before quoting the full result let us detail a few points of the computation. The $B$-meson DA used is [@Beneke:2000wa; @Beneke:2000ry] $${\Braket{0|\bar q_\alpha(x) [x,0] b_\beta(0)|B}} = \frac{-i f_B m_B}{4}\int_0^\infty dl_+ e^{-il_+ x_-/2}
\left[\frac{1+\slashed v}{2}\left\{\phi_+(l_+)\slashed n_+ + \phi_-(l_+)\slashed n_-\right\}\gamma_5\right]_{\beta\alpha}
\label{eq:b-meson-da}$$ Definitions of the vectors and various terms involved along with a more complete version of this formula are given in appendix \[app:B-DA\], however this version of the formula contains all terms involved in our computation of the diagram in Fig. \[fig:quark-loop-spectator\].
To this end let us mention that corrections of ${\cal O}(q^2/m_B^2)$ which come from neglecting the $l_-$-direction of the light quark in the $B$-meson DA and aspects of the $B$-meson DA including the transverse derivative are discussed in appendix \[app:O(q2/mB2)\]. Since we have restricted ourselves to $q^2<4m_c^2$, using the $B$-meson light-cone DA seems reasonable. A more interesting question is to what extent the shape of the $q^2$-distribution is accurate or trustworthy.
We write the results directly in the helicity basis, $S_{\pm,0}$, whose transformation to the ${\mathcal{T}}_{1,2,3}$ basis is given in , for the $K^*$-meson: $$\begin{aligned}
\begin{split}
S_-^q(q^2) =& \sqrt{2} Q_q \frac{C_F}{N_c} \frac{16\pi^3\alpha_s f_B m_B}{m_b}
\int_0^1 du\, \left(F_{1,L}(\bar u m_B^2 + uq^2) - \frac{1}{m_B} F_{2,R}(\bar u m_B^2 + uq^2)\right) \\
& \times\left[ \frac{f_{K^*}^\perp\phi_\perp(u)}{\bar u m_B^2 + uq^2}
- \frac{f_{K^*} m_{K^*}}{2\lambda_+(q^2)(m_B^2-q^2)}\left(g_\perp^{(v)}(u) - \frac{g_\perp^{(a)'}(u)}{4}\right)\right] \\
& - \frac{F_{2,R}(\bar u m_B^2 + uq^2)}{m_B}\Bigg[
\frac{f_{K^*}^\perp\phi_\perp(u) u (m_B^2-q^2)}{2(\bar um_B^2 + uq^2)^2} - \frac{f_{K^*} m_{K^*}}{2\lambda_+(q^2)(m_B^2-q^2)}\frac{g^{(a)}_\perp(u)}{4\bar u}
\Bigg] \;,
\label{eq:charm-loop-perp}
\end{split} \\
S_+^q(q^2) =& \; (L \leftrightarrow R) \;, \\
\begin{split}
\label{eq:S0}
d \cdot S^{q,V}_0(q^2) &= - \, Q_q \frac{C_F}{N_c} \frac{32\pi^3\alpha_s f_B m_B}{m_b}
\frac{f_{K^*} m_{K^*}}{\lambda_-(q^2)(m_B^2-q^2)}
\int_0^1 du\,\phi_\parallel(u) \\
& \times \left[F_{1,A}(\bar u m_B^2 + uq^2) + \frac{m_B}{\bar u(m_B^2-q^2)}F_{2,A}(\bar u m_B^2 + uq^2)\right] \;,
\end{split} \end{aligned}$$ with $d \equiv -\frac{\sqrt{2} m_B m_V}{\sqrt{q^2} E}$. For the $K$-meson we get $$\begin{aligned}
\begin{split}
\label{eq:ST}
S^q_T(q^2) =& -Q_q\frac{C_F}{N_c} \frac{(m_B+m_K) 16 \pi^3 \alpha_s f_B f_K}{m_B m_b \lambda_-(q^2)}
\int_0^1 du\,\phi_K(u) \\
& \times \left[F_{1,V}(\bar u m_B^2 + uq^2) - \frac{m_B}{\bar u(m_B^2-q^2)}F_{2,V}(\bar u m_B^2 + uq^2)\right] \;,
\end{split}\end{aligned}$$ where we have used $F_{1,V(A)}(s) \equiv F_{1,R}(s) \pm F_{1,L}(s)$ for the sake of compact notation. At this point we would like to specify some details of the computation. There are two types of terms that appear: $$\begin{aligned}
X_1 &=& \int_0^\infty dl_+ \phi_\pm(l_+) H_1(l_+) \;, \\[0.1cm]
X_2 &=& \int_0^\infty dl_+ \phi_\pm(l_+) \frac{H_2(l_+)}{l_+ - q^2/m_B - i\epsilon} \;,\end{aligned}$$ where the kernels $H(l_+)$ are smooth and the denominator in the second term originates from a propagator which in turn cancels for the type one term. The following recipe is applied: $$\begin{aligned}
X_1 &\to& \left( \int_0^\infty dl_+ \phi_\pm(l_+) \right) H_1(0) = \text{constant} \cdot H_1(0) \;,
\\[0.1cm]
X_2 &\to& \left( \int_0^\infty dl_+ \frac{\phi_\pm(l_+)}{l_+ - q^2/m_B - i\epsilon} \right) H_2(\bar l_+) =
\frac{H_2(\bar l_+)}{\lambda_\pm(q^2)} \;, \end{aligned}$$ where $\bar l_+ \equiv q^2/m_B$, $1/\lambda_\pm(q^2)$ is further detailed in appendix \[app:B-DA\]. The term in proportional to $\phi_\perp(u)$ is of the first type and all others are of the second type as can be seen in Eqs. (\[eq:charm-loop-perp\]-\[eq:ST\]). The equation disagrees with [@Feldmann:2002iw eq. (24)] by a factor of 2 in the $g^{(v,a)}_\perp$ term but agrees with the result in [@Kagan:2001zk] in the limit $q^2 \to 0$. The definitions of the $B$-meson moment functions $\lambda_\pm(q^2)$ and the $K$ and $K^*$ DA functions are given in appendix \[app:light-DA\]. An important remark is that the Wandzura-Wilczek type equations of motions ($m_s=0$) for the $K^*$ have been used.
We note that we have included the $K^*$ DAs $\phi_\parallel$, $\phi_\perp$ and $g^{(v,a)}_\perp$. In light of Tab. \[tab:OWA\] it might seem that we should have also included $h^{(s,t)}_\parallel$, however here we are considering the leading $1/m_B$ term, so it is the $g^{(v,a)}_\perp$ term which requires justification. It is included because the $\phi_\perp$ coefficient does not contain a $1/\lambda_\pm$ factor as it might, and therefore occurs at the same power of $1/m_B$ as $g^{(v,a)}_\perp$. Since the $\phi_\parallel$ term comes with a $1/\lambda_\pm$ factor, an $h^{(s,t)}_\parallel$ term would be ${{\cal O}}(1/m_B)$ suppressed so we neglect it.
It should be noted that there is an endpoint (infrared) divergence proportional to $F_{2,(R,L)}(0)$ in $S_\pm(q^2\to 0)$ arising from the $\bar u\to 0$ integration region which is of the same type as ${\cal O}_8$. There are three ways to deal with it: a) only use it for $q^2 > 0$ in which case an IR sensitivity remains; b) employ the cut-off model [@Kagan:2001zk; @Feldmann:2002iw], or c) perform a local subtraction to render the QCDF result finite and then use the IR finite result from LCSR [@DLZ12] to compensate. We choose option (c). To get an infrared finite result we write $$F_{2,i}(r^2) = \left[ F_{2,i}(0) \right]_{\rm LCSR} + \left[ F_{2,i}(r^2) - F_{2,i}(0) \right]_{\rm QCDF} \;,$$ where the contribution of each term in square brackets to $B\to K^{(*)}ll$ is computed as indicated in the subscript. The LCSR term is therefore a local operator and the ${{\cal O}}_8$ result [@DLZ12] applies, and the QCDF term vanishes for $r^2\rightarrow 0$ restoring IR finiteness of at $q^2=0$. The slightly inconsistent feature is that the LCSR computation contains LD contributions which are not present at this level of approximation in QCDF as explained at the very beginning of this section.
At last we wish to add some remarks about imaginary parts. In the partonic picture the charm quark can go on-shell, whose importance has been emphasised in [@Kim:2008rz], as is visible from the formulae. Fortunately the momentum that enters the charm loop depends on the momentum fraction of the light meson as $\bar u m_B^2 + u q^2$ and is sufficiently smeared out that a partonic description seems tolerable. Conversely the interpretation of such effects in the real hadronic world would be a $D \bar D$-thresholds for which is, compared to a single resonance, sufficiently tame to be described by partons within our quoted uncertainties.
Projection on SM-basis (QLSS in the SM) {#sec:QLSSinSM}
---------------------------------------
In the SM using naïve dimensional regularisation we have [@Feldmann:2002iw] $$\begin{aligned}
\text{SM:} \quad F_{1,L}(s) &=& \frac{3}{32\pi^2}\Bigg[h(s,m_c)\left(-\frac{\lambda_c}{\lambda_t}{C}_2 + {C}_4 + {C}_6\right) + h(s,m_b)({C}_3 + {C}_4 + {C}_6) \nonumber \;, \\
&+& h(s,0)\left(-\frac{\lambda_u}{\lambda_t}{C}_2 + {C}_3 + 3{C}_4 + 3{C}_6\right) - \frac{8}{27}({C}_3 - {C}_5 - 15{C}_6)\Bigg] \;, \nonumber \\
F_{1,R}(s) &=& 0 \;, \\
F_{2,R}(s) &=& \frac{m_b}{8\pi^2}(C_8^{\rm eff} - C_8) \;, \nonumber
\\
F_{2,L}(s) &=& \frac{m_s}{8\pi^2}(C_8^{\rm eff} - C_8) \to 0 + {\cal O}(m_s) \;.\end{aligned}$$ The MFV-symmetry of the SM implies that $F_{1,R} =0$. The operators $Q^{4f}_{2\chi}$ are not present in the SM in $d=4$ but give contributions in the spirit of evanescent operators in naive dimensional regularisation. They render the effective WC $C_8^{\rm eff}$ scheme independent [@Misiak:1991dj; @Ciuchini:1993ks]. It is worth pointing out that in the SM the charm loop dominates as it originates from ${{\cal O}}_2^c$ which is proportional to a large WC $C_2\approx 1$ and is not CKM suppressed. All other WCs are small as can be seen in Tab. \[tbl:wilson-coefficient-example\].
Isospin asymmetries $B \to K^{(*)} \gamma/ ll$ {#sec:iso}
==============================================
We shall first make a few generic remarks on selection rules and related issues in subsection \[sec:selection\], reflect on the $q^2$-behaviour from various viewpoints in subsection \[sec:q2-dependence\] and then discuss the isospin asymmetries of $B \to K^{(*)}$ in the SM in section \[sec:isospinSM\]. Discussion of isospin asymmetry beyond the SM is deferred to section \[sec:isospinBSM\].
Generic remarks on selection rules {#sec:selection}
----------------------------------
In total there are $32$ operators potentially contributing to the isospin asymmetry at the level of ${\cal O}(\alpha_s)$-correction we are considering. Schematically they decompose as follows: $$\label{eq:32}
32 = 2_{{\cal O}_8^{(')} \eqref{eq:SMbasis}} + 20_{WA \eqref{eq:OWA}} + 10_{\rm QLSS \eqref{eq:OQLSS}}\;,$$ where the prime denotes [$V$+$A$]{} chirality as previously defined. We note that ${\cal O}^{SU(3)}_{2L(R)}$ gives no contribution in the limit of all light quark masses set to zero since it is proportional to $m_f$ as pointed out in section \[sec:QLSS\]. The number $32$ will be reduced further for the $K$ and $K^*$ below.
We shall discuss below general selection rules for the $K$ in subsection \[sec:Ksel\] before discussing more specific selection rules for WA in the factorisation approximation in subsection \[sec:WAsel\] and then comment on the (non)-relation between the $K$ and $K^*_\parallel$-amplitude in subsection \[sec:non-relation\].
### Parity & angular momentum selection rule for $K$ {#sec:Ksel}
For the $K$ there is a parity selection rule. We note that $$B[0^-] \to K[0^-] (\gamma^*[1^-] \to l^+l^-[1^-]) \quad \Rightarrow \quad \text{ p-wave; i.e.} \;\;
l =1 \;, \quad$$ where $[J^P]$ denotes total angular momentum and parity respectively and $l$ is the spatial angular momentum of the decay product. Thus the (left hand side) LHS and (right hand side) RHS of the decay have odd parity and the decay is therefore induced by parity conserving (PC) operators. This means that operators of the type $\bar s\dotsm\gamma_5 q\,\bar q \dotsm b$, $\bar s\dotsm q\bar q \dotsm \gamma_5 b$, where $\dotsm$ stand for strings of $\gamma$-matrices not including $\gamma_5$, do not contribute. This reduces the number of operators for the $K$ (by a factor of two) down to $1_{{\cal O}_8}$ and $5_{\rm QLSS}$ using the notation of Eq. . It seems worthwhile to emphasize that the selection rules are generic. In the next subsection we are going to discuss WA in the factorisation approximation for which there are additional selection rules.
### WA selection rules in the factorisation approximation {#sec:WAsel}
In the factorisation approximation, automatic at ${\cal O}(\alpha_s^0)$ we are considering for WA, there are more stringent selection rules. They come from the fact that the Dirac traces of the $B$-meson and the $K^*$-meson close separately, and so $\gamma_5$-matrices cannot be commuted from one end to the other. Selection rules arising due this effect derive from the matrix element which does not emit the photon, i.e. the initial state in a FSR diagram and vice-versa. We call the matrix element imposing the selection rule the local matrix element (LME) since it is the matrix element of an external state coupling to a local operator.
The $O^{\rm WA}_{9,10}$ operators must be considered separately: in the case of the $K$ they do not contribute in the factorisation approximation since the LME will be a pseudoscalar coupling to an antisymmetric tensor operator and no such tensor can be formed from a single vector. On the other hand in the case of the $K^*$ both operators contribute since an antisymmetric tensor $p^{[\mu}\eta^{\nu]}$ is available and by $\epsilon^{\mu\nu\rho\sigma}\sigma_{\rho\sigma}=2i\sigma^{\mu\nu}\gamma_5$ the two different parities are trivially related. For $O^{\rm WA}_{1\dots8}$, the LME will impose a selection rule since the external state will only couple to a local scalar or vector operator of the correct parity. This reduces the number of applicable operators by a factor of $2$. If this is further combined with the global parity constraint for the $K$ case so for $B\to Kll$ only 2 of the 8 operators remain.
Combining these rules we expect $8/2 + 2 = 6$ and $8/2/2+0 = 2$ operators to contribute to WA in the factorisation approximation for the $K^*$ and the $K$-respectively. This is indeed the case as the reader may verify from Tab. \[tab:OWA\] or Tab. \[tab:breakdown\]. With respect to the latter table note that we have not taken into account the degeneracy in $q = u,d$ in the previous wording and this is why the numbers are $12$ and $4$ rather than $6$ and $2$.
----------------- ------------- --------- ---------------------- --------- -------------------- ---------
$C^{(')}_8$ WA Eq. QLSS Eq. total
\[0.1cm\] $K^*$ 2\[1\] 12\[3\] $a^q_{2,4,5,6,9,10}$ 10\[3\] all no i=2,f=SU(3) 24\[7\]
$K$ 1\[1\] 4\[3\] $a^q_{4,8}$ 5\[3\] idem no $\chi=A$ 10\[7\]
----------------- ------------- --------- ---------------------- --------- -------------------- ---------
: Operators contributing to isospin in $B \to K^{(*)} ll$. In square brackets we denote the number of operators that are present in the SM for the respective channel. In this counting we neglect $C_8'$ as $C_8'/C_8 \simeq m_s/m_b$. []{data-label="tab:breakdown"}
### On the (non)-relation between $K^*_{\parallel}$ and $K$ {#sec:non-relation}
There is some conventional wisdom, throughout the literature, that the longitudinal polarisation of the $K^*$ corresponds to that of the $K$. We shall argue that this is true in the SM at leading twist and falls apart thereafter.
The main points follow from the fact the the longitudinal polarisation can be decomposed as follows: $$\label{eq:eta0_dec}
\eta(0)^\mu \equiv \eta^\mu_\parallel =
\frac{p^\mu}{m_{K^*}} + (q^\mu {{\cal O}}(m_{K^*}) + p^{\mu} {{\cal O}}(m_{K^*})) \;.$$ Thus at leading twist, $m_{K^*}^2 =0$, we see that $\eta^\mu_\parallel$ and $p^\mu$ play the same rôle. Since the former is a pseudo-vector and the latter is a vector we also see that they couple to opposite parity: $K$ only couples to PC operators, as pointed out in subsection \[sec:Ksel\], and $K^*_\parallel$ only couples to PV operators. Due to the [$V$-$A$]{}-interactions in the SM there is a link between the corresponding WCs and this makes it clear that the statement at the beginning of this subsection is true.
On the other hand it is then also clear that the presence of right-handed currents, i.e. [$V$+$A$]{}-interactions, invalidates the statement. Furthermore the $ {{\cal O}}(m_{K^*})$-corrections, by virtue of , are going to bring in new structures as well and we can therefore not expect the correspondence to hold at twist $4$. Examples:
- *Isospin asymmetry plots $K$ versus $K^*_{\parallel}$ (Fig. \[fig:1\]):* We notice that the $K$ and $K^*_{\parallel}$ are correlated since the SM, due to the $V$-$A$-interactions, satisfy the conditions discussed above. The differences, which is essentially a shift of the shape, are due to sizeable next-leading twist effects.
- *Working example at leading twist:* From the formulae in appendix \[app:wa-formulae\] one infers that the parity related $O^{\rm WA}_6$ and $O^{\rm WA}_8$ contributions are (indeed) proportional to each other ($a_6(K^*_\parallel) \sim a_8(K)$).
- *Non-working example at non-leading twist:* From Tab. \[tab:OWA\] we infer that $O_4^{\rm WA}$ couples to ISR for the $K$ but the corresponding PV operator $O_2^{\rm WA}$ does not for the $K^*$.
The latter point deserves some further explanation. Should there be an extension of the correspondence from $\phi_{p,\sigma}$ to $K^*$-amplitudes then it would be through the same chirality DA and necessarily involve the chiral-odd DA $\phi_\perp$ and $h_\parallel^{(s,t)}$ in Tab.\[tab:OWA\]. That this cannot hold can also be seen as follows: the chiral-odd $K^*$ 2-particle DAs included in our calculation have independent coefficients to the chiral-even ones. In the case of the $K$ this is not so: the chiral-odd DAs are fully constrained by equations of motion and arise from finite quark masses, 3-particle and higher twist DAs and chiral symmetry breaking, the last of which is the only effect we include.
### Implications of selection rules on twist-expansion hierarchy {#sec:comment}
In practice selection rules such as the ones depicted in Tab. \[tab:OWA\] enforce a rethinking of the matters of the twist expansion. More precisely we mean that if a large WC does not contribute at leading twist but say only at next leading twist then it does not seem wise to truncate at leading twist. Thus in practice this implies that one should expand to the twist order such that all sizeable WC, allowed by the fundamental selection rules such as the ones quoted in section \[sec:Ksel\], contribute to the amplitude.
The $K$ shall serve as an explicit example. For the latter we see that at leading and next leading twist $a_8^q$ and $a_4^q$ contribute which correspond to $(C_3/N_c+ C_4)$ and $(C_5/N_c+ C_6)$ in the SM . From the size of the WC \[tbl:wilson-coefficient-example\], we infer that the latter could be of importance especially in view of the fact that the next leading twist DA $\phi_{p,\sigma}$ is known to be chirally enhanced which can be inferred from its normalisation . The reader is referred to Figs. \[fig:1\],\[fig:2\] to convince him or herself of this fact.
Generic remarks on $q^2$-dependence {#sec:q2-dependence}
-----------------------------------
Below we add a few generic remarks on the $q^2$-dependence ranging from the validity the LCSR up to pointing out the dominant contributions. The latter are particularly useful for understanding the isospin asymmetries within and beyond the SM.
- *Physical spectrum and approximation ranges:* the physical spectrum of the decays ranges from $4m_l^2 < q^2 < (m_B-m_K^{(*)})^2 = 22.9(19.3){\,{\rm GeV}}^2$. In this work we compute the isospin asymmetries at low $q^2$ (large recoil) where the LCSR (WA and ${\cal O}_8$) and QCDF (QLSS) results are naturally trustworthy. We restrict ourselves to the interval of $[1,8]\, {\,{\rm GeV}}^2$ whose boundary is limited by the nearby $\omega,\rho,\rho'$ resonances from below and the charmonium resonances, commencing at $q^2 = m_{J/\Psi}^2 \simeq (3.1GeV)^2 \simeq 9.6 {\,{\rm GeV}}^2$, from above. While it is plausible to assess effects of the latter close to these regions we consider it too difficult to asses them locally and thus refrain from doing so.
- *Isospin asymmetry in $B\rightarrow K^*ll$ decreases for high $q^2$*: to understand the possible size of isospin asymmetry for a given WC as a function of $q^2$ it is helpful to look at the WCs $C_{9,10}$ and note that:
- They are large as compared to the other WC (c.f.Tab.\[tbl:wilson-coefficient-example\]), partially as a result of a $1/\sin \theta_W^2 \simeq 4$ enhancement, where $\theta_W$ is the Glashow-Weinberg angle.
- We may write the leading terms in the $B\rightarrow Mll$ decay rate as: $$\begin{aligned}
\label{eq:hasq2}
h_T &\sim& \phantom{\sqrt{q^2}} [ C_{9,10}^{\rm eff} {\cal O}(1) + C_7^{\rm eff} {\cal O}(1)] \;, \nonumber \\[0.1cm]
h_0 &\sim&\sqrt{q^2}[ C_{9,10}^{\rm eff} {\cal O}(1) + C_7^{\rm eff} {\cal O}(1)] \;,\nonumber \\[0.1cm]
h_\pm &\sim& \phantom{\sqrt{q^2}} [ C_{9,10}^{\rm eff} {\cal O}(q^2/m_B^2) + C_7^{\rm eff} {\cal O}(1)] \;,\end{aligned}$$ This behaviour can be inferred from Eqs. (\[eq:Btrafo\],\[eq:lepton-vector-sym-ff\],\[eq:lepton-axial-ff\]). Another way to look at it is to realise that ${C}_{9,10}$ should never be sensitive to $1/q^2$ in front of the rate as they are *not* generated by an intermediate photon but through intermediate $Z$-bosons and box diagrams.
We therefore see that at low $q^2$ in $B\rightarrow K^*ll$ isospin violating terms only compete against $C_7^{\rm eff}$, but at high $q^2$ they must compete with the much larger $C_{9,10}$ and hence the asymmetry decreases for large $q^2$. In $B\rightarrow Kll$ no such argument applies as in $h_T$ $C_7^{\rm eff}$ and $C_{9,10}$ are on equal footing.
- *High $q^2 \leq (m_B-m_K^{(*)})^2$ region:* In this paper we have not assessed the isospin asymmetry at high $q^2$, that is low recoil, per se. We shall discuss it from two viewpoints which fortunately lead to the same conclusion, namely that the isospin violating effects get smaller for large $q^2$; that is to say the short-distance form factor contribution with small isospin effects are dominant.
- *Form factor* contributions (FFCs) in the high-$q^2$ region. In that region the $C_{7,9,10}$-FFC are expected to be enhanced by the presence of the nearby resonance at $q^2 = m_{B_s^*}^2$, which can for be seen from the plots and form factor parametrisations in [@Ball:2004rg] whereas no such enhancement is present in the isospin violating (IVQE) terms[^12]. Let us add that IVQE terms, arising from intermediate off-shell photons, will be enhanced by light resonances at $q^2 = m_\rho^2, m_\omega^2,\dots$, as can be seen for example in Fig. \[fig:wak8\], and also by a heavy resonance $\Upsilon(\bar bb)$. Thus in summary the isospin asymmetry is expected to be suppressed both by small WCs and competing with a resonant isospin-symmetric term, and thus should be very small at high $q^2$.
- *Low recoil-OPE:* Some time ago an OPE in $q^2$ and $m_b^2$ was proposed [@Grinstein:2004vb] for the low recoil region, which was implemented into phenomenology [@Bobeth:2010wg] and reinvestigated from a theoretical viewpoint in [@Beylich:2011aq]. In this language the FFC come as dimension three matrix elements and IVQE originate from higher dimensional operators (dimension 6 for WA and dimension 5 for QLSS and ${{\cal O}}_8$) and are therefore naturally small.
Isospin asymmetries $B \to K^{(*)} \gamma/ ll$ in the SM {#sec:isospinSM}
--------------------------------------------------------
The plots of the $B \to K^{(*)}ll$ isospin asymmetries are given in Fig. \[fig:1\], including a plot of the longitudinal part (zero helicity) of the $K^*$ DA (c.f. section \[sec:non-relation\] for comments), and the values are tabulated in Tab. \[tab:1\] (appendix \[app:tables\]). Important aspects on which operators or WC contribute were discussed in the previous subsection. The feature that is obvious is that the isospin asymmetry is small on the scale of $-100\%$ to $100\%$ for $B \to K^{(*)}ll$ for $q^2 > 1 {\,{\rm GeV}}^2$; specifically below the $2\%$ level. Qualitatively they agree with previous determination e.g. $B \to K^*ll$ [@Feldmann:2002iw] and $B \to K ll$ [@Khodjamirian:2012rm][^13]. A few qualitative remarks on the size of the contributions can be found in the caption. Generically the asymmetries are dominated by WA which can also be inferred indirectly from Fig. \[fig:2\] in the next subsection. Let us quote here the world average of the $B \to K^* \gamma$ isospin asymmetry from the Heavy Flavour Averaging Group (HFAG) [@Amhis:2012bh] $$\label{eq:HFAG}
\bar a_I(K^* \gamma)_{\rm HFAG} = 5.2(2.6)\% \;, \qquad \bar a_I(K^* \gamma)_{\rm LZ} = 4.9(2.6)\% \;.$$ which compared with our value turns out to be really close. Our value is also close to values previously found by [@Kagan:2001zk; @Feldmann:2002iw; @Ball:2006eu]. The calculation of the theoretical uncertainty is detailed in appendix \[app:uncertainty\]. To what extent this constrains the dimension six operators and therefore $B \to K^{(*)}ll$ is discussed in section \[sec:constraints\].
Let us briefly discuss the three contributions in Fig. \[fig:isoSM\] considered in this paper.
- *WA:* The SM contributions $[a_i^q]^{SM}$ are given in term of the $C_i$ in Eq. . For WA one has to distinguish between $\bar q b \bar s q $ operators (omitting the Lorentz indices) as generated from tree and penguin processes. When originating from penguin processes ${\cal O}_{3-6}$, an equal amount of $q = u,d$ is generated and the process is dominated by the top quark penguin which results in $\lambda_t \sim \lambda^2$ CKM prefactor. The $q = u$ case also has a tree contribution ${{\cal O}}^u_{1,2}$ which is then proportional to $\lambda_u \sim \lambda^4$. Thus a priori it seems difficult to judge whether the loop suppression or the CKM-suppression is more effective[^14]. Inspecting Fig. \[fig:1\] and taking into account that WA is the leading effect we see that the answer depends on $q^2$ and the Dirac structure: ${C}_6$ dominates the isospin asymmetry for $B\to K^*ll$ but for $B\to Kll$ the ${C}_{2,4}$ contributions are of similar magnitude to $C_6$.
- *QLSS:* QLSS is dominated by the charm loop as the latter originates from the tree operators ${\cal O}^c_{1,2}$. Whereas this contribution is not CKM suppressed $\lambda_c \sim \lambda^2$ it is of course loop suppressed.
- *${\cal O}_8$:* The chromomagnetic ${\cal O}_8$-contribution has been discussed in a separate paper [@DLZ12]. For the $B \to K^{(*)}$-transition the matrix element is found it to be rather small; as compared to the QCD penguin form factors $T_1(0)$. The total and isospin violating parts were found to be in the $6\%$ and $2\%$-range, as compared to $T_1(0)$, respectively. An interesting aspect is the large strong phase attributed to LD contributions. The phase is of importance for CP-violation in new physics searches in $D \to V\gamma$ [@LZ12], but not for CP-averaged isospin as the latter is only sensitive to the real part of strong phases; at least in the linear approximation c.f. . Furthermore we should point out that we neglect the ${{\cal O}}_8'$ contribution in the SM, as $C_8'/C_8 \simeq m_s/m_b$ by virtue of the MFV-symmetry.
Some of the points discussed above and in the previous subsection are summarised in Tab. \[tab:Ooverview\].
$b \to s(d)$ WA QLSS ${{\cal O}}_8$
------------------- ------------- --------------------------------------- ---------------- --------------------------------------- ------ ----------------------------------------- ------
${{\cal O}}_X$ WC CKM M.E. CKM M.E. CKM M.E.
${\cal O}_{1,2}$ tree $\lambda_u \sim \lambda^4(\lambda^3)$ tree $\lambda_c \sim \lambda^2(\lambda^3)$ loop - -
${\cal O}_{3-6}$ penguin $\lambda_t \sim \lambda^2(\lambda^3)$ tree $\lambda_t \sim \lambda^2(\lambda^3)$ loop - -
${\cal O}_8$ penguin - - - - $\lambda_t \sim$ $\lambda^2(\lambda^3)$ loop
${\cal O}_7$ penguin
${\cal O}_{9,10}$ penguin/box
: SM operators contributing to the isospin asymmetry ${{\cal O}}_{1-6,8}$ and operators not contributing to the asymmetry ${{\cal O}}_{7,9,10}$. This table summarises the discussion in section \[sec:isospinSM\]. *WC* denotes whether the operator is generated by a tree or penguin process. *CKM* denotes the CKM-suppression and $\lambda \simeq 0.22$ stands for the Wolfenstein parameter. In anticipation of $B \to \rho ll$ we have indicated the CKM hierarchy for $b \to d$ in parenthesis. *M.E.* denotes whether the matrix element is a tree or loop level process.[]{data-label="tab:Ooverview"}
![(left(right),first row) Isospin asymmetry for $B \to K^{(*)} ll$ with green error bands. (left(right),second row) Isospin asymmetry for $B \to K^{*}_{\parallel} ll$ for the longitudinal ($0$-helicity $L$ and $\parallel$ mean the same in this context!) part of $K^*$-meson denoted by subscript $L$ as well as the three previous graphs shown on one plot. Comments are deferred to the text. (left(right),third and fourth row) Contribution of different SM operators to the isospin asymmetry in $B \to K^{(*)} ll$. The bottom ones are the sizeable contributions. The dominance of $[{C}_6 +({C}_5/3)]$ has been found previously. Its decrease is due to the relevant operators $O^{\rm WA}_{1-4}$ entering at subleading twist in the longitudinal part which is dominant at high $q^2$. See appendix \[app:uncertainty\] for details of the calculation of the green error bands. []{data-label="fig:1"}](isospin_lcsr_kstar_total "fig:"){width="40.00000%"} ![(left(right),first row) Isospin asymmetry for $B \to K^{(*)} ll$ with green error bands. (left(right),second row) Isospin asymmetry for $B \to K^{*}_{\parallel} ll$ for the longitudinal ($0$-helicity $L$ and $\parallel$ mean the same in this context!) part of $K^*$-meson denoted by subscript $L$ as well as the three previous graphs shown on one plot. Comments are deferred to the text. (left(right),third and fourth row) Contribution of different SM operators to the isospin asymmetry in $B \to K^{(*)} ll$. The bottom ones are the sizeable contributions. The dominance of $[{C}_6 +({C}_5/3)]$ has been found previously. Its decrease is due to the relevant operators $O^{\rm WA}_{1-4}$ entering at subleading twist in the longitudinal part which is dominant at high $q^2$. See appendix \[app:uncertainty\] for details of the calculation of the green error bands. []{data-label="fig:1"}](isospin_lcsr_k_total "fig:"){width="40.00000%"} ![(left(right),first row) Isospin asymmetry for $B \to K^{(*)} ll$ with green error bands. (left(right),second row) Isospin asymmetry for $B \to K^{*}_{\parallel} ll$ for the longitudinal ($0$-helicity $L$ and $\parallel$ mean the same in this context!) part of $K^*$-meson denoted by subscript $L$ as well as the three previous graphs shown on one plot. Comments are deferred to the text. (left(right),third and fourth row) Contribution of different SM operators to the isospin asymmetry in $B \to K^{(*)} ll$. The bottom ones are the sizeable contributions. The dominance of $[{C}_6 +({C}_5/3)]$ has been found previously. Its decrease is due to the relevant operators $O^{\rm WA}_{1-4}$ entering at subleading twist in the longitudinal part which is dominant at high $q^2$. See appendix \[app:uncertainty\] for details of the calculation of the green error bands. []{data-label="fig:1"}](isospin_lcsr_kstar0_total "fig:"){width="40.00000%"} ![(left(right),first row) Isospin asymmetry for $B \to K^{(*)} ll$ with green error bands. (left(right),second row) Isospin asymmetry for $B \to K^{*}_{\parallel} ll$ for the longitudinal ($0$-helicity $L$ and $\parallel$ mean the same in this context!) part of $K^*$-meson denoted by subscript $L$ as well as the three previous graphs shown on one plot. Comments are deferred to the text. (left(right),third and fourth row) Contribution of different SM operators to the isospin asymmetry in $B \to K^{(*)} ll$. The bottom ones are the sizeable contributions. The dominance of $[{C}_6 +({C}_5/3)]$ has been found previously. Its decrease is due to the relevant operators $O^{\rm WA}_{1-4}$ entering at subleading twist in the longitudinal part which is dominant at high $q^2$. See appendix \[app:uncertainty\] for details of the calculation of the green error bands. []{data-label="fig:1"}](isospin_lcsr_combined "fig:"){width="40.00000%"} ![(left(right),first row) Isospin asymmetry for $B \to K^{(*)} ll$ with green error bands. (left(right),second row) Isospin asymmetry for $B \to K^{*}_{\parallel} ll$ for the longitudinal ($0$-helicity $L$ and $\parallel$ mean the same in this context!) part of $K^*$-meson denoted by subscript $L$ as well as the three previous graphs shown on one plot. Comments are deferred to the text. (left(right),third and fourth row) Contribution of different SM operators to the isospin asymmetry in $B \to K^{(*)} ll$. The bottom ones are the sizeable contributions. The dominance of $[{C}_6 +({C}_5/3)]$ has been found previously. Its decrease is due to the relevant operators $O^{\rm WA}_{1-4}$ entering at subleading twist in the longitudinal part which is dominant at high $q^2$. See appendix \[app:uncertainty\] for details of the calculation of the green error bands. []{data-label="fig:1"}](isospin_lcsr_kstar_smsplit "fig:"){width="35.00000%"} ![(left(right),first row) Isospin asymmetry for $B \to K^{(*)} ll$ with green error bands. (left(right),second row) Isospin asymmetry for $B \to K^{*}_{\parallel} ll$ for the longitudinal ($0$-helicity $L$ and $\parallel$ mean the same in this context!) part of $K^*$-meson denoted by subscript $L$ as well as the three previous graphs shown on one plot. Comments are deferred to the text. (left(right),third and fourth row) Contribution of different SM operators to the isospin asymmetry in $B \to K^{(*)} ll$. The bottom ones are the sizeable contributions. The dominance of $[{C}_6 +({C}_5/3)]$ has been found previously. Its decrease is due to the relevant operators $O^{\rm WA}_{1-4}$ entering at subleading twist in the longitudinal part which is dominant at high $q^2$. See appendix \[app:uncertainty\] for details of the calculation of the green error bands. []{data-label="fig:1"}](isospin_lcsr_k_smsplit "fig:"){width="35.00000%"} ![(left(right),first row) Isospin asymmetry for $B \to K^{(*)} ll$ with green error bands. (left(right),second row) Isospin asymmetry for $B \to K^{*}_{\parallel} ll$ for the longitudinal ($0$-helicity $L$ and $\parallel$ mean the same in this context!) part of $K^*$-meson denoted by subscript $L$ as well as the three previous graphs shown on one plot. Comments are deferred to the text. (left(right),third and fourth row) Contribution of different SM operators to the isospin asymmetry in $B \to K^{(*)} ll$. The bottom ones are the sizeable contributions. The dominance of $[{C}_6 +({C}_5/3)]$ has been found previously. Its decrease is due to the relevant operators $O^{\rm WA}_{1-4}$ entering at subleading twist in the longitudinal part which is dominant at high $q^2$. See appendix \[app:uncertainty\] for details of the calculation of the green error bands. []{data-label="fig:1"}](isospin_lcsr_kstar_smsplit2 "fig:"){width="35.00000%"} ![(left(right),first row) Isospin asymmetry for $B \to K^{(*)} ll$ with green error bands. (left(right),second row) Isospin asymmetry for $B \to K^{*}_{\parallel} ll$ for the longitudinal ($0$-helicity $L$ and $\parallel$ mean the same in this context!) part of $K^*$-meson denoted by subscript $L$ as well as the three previous graphs shown on one plot. Comments are deferred to the text. (left(right),third and fourth row) Contribution of different SM operators to the isospin asymmetry in $B \to K^{(*)} ll$. The bottom ones are the sizeable contributions. The dominance of $[{C}_6 +({C}_5/3)]$ has been found previously. Its decrease is due to the relevant operators $O^{\rm WA}_{1-4}$ entering at subleading twist in the longitudinal part which is dominant at high $q^2$. See appendix \[app:uncertainty\] for details of the calculation of the green error bands. []{data-label="fig:1"}](isospin_lcsr_k_smsplit2 "fig:"){width="35.00000%"}
Isospin asymmetries in $B\to \rho \gamma/ll$ {#sec:rho-meson}
============================================
$B\to \rho$ ($ b \to d$) decays[^15] differ from $B\rightarrow K^*$ ($ b \to s$) decays in two important respects: 1) WCs of the operators $\mathcal O_{1,2}$ are not CKM suppressed (c.f. Tab. \[tab:Ooverview\]) and 2) $B^0\to \rho^0$, by virtue of $\rho^0 \sim (\bar u u - \bar d d)$, contains additional diagrams with different arrangements of the four quark operators, and as a consequence also couples to colour octet operators (octet w.r.t. the basis ). We shall see shortly that the first point is effectively irrelevant as the relevant CKM angle $\alpha_{\rm CKM}=89(4)^\circ$ [@Beringer:1900zz] chooses to be close to Pythagorian perfection.
More precisely the $\mathcal O_{1,2}$-contribution in the SM comes with CKM-prefactor $$\label{eq:alpha}
\frac{\lambda^{bd}_u}{\lambda^{bd}_t} = -\left|\frac{\lambda^{bd}_u}{\lambda^{bd}_t}\right|e^{-i\alpha_{\rm CKM}} \;,$$ where $\lambda^{bd}_i \equiv V_{id}^*V_{ib}$, in close analogy to $\lambda \equiv \lambda^{bs}_i \equiv V_{id}^*V_{ib}$ used previously. Since the CP-averaged isospin asymmetry is sensitive to the real part, giving $\cos\alpha_{\rm CKM}=0.02(7)$, the relatively large magnitude of $\lambda^{bd}_u/\lambda^{bd}_t$ is overruled and thus the overall contribution from $\mathcal O_{1,2}$ is very small. Essentially there is then no interference of the $\mathcal O_{1,2}|_{\rm WA}$ with the leading contributions. This is why the non-CP averaged isospin asymmetry leads to rather different results (already in the SM c.f. section \[sec:CP-averaging\]).
Extending the effective Hamiltonian for $B^0\to\rho^0\gamma/ll$ {#sec:Heffrho}
---------------------------------------------------------------
For the $B^0\to\rho^0\gamma/ll$ decay ($\rho^0 \sim \bar u u - \bar d d$), the basis has to be extended to include $$O^{{\rm WA}}_i = \bar q\Gamma_1b \, \bar d\Gamma_2 q
\implies O^{{\rm WA,8}}_i = \frac{1}{4} \bar q \lambda^a\Gamma_1b \, \bar d \lambda^a\Gamma_2 q\;,
\label{eq:OWA8}$$ so that for example $O^{{\rm WA,8}}_1=\frac{1}{4}\bar q\lambda^ab\,\bar d\lambda^a q$, and we modify the effective Hamiltonian to: $${\cal H}^{{\rm WA},q} = -\frac{G_F}{\sqrt 2}\lambda_t\sum_{i=i}^{10}\left[a^q_i O_i^{\rm WA} + a^{8q}_i O_i^{\rm WA,8}\right] \;.
\label{eq:h-effective-wa-8}$$ In spite of all these operators being present, the basic situation presented in Tab. \[tab:OWA\] has not changed: our calculation only picks up 6 linearly independent combinations of WCs in the $B^0\to\rho^0\gamma/ll$ case. We therefore choose to present the isospin asymmetry for the $\rho$-meson in the following schematic way: $$\label{eq:atildeandrho0}
\rho^\pm \leftrightarrow a_i^u \;, \qquad \rho^0 \leftrightarrow \tilde a_i^d = c_i^d a_i^d + c_i^{8d} a_i^{8d} +
c_i^{8u} a_i^{8u}$$ with $c_i^x$ given in appendix \[app:rho0-effective-coefficients\].
Isospin asymmetries in $B\to \rho \gamma/ll$ in the SM
------------------------------------------------------
The SM values of the new colour octet coefficients are: $$\begin{aligned}
\label{eq:a8SM}
a_1^{8q} &= -a_2^{8q} = a_3^{8q} = -a_4^{8q} = -4 C_5 \;. \nonumber \\
a_5^{8q} &= -a_6^{8q} = -a_7^{8q} = a_8^{8q} = 2C_3 - 2\delta_{qu}\frac{\lambda_u}{\lambda_t} C_1 \;, \\
a_9^{8q} &= a_{10}^{8q} = 0 \;.\nonumber\end{aligned}$$ The ones for the colour singlet operators are the same as for the $K^*$ . The formulae for $\tilde a$, in relation to $\rho^0$ , ar given in appendix \[app:rho0-effective-coefficientsSM\] for the SM.
![(top) Isospin asymmetry for $B \to \rho ll$ with grey error bands. (left(right),middle) Contribution of different SM operators to the isospin asymmetry in $B \to \rho ll$. The right hand graph shows sizeable contributions. Note that unlike at $q^2=0$ the ${C}_2$ contribution is comparable to the ${C}_6$ contribution here; this is due to a small weak phase arising from $C_9^{\rm eff}$ alleviating the $\cos\alpha_{\rm CKM}$ suppression a little. See appendix \[app:uncertainty\] for details of the calculation of the grey error band. (left(right),bottom) Isospin asymmetry for $B \to \rho ll$ not CP-averaged $b \to d$ and $\bar b \to \bar d$-type. They do add up to the CP-average (top) but do deviate significantly from the latter as a result of strong and weak phases as discussed in section \[sec:CP-averaging\]. No such effect is observed for the $K^*$ as explained in some detail in that section. []{data-label="fig:1rho"}](isospin_lcsr_rho_total "fig:"){width="48.00000%"}\
![(top) Isospin asymmetry for $B \to \rho ll$ with grey error bands. (left(right),middle) Contribution of different SM operators to the isospin asymmetry in $B \to \rho ll$. The right hand graph shows sizeable contributions. Note that unlike at $q^2=0$ the ${C}_2$ contribution is comparable to the ${C}_6$ contribution here; this is due to a small weak phase arising from $C_9^{\rm eff}$ alleviating the $\cos\alpha_{\rm CKM}$ suppression a little. See appendix \[app:uncertainty\] for details of the calculation of the grey error band. (left(right),bottom) Isospin asymmetry for $B \to \rho ll$ not CP-averaged $b \to d$ and $\bar b \to \bar d$-type. They do add up to the CP-average (top) but do deviate significantly from the latter as a result of strong and weak phases as discussed in section \[sec:CP-averaging\]. No such effect is observed for the $K^*$ as explained in some detail in that section. []{data-label="fig:1rho"}](isospin_lcsr_rho_smsplit "fig:"){width="49.00000%"} ![(top) Isospin asymmetry for $B \to \rho ll$ with grey error bands. (left(right),middle) Contribution of different SM operators to the isospin asymmetry in $B \to \rho ll$. The right hand graph shows sizeable contributions. Note that unlike at $q^2=0$ the ${C}_2$ contribution is comparable to the ${C}_6$ contribution here; this is due to a small weak phase arising from $C_9^{\rm eff}$ alleviating the $\cos\alpha_{\rm CKM}$ suppression a little. See appendix \[app:uncertainty\] for details of the calculation of the grey error band. (left(right),bottom) Isospin asymmetry for $B \to \rho ll$ not CP-averaged $b \to d$ and $\bar b \to \bar d$-type. They do add up to the CP-average (top) but do deviate significantly from the latter as a result of strong and weak phases as discussed in section \[sec:CP-averaging\]. No such effect is observed for the $K^*$ as explained in some detail in that section. []{data-label="fig:1rho"}](isospin_lcsr_rho_smsplit2 "fig:"){width="49.00000%"}\
![(top) Isospin asymmetry for $B \to \rho ll$ with grey error bands. (left(right),middle) Contribution of different SM operators to the isospin asymmetry in $B \to \rho ll$. The right hand graph shows sizeable contributions. Note that unlike at $q^2=0$ the ${C}_2$ contribution is comparable to the ${C}_6$ contribution here; this is due to a small weak phase arising from $C_9^{\rm eff}$ alleviating the $\cos\alpha_{\rm CKM}$ suppression a little. See appendix \[app:uncertainty\] for details of the calculation of the grey error band. (left(right),bottom) Isospin asymmetry for $B \to \rho ll$ not CP-averaged $b \to d$ and $\bar b \to \bar d$-type. They do add up to the CP-average (top) but do deviate significantly from the latter as a result of strong and weak phases as discussed in section \[sec:CP-averaging\]. No such effect is observed for the $K^*$ as explained in some detail in that section. []{data-label="fig:1rho"}](isospin_lcsr_rho-c_total "fig:"){width="48.00000%"} ![(top) Isospin asymmetry for $B \to \rho ll$ with grey error bands. (left(right),middle) Contribution of different SM operators to the isospin asymmetry in $B \to \rho ll$. The right hand graph shows sizeable contributions. Note that unlike at $q^2=0$ the ${C}_2$ contribution is comparable to the ${C}_6$ contribution here; this is due to a small weak phase arising from $C_9^{\rm eff}$ alleviating the $\cos\alpha_{\rm CKM}$ suppression a little. See appendix \[app:uncertainty\] for details of the calculation of the grey error band. (left(right),bottom) Isospin asymmetry for $B \to \rho ll$ not CP-averaged $b \to d$ and $\bar b \to \bar d$-type. They do add up to the CP-average (top) but do deviate significantly from the latter as a result of strong and weak phases as discussed in section \[sec:CP-averaging\]. No such effect is observed for the $K^*$ as explained in some detail in that section. []{data-label="fig:1rho"}](isospin_lcsr_rho-n_total "fig:"){width="48.00000%"}
Our results for $B\to \rho ll$, including breakdowns of operator dependence, are shown in Fig. \[fig:1rho\] and Fig. \[fig:2rho\], and tabulated data is given in appendix \[app:tables\] in Tab. \[tab:1rho\]. The experimental measurement of the isospin asymmetry is defined differently to the $K^*$ case, as [@Taniguchi:2008ty] $$\label{eq:Delta-aI-releation}
\Delta(\rho\gamma) = \frac{\tau_{B^0}}{2\tau_{B^+}}\frac{{\cal B}(B^+\to\rho^+\gamma)}{{\cal B}(B^0\to\rho^0\gamma)} - 1 = \frac{ -2\bar a_I(\rho\gamma) }{1 + \bar a_I(\rho\gamma)} \stackrel{a_I(\rho\gamma) \ll 1}{\approx} -2\bar a_I(\rho\gamma) \;,$$ ($ a_I(\rho\gamma) = - \Delta(\rho\gamma) /(2 + \Delta(\rho\gamma) )$) where a CP-averaged branching fraction is used. In this normalisation, our result compares with the experimental result as [@Amhis:2012bh] $$\begin{aligned}
\label{eq:Delta_rho}
\Delta(\rho\gamma)_{\rm HFAG} &= -46(17)\% \;, &
\Delta(\rho\gamma)_{\rm LZ} &= -10(6)\% \;.\end{aligned}$$ We shall quote $\Delta$ in percentage even though, contrary to $-1 \leq a_I \leq 1$, $\Delta$ is not bounded when $a_I \to -1$. For completeness we further quote our result for the CP-averaged isospin asymmetry in $B\rightarrow\rho\gamma$ in the SM as $$\begin{aligned}
\label{eq:aIrho}
\bar a_I(\rho\gamma)_{\rm HFAG} &= 30(^{-13}_{+16})\% \;, & \bar a_I(\rho\gamma)_{\rm LZ} = 5.2(2.8)\% \;,\end{aligned}$$ where we have used Eqs. (\[eq:Delta\_rho\],\[eq:Delta-aI-releation\]) for computing what we call the HFAG value above. Our result is comparable to that obtained in [@Ball:2006eu][^16] and somewhat larger than that in [@Beneke:2004dp], principally due to a different choice of $\alpha_{\rm CKM}$. Our SM result is marginally consistent with the current experimental value, that is to say they are exactly two standard deviations apart. There is another way one can reflect on the experimental value , namely one can extract $|V_{\rm td}/V_{\rm ts}|$ from the ratio of branching fractions $R_{\rho/K^*} = \mathcal B(B \to\rho \gamma)/\mathcal B(B \to K^{*}\gamma) $ which can be applied for charged and neutral case separately. In view of the fact, to be discussed in the next section, that the isospin splitting of the ratios of $\rho$ and $K^*$-channel is accidentally small (i.e. SM: $R_{\rho^0/K^{*0}} \approx R_{\rho^+/K^{*+}}$ for current CKM angles), we may infer from table 12 in Ref. [@Ball:2006eu] that $$\left| \frac{V_{\rm td}}{V_{\rm ts}} \right|_{R_{\rho^0/K^{*0}}} = 0.229(25\%) \;, \quad
\left| \frac{V_{\rm td}}{V_{\rm ts}} \right|_{R_{\rho^+/K^{*+}}} = 0.165(25\%) \;, \quad
\left|\frac{V_{\rm td}}{V_{\rm ts}}\right|_{\rm PDG\cite{Beringer:1900zz}} = 0.211(7) \;,$$ and we have quoted the current value from Particle Data Group (PDG) for comparison. We have given a rough estimate of the error which is mainly due to the $B \to \rho \gamma$ branching fraction (c.f. appendix \[app:delta-ai-calc\]). Thus we infer that the discrepancy in $\Delta(\rho \gamma)$ is presumably due to the $\rho^+$- rather than the $\rho^0$-channel.
On subtleties of CP-averaging the isospin asymmetries {#sec:CP-averaging}
-----------------------------------------------------
In this paper we have computed CP averaged quantities which results in the linear approximation to taking the real part of the strong and weak phase separately, whereas no CP average implies taking real part of the product of the strong and weak phase. Schematically: $$\text{CP-average:} \quad {\rm Re}[e^{i \delta_{\rm strong}}] {\rm Re}[ e^{i \phi_{\rm weak}} ]
\;, \qquad \text{no CP-average:} \quad {\rm Re}[e^{i \delta_{\rm strong}}e^{i \phi_{\rm weak}} ] \;.$$ To be more precise the weak and the strong phase is the difference between the isospin-violating and the isospin-conserving amplitude. Thus in general there can be significant differences if both $\delta_{\rm strong}$ and $\phi_{\rm weak}$ are sizeable.
Are there sizeable strong phase differences? The isospin conserving amplitude has a very small strong phase in the region we are considering and thus the question is whether there is a sizeable strong phase in the isospin violating amplitude. The answer to this is no for $q^2 = 0$, as only ${{\cal O}}_8{(')}$ contributes with a strong phase at leading order in $\alpha_s$ (which is at least small in the SM). For $1{\,{\rm GeV}}^2 \leq q^2 \leq 4m_c^2$ however the answer is yes: the photon emitted from a light quark converts via an intermediate $\rho, \omega$-meson and gives raise to a tail in the imaginary part. This is the case for all IR isospin violation and we refer the reader to figure 4(left) in [@DLZ12] for an illustration.
Are there large sizeable weak phase differences? In the SM this is the case for $B \to \rho ( b \to d)$ as can be seen from with $\alpha_{\rm CKM}=89(4)$ but not for $B \to K,K^*(b \to s)$. In BSM scenarios this question is open modulo constraints, in particular CP-observables.
We summarise the conclusions to be drawn from the discussion above in Tab. \[tab:CP-averaging\]. The plots for the non CP-averaged isospin asymmetries in $B \to \rho ll$ are shown in Fig. \[fig:2rho\]. We see that the asymmetries raise up to $\pm 5\%$ in the $1{\,{\rm GeV}}^2 \leq q^2 \leq 4m_c^2$-region.
$\overline{\rm CP}$ effect $B\to (K^*,\rho)\gamma$ $B\to K^{(*)} ll$ $B\to \rho ll$
----------------------------------- ------------------------- ------------------- ----------------
SM
BSM ($\phi_{\rm weak}^{\rm BSM}$)
: $\overline{\rm CP}$ effect stands for CP-averaging effect on the isospin asymmetries and () mean (in)significant. Overview of the conclusions to be drawn from the analysis of section \[sec:CP-averaging\]. Note that a enhancement of ${{\cal O}}_8$ or sizeable radiative corrections to WA or QLSS would raise $\delta_{\rm strong}$ and could shift the situation slightly.[]{data-label="tab:CP-averaging"}
In general it might therefore be interesting to measure non CP-averaged isospin asymmetries in future experimental determinations. This is certainly possible for the $K^*$ and the $\rho$ but not for the $K$, as it is observed through $K_S^0$ which is a superposition of the strangeness eigenstates $K^0$ and $\bar K^0$.
Isospin asymmetries beyond the SM {#sec:isospinBSM}
=================================
The extension of the SM basis was discussed throughout the main text and summarised in subsection \[sec:selection\]. Possibly we should reemphasize, for the sake of clarity, that ${{\cal O}}_{7,9,10}'$-operators of [$V$+$A$]{}-chirality are of no interest to the isospin asymmetry as they do not violate isospin. Of course if they become extremely large then they would affect the rate. Yet it is already known that they cannot be too large e.g. [@Altmannshofer:2011gn; @Altmannshofer:2012az; @DescotesGenon:2012zf]. The various contributions of the extended basis are detailed in Figs. \[fig:2\],\[fig:2rho\] and tabulated in Tabs. \[tab:2\],\[tab:1\]&\[tab:1rho\] (appendix \[app:tables\]) for the $K$, $K^*$ and $\rho$ channels respectively. One aspect that is immediately apparent from these graphs is that there are overwhelmingly many contributions that can give rise to a sizeable isospin asymmetry at low $q^2$. In fact there are so many that by the rules of probability one would expect cancellations in the generic case. Fortunately this is where the $q^2$-spectrum should help us, should there be new physics, one cannot expect to be unlucky over the entire $q^2$-range.
In subsection \[sec:non-relation\] we have discussed that only for leading twist and SM chirality the $K$ and the $K^*_\parallel$ are related. As noted there this link breaks down in the presence of right-handed currents, which are only partially constrained, and thus in a generic scenario the link between the $K$ and the $K^*$ isospin asymmetry is lost. The reader can convince him or herself of this fact directly from the corresponding tables and figures referred to above.
$B\to K^*\gamma$ Min. SM Max. Min. SM Max.
------------------ -------- ------------------ ------- ------------ -------- -------- -------
$a_2^u$ -0.39 -0.068 0.25 $a_2^d$ -0.24 -0.068 0.11
$a_4^u$ -0.38 -0.068 0.25 $a_4^d$ -0.24 -0.068 0.10
$a_5^u$ -0.41 $-0.021+0.019 i$ 0.37 $a_5^d$ -0.67 -0.028 0.61
$a_6^u$ -0.62 $0.021 -0.019 i$ 0.57 $a_6^d$ -1.0 0.028 1.0
$a_9^u$ -0.049 0 0.049 $a_9^d$ -0.080 0 0.080
$a_{10}^u$ -0.048 0 0.048 $a_{10}^d$ -0.080 0 0.080
: Constraints on WCs $a_i^q$ from $B\to K^*\gamma$ at $2\sigma$, assuming no accidental cancellations occur, along with SM values. We assume $0<\bar a_I(K^*\gamma)<10\%$, and derive constraints from Tab. \[tab:1\] assuming that only a single coefficient $a_i^q$ deviates from its SM value. SM values are calculated from and table \[tbl:wilson-coefficient-example\]. All constraints are for the *real* part of these coefficients, the imaginary part is not constrained by the isospin asymmetry.[]{data-label="tbl:kstar-constraints"}
$B\to \rho\gamma$ SM Bound SM Bound
------------------- ----------------- ------------------------- ------------------- ------------------ -------------------------
$a_2^u$ -0.068 -4.1 $\tilde a_2^d$ -0.068 -2.1
$a_4^u$ -0.068 -4.0 $\tilde a_4^d$ -0.068 -2.0
$a_5^u$ $-0.021+0.402i$ $0.26 e^{-i 87^\circ}$ $\tilde a_5^d$ $-0.028+0.088 i$ $0.42 e^{-i 72^\circ}$
$a_6^u$ $0.021-0.402i$ $-0.40 e^{-i 87^\circ}$ $\tilde a_6^d$ $0.028-0.088 i$ $-0.68 e^{-i 72^\circ}$
$a_9^u$ 0 0.56 $\tilde a_9^d$ 0 0.94
$a_{10}^u$ 0 0.56 $\tilde a_{10}^d$ 0 0.93
: Constraints on operators $a_i^q$ from $B\to \rho\gamma$ at $2\sigma$, assuming no accidental cancellations occur, along with SM values. We assume $6\%<\bar a_I(\rho\gamma)<67\%$, and derive as described below Tab. \[tbl:kstar-constraints\]. The fact that the real part of $a_{5,6}^u$ is the same (on the level given digits) as for $B \to K^*$ in tab \[tbl:kstar-constraints\] is an numerical accident. The large imaginary parts in $a_{5,6}^u$ and $\tilde a_{5,6}^u$ imply that the constraints applies in the same direction in the complex plane. Note: in the published version (arXiv v2) only real WC were assumed in which case the constraint on $a_{5}^u$ becomes $0.26/ \cos(-i 87^\circ) \simeq 4.9$ which matches the earlier result. Since our calculated SM value is the lower bound of this range (within uncertainties), we quote the SM value of the coefficient and the other bound; the true value is expected to lie in this range. Complementary constraints from $B \to (\pi/\rho) (\pi/\rho)$ are presented in [@Bobeth:2014rda] (c.f. figure 1).[]{data-label="tbl:rho-constraints"}
Constraints on isospin sensitive four Fermi operators {#sec:constraints}
-----------------------------------------------------
We shall now briefly turn to the question to what extent these operators are already constrained. We identify non-leptonic decays[^17] as well as $B \to \rho/K^* \gamma$ isospin asymmetries themselves as the main sources for constraints:
- *$B \to \rho/K^* \gamma$ isospin asymmetries*: the experimental values are quoted in , respectively. These isospin asymmertries are sensitive to $a^q_{2,4,5,6,9,10}$ of WA in particular. Of course one number such as $\bar a_I(K^* \gamma)$ can not seriously bound twelve numbers. We might though give indicative constraints by imposing that each of the coefficients shall not be more than two standard deviations away from the central value, which roughly amounts to $ 0 < \bar a_I(K^* \gamma) < 10\%$ and $ 6 < \bar a_I(\rho \gamma) < 67\%$ ($ -80\% < \Delta(\rho\gamma) < -12\%$). The results of this procedure are collected in Tab. \[tbl:kstar-constraints\] and Tab. \[tbl:rho-constraints\] respectively.
- *Non-leptonic decays*: four Fermi operators do affect non-leptonic decays such as $B \to \rho/\pi K^{(*)}$, $B_s \to K^{(*)}\phi$ etc. The disadvantage is that they are difficult to predict from a theoretical viewpoint. Especially in the absence of a first principle approach to final state rescattering. The uncertainty in strong phases obscures interference effects which affects all observables, let alone CP-asymmetries. The advantage though is that there is a plethora of channels which allows theorists to constrain certain weak topologies e.g. [@Fleischer:2010ib; @Ciuchini:2012gd; @Bhattacharya:2012ph] and permits them to cross-check their methods. Interesting constraints on four Fermi operators, such as the so-called electroweak penguins present in the SM, have been obtained in Ref. [@Hofer:2010ee; @Hofer:2012vc] for instance in the framework of QCD factorisation. We would like to add two remarks. First, these operators do partially overlap with ours and would indeed bring in additional constraints. Yet only global fits lead to solid constraints which is beyond the scope of this work. Second, from the plots Ref. [@Hofer:2010ee; @Hofer:2012vc] one infers that it is rather unlikely that the NP contributions to the WC exceeds the SM values by a factor of five but could easily be out by a factor of two. In view of the multitude of channels this might very well be true for SM-operators. It seems more difficult to come to a quick judgement for non SM-operators (by which we mean operators with small WCs). Partial studies do exist: e.g. an interesting direction, in view of right-handed currents, is the investigation of polarisation in $B \to VV$ decays [@Bhattacharya:2012ph] which was carried out in [@Beneke:2006hg] in the framework of QCD factorisation.
![Breakdown of contributions of WA ($a_i$), QLSS ($s^f_{x,\chi}$) and ${\cal O}_8^{(')}$ to the isospin asymmetry $B \to K^{(*)}ll$ in the linear approximation . We have split the contributions as detailed in Tab. \[tab:breakdown\] into different graphs in order to make them more readable. Note that we use $a^q_i=0.1$ and $s^f_{x,\chi}=1$ to produce these figures, as in the tables.[]{data-label="fig:2"}](isospin_lcsr_k_wa_split "fig:"){width="49.00000%"} ![Breakdown of contributions of WA ($a_i$), QLSS ($s^f_{x,\chi}$) and ${\cal O}_8^{(')}$ to the isospin asymmetry $B \to K^{(*)}ll$ in the linear approximation . We have split the contributions as detailed in Tab. \[tab:breakdown\] into different graphs in order to make them more readable. Note that we use $a^q_i=0.1$ and $s^f_{x,\chi}=1$ to produce these figures, as in the tables.[]{data-label="fig:2"}](isospin_lcsr_k_qlss_split "fig:"){width="49.00000%"} ![Breakdown of contributions of WA ($a_i$), QLSS ($s^f_{x,\chi}$) and ${\cal O}_8^{(')}$ to the isospin asymmetry $B \to K^{(*)}ll$ in the linear approximation . We have split the contributions as detailed in Tab. \[tab:breakdown\] into different graphs in order to make them more readable. Note that we use $a^q_i=0.1$ and $s^f_{x,\chi}=1$ to produce these figures, as in the tables.[]{data-label="fig:2"}](isospin_lcsr_kstar_wa_u_split "fig:"){width="49.00000%"} ![Breakdown of contributions of WA ($a_i$), QLSS ($s^f_{x,\chi}$) and ${\cal O}_8^{(')}$ to the isospin asymmetry $B \to K^{(*)}ll$ in the linear approximation . We have split the contributions as detailed in Tab. \[tab:breakdown\] into different graphs in order to make them more readable. Note that we use $a^q_i=0.1$ and $s^f_{x,\chi}=1$ to produce these figures, as in the tables.[]{data-label="fig:2"}](isospin_lcsr_kstar_qlss_odd_split "fig:"){width="49.00000%"} ![Breakdown of contributions of WA ($a_i$), QLSS ($s^f_{x,\chi}$) and ${\cal O}_8^{(')}$ to the isospin asymmetry $B \to K^{(*)}ll$ in the linear approximation . We have split the contributions as detailed in Tab. \[tab:breakdown\] into different graphs in order to make them more readable. Note that we use $a^q_i=0.1$ and $s^f_{x,\chi}=1$ to produce these figures, as in the tables.[]{data-label="fig:2"}](isospin_lcsr_kstar_wa_d_split "fig:"){width="49.00000%"} ![Breakdown of contributions of WA ($a_i$), QLSS ($s^f_{x,\chi}$) and ${\cal O}_8^{(')}$ to the isospin asymmetry $B \to K^{(*)}ll$ in the linear approximation . We have split the contributions as detailed in Tab. \[tab:breakdown\] into different graphs in order to make them more readable. Note that we use $a^q_i=0.1$ and $s^f_{x,\chi}=1$ to produce these figures, as in the tables.[]{data-label="fig:2"}](isospin_lcsr_kstar_qlss_even_split "fig:"){width="49.00000%"}
![Breakdown of contributions of WA ($a_i$), QLSS ($s^f_{x,\chi}$) and ${\cal O}_8^{(')}$ to the isospin asymmetry $B \to \rho ll$ in the linear approximation . We have split the contributions as detailed in Tab. \[tab:breakdown\] into different graphs in order to make them more readable. Note that we use $a^u_i=0.1$, $\tilde a^d_i=0.1$ and $s^f_{x,\chi}=1$ to produce these figures, as in the tables.[]{data-label="fig:2rho"}](isospin_lcsr_rho_wa_u_split "fig:"){width="49.00000%"} ![Breakdown of contributions of WA ($a_i$), QLSS ($s^f_{x,\chi}$) and ${\cal O}_8^{(')}$ to the isospin asymmetry $B \to \rho ll$ in the linear approximation . We have split the contributions as detailed in Tab. \[tab:breakdown\] into different graphs in order to make them more readable. Note that we use $a^u_i=0.1$, $\tilde a^d_i=0.1$ and $s^f_{x,\chi}=1$ to produce these figures, as in the tables.[]{data-label="fig:2rho"}](isospin_lcsr_rho_qlss_odd_split "fig:"){width="49.00000%"} ![Breakdown of contributions of WA ($a_i$), QLSS ($s^f_{x,\chi}$) and ${\cal O}_8^{(')}$ to the isospin asymmetry $B \to \rho ll$ in the linear approximation . We have split the contributions as detailed in Tab. \[tab:breakdown\] into different graphs in order to make them more readable. Note that we use $a^u_i=0.1$, $\tilde a^d_i=0.1$ and $s^f_{x,\chi}=1$ to produce these figures, as in the tables.[]{data-label="fig:2rho"}](isospin_lcsr_rho_wa_d_split "fig:"){width="49.00000%"} ![Breakdown of contributions of WA ($a_i$), QLSS ($s^f_{x,\chi}$) and ${\cal O}_8^{(')}$ to the isospin asymmetry $B \to \rho ll$ in the linear approximation . We have split the contributions as detailed in Tab. \[tab:breakdown\] into different graphs in order to make them more readable. Note that we use $a^u_i=0.1$, $\tilde a^d_i=0.1$ and $s^f_{x,\chi}=1$ to produce these figures, as in the tables.[]{data-label="fig:2rho"}](isospin_lcsr_rho_qlss_even_split "fig:"){width="49.00000%"}
$B \to K^*/\rho \gamma$ isospin asymmetry splitting - (quasi) SM null test {#sec:dai}
--------------------------------------------------------------------------
![Plot of the effective $\rho$ to $K^*$ isospin asymmetry difference $\delta_{a_I}$ . Vertical lines indicate the current experimental value of $\alpha_{\rm CKM}$ [@Beringer:1900zz] and its uncertainty. At the present small value of $\cos\alpha_{\rm CKM}$, $\delta_{a_I}$ is well determined theoretically.[]{data-label="fig:delta-ai"}](isospin_delta_ai){width="50.00000%"}
The closeness of $\alpha_{\rm CKM}$ to ninety degrees may be exploited to predict an oberservable with much smaller theoretical uncertainty, albeit at the expense of larger current experimental uncertainty.
Our prediction is essentially that $\bar a_I(\rho\gamma)$ and $\bar a_I(K^*\gamma)$ should be similar, up to form factor and hadronic parameter differences[^18]. A major source of uncertainty in determining $\bar a_I(K^*\gamma)$ and $\bar a_I(\rho\gamma)$ however is the renormalisation scale used to compute the WCs, and because of this it is worthwhile to calculate a quantity in which the leading scale dependence and form factor differences cancel, namely $$\delta_{a_I} \equiv 1 - \frac{\bar a_I(\rho\gamma)}{\bar a_I(K^*\gamma)}
R_{\rho K^*}
=1 + \frac{\Delta(\rho\gamma)}{(2+\Delta(\rho\gamma)) \bar a_I(K^*\gamma)} R_{\rho K^*} \;,
\label{eq:delta-ai-def}$$ where $$\label{eq:RrhoKs}
R_{\rho K^*} \equiv \sqrt{\frac{\bar \Gamma(B\to\rho\gamma)}{\bar \Gamma(B\to K^*\gamma)}}\left|\frac{V_{ts}}{V_{td}}\right| \;,$$ and a barred partial width $\bar \Gamma$ implies a CP-average, and omission of charges implies an isospin average[^19]. The dominant contributions to the RHS of are $$\begin{aligned}
\label{eq:crude}
a_I(V\gamma) &\approx \frac{C_6 + C_5/3}{C_7^{\rm eff}} \frac{f_V^\perp F^{\rm WA}(0) }{T_1^V(0)} + \dots &
\bar\Gamma(B\to V\gamma) &\approx \frac{3\alpha c_F}{8\pi} \left|\lambda_t C_7^{\rm eff}\right|^2 |T_1^V(0)|^2\end{aligned}$$ where the dots stand for $C_{3,4}$-contributions, which are small as the $K^*$ and $\rho$ cases are very similar, quark masses and $B^0\to\rho^0$ diagrams at ${{\cal O}}(\alpha_s^2)$ where the different structure of the $\rho^0$ matters even for small $\cos\alpha_{\rm CKM}$. The function $f_V^\perp F^{\rm WA}(0)$ stands for final state emission where we have explicitly factored out the $f^\perp$ decay constant as compared with . More precisely: $f_V^\perp F^{\rm WA}(q^2) = \sum_{i=2,4} \left(F^d_i(q^2) - F^u_i(q^2) \right)$ ($i =2,4$ are the operators proportional to $C_6 + C_5/3$) in the notation of , and $F^{\rm WA}$ is the same for the $K^*$ and the $\rho$ in our approximation up to small corrections from different Gegenbauer moments. The correction factor $R_{\rho K^*}$ serves the purpose of eliminating the form factor ratio as $\bar a_I(\rho\gamma)/\bar a_I(K^*\gamma) \simeq T_1^{B \to K^*}(0)/T_1^{B \to \rho}(0)$ which follows from Eq. . Since the WA contribution $f^\perp F^{\rm WA}(0)$ is essentially proportional to $f^\perp$, it then follows that $$\delta_{a_I}=1-f_\rho^\perp/f_{K^*}^\perp + \text{small corrections}\;,$$ where the principal source of uncertainty, the scale dependence of $C_6 + C_5/3$, drops out. Note that by ‘small corrections’ we mean small as compared to $1$. The quantity $\delta_{a_I}$ is particularly sensitive to corrections to the isospin asymmetry and we therefore include terms quadratic in WA amplitudes present in but neglected in and elsewhere. Comparing our prediction with a naive combination of PDG [@Beringer:1900zz] results for these quantities gives: $$\begin{aligned}
\left[\delta_{a_I}\right]_{\rm exp} &= -4.0(3.5) \;, &
\left[\delta_{a_I}\right]_{\rm LZ} &= 0.10(11) \;.
\label{eq:delta-ai-exp}\end{aligned}$$ The theoretical uncertainty should be compared with $1$ as it is a ratio, as above and thus is at $11\%$, is under rather good control, as compared to roughly fifty percent in the individual asymmetries. See appendix \[app:delta-ai-calc\] for the experimental input used as well as brief comments on the uncertainty. Let us briefly add that the uncertainty due to the difference in $B$-meson lifetimes and $|V_{ts}/V_{td}|$ is negligible. Experimental and theoretical values agree within uncertainties, though the central value is very different and an improved experimental determination is desirable since the theoretical errors are under good control. The experimental uncertainty due to all four branching fractions involved in $\delta_{a_I}$ is rather similar, and thus *all* of them need to be reduced to significantly improve the overall uncertainty. It should also be added that if the asymmetries are measured in the same experiment (some) systematic uncertainties can be expected to cancel.
$x$ $\delta_{a_I}^{a_1^d + x}$ $\delta_{a_I}^{a_8^d + x}$
------ ---------------------------- ----------------------------
-0.3 $ 1.16(15)$ $ 1.71(20)$
-0.2 $ 0.82(11)$ $ 1.21(13)$
-0.1 $ 0.47(9)$ $ 0.67(9)$
0.1 $ -0.29(14)$ $ -0.51(15)$
0.2 $ -0.68(18)$ $ -1.14(21)$
0.3 $ -1.08(23)$ $ -1.78(28)$
: Effect of varying $a^d_i$ from their SM values on the isospin splitting $\delta_{a_I}$. We fix all $a^q_i$ to their SM values and then alter a single one by the specified amount. More precisely $\delta_{a_I}[{a_8^d + x}] \leftrightarrow \delta_{a_I}[{ a^{d,\rm SM}_8+x}]$ above. The resulting variation of $\delta_{a_I}$ can be large and is primarily the result of the $\rho^0$ coupling to a different combination of $a_i$ as discussed in section \[sec:Heffrho\], and is therefore an example of UV isospin violation (but not MFV violation). The uncertainties quoted in this table do not include uncertainty from varying the renormalisation scale: this would require a computation of the scale dependence of the Hamiltonian and is thus beyond the scope of this work. The renormalisation scale is taken to be the usual central value, $\mu=4.7{\,{\rm GeV}}$. []{data-label="tab:dai-violation"}
The behaviour of $\delta_{a_I}$ and its uncertainty as a function of $\alpha_{\rm CKM}$ are shown in Fig. \[fig:delta-ai\]. We provide a fit for this plot, $$\left[\delta_{a_I}\right]_{\rm LZ} = 0.10 - 0.87\cos\alpha_{\rm CKM} \;,$$ where the $1\sigma$ bounds are given by $\left[\delta_{a_I}\right]_{\rm LZ} \pm \left[\sigma\right]_{\rm LZ}$ where $[\sigma]_{\rm LZ} = 0.10 + 0.14\cos^2\alpha_{\rm CKM}$ is a good fit for the error band shown in Fig. \[fig:delta-ai\].
It is clear that the structure of the SM is responsible for the smallness of $\delta_{a_I}$ . In general the quantity $\delta_{a_I}$ is thus highly sensitive to new physics. Two examples are:
- *Non-MFV isospin violation*: E.g. $(a_i^q|_{b \to s}) / ( a_i^q|_{b \to d})
\neq \lambda^{bs}_t / \lambda^{bd}_t$ C.f. Eq. and therafter for the definition of $a_i^q$.
- *UV isospin violation*: Four fermi operators of the type in unequal proportion of $q =u,d$ quarks. Such a difference is sensitive to the structure of the $K^{*,0}$ and $\rho^0$ parton content.
We provide some example values for the case of UV isospin violation in Tab. \[tab:dai-violation\].
Conclusion {#sec:discussion}
==========
Isospin violating effects considered in this paper are of the UV-type, i.e. $H^{\rm eff}$ is asymmetric under $u \leftrightarrow d$, as well as IR-isospin violation which manifests itself in photon emission from the spectator quark. We have found that CP-averaged isospin asymmetries in the SM are small, below $1.5\%$, for $B \to (K,K^*\rho) ll$ at lepton pair momentum $1{\,{\rm GeV}}^2 \leq q^2 \leq 4m_c^2$ as can be inferred from Figs. \[fig:1\],\[fig:2\] as well as the actual breakdown of the various operator contributions. In fact in the SM the $(K,K^*)ll$ and $\rho ll$ are somewhat accidentally small. In the former case the large Wilson coefficient $C_2^u$ is suppressed by a small CKM-prefactor $|\lambda_u/\lambda_t| \simeq \lambda^2 \approx 0.04$ and in the latter case it is the smallness of $\cos \alpha_{\rm CKM}$ which suppresses the tree-level WC $C_2^u$. The latter point is also the reason why the non CP-averged isospin asymmetry for $B \to \rho ll$ deviates from the CP-averged one c.f. section \[sec:CP-averaging\]. Not performing the CP-average, which is possible for the $\rho$ and $K^*$, is certainly an interesting option for the former per se c.f. Fig.\[fig:2\](bottom) and for the latter in presence of new weak phases.
Isospin asymmetries of $B \to K^*/\rho \gamma$ are a bit higher, around $5\%$ each, due to the photon pole enhancement and are measured with reasonable accuracy (\[eq:HFAG\],\[eq:Delta\_rho\]). Whereas the $K^*$ experimental result is in perfect agreement with our prediction the $\rho$-asymmetry is off by two standard deviations and calls for further experimental data. In both cases we use these results to give indicative constraints on the WA WCs, c.f. Tabs. \[tbl:kstar-constraints\],\[tbl:rho-constraints\], by demanding that no coefficient is more than two standard deviations away from the experimental results. The smallness of $\cos \alpha_{\rm CKM}$ implies that the $K^*/\rho \gamma$ SM isospin asymmetries are structurally very similar, resulting in the almost identical numerical result, which prompted us define a (quasi) null test of the SM $\delta_{a_I}$ in section \[sec:dai\].
We have not systematically investigated the isospin asymmetry in the high $q^2$-region in this work. Nevertheless we have argued that it has to be small as it is a) no longer artificially enhanced as at low $q^2$ by the photon pole, through which isospin effects propagate, b) its contribution is further suppressed relative to the form factor contributions as the latter feel the closeness of the t-channel pole at $q^2 = m_{B_s^*}^2$. On grounds of these arguments, modulo magic cancellation at low $q^2$, one expects the isospin asymmetry to decrease. We should add, that the authors of reference [@Beylich:2011aq] had come to the same conclusion using arguments of a high $q^2$-OPE.
We have introduced the most general basis of dimension six operators for WA and QLSS and have detailed various contributions in Tabs. \[tab:2\],\[tab:1\],\[tab:1rho\] in appendix \[app:tables\] as well as Figs.\[fig:2\],\[fig:2rho\] in section \[sec:isospinBSM\] respectively. Generic selection rules for the $B \to Kll$, valid for any scalar $\to$ scalar $ll$ transition, were discussed in section \[sec:Ksel\]. Selection rules for WA, which are more stringent, and were worked out in section \[sec:WAsel\] for vectors and pseudoscalars. After applying all selection rules $24$ and $10$ operators remain for a vector and pseudoscalar meson final state, which compares with $7$ operators in the SM for the $K^*$ and the $K$-meson. In view of the large number of operators that can contribute, as detailed in Fig. \[fig:1\] and Tabs. \[tab:2\],\[tab:1\] respectively, one might even wonder whether by the laws of probability cancellation of new physics is the rule rather than the exception. One would hope that a refined experimental analysis in $q^2$ would reveal the deviation in one bin or another. In this paper we have not attempted to constrain the four Fermi operators through non-leptonic decays but have, for the time being[^20], contented ourselves with a few generic remarks in section \[sec:constraints\]. In the future data from isospin asymmetries in $B \to P,V \gamma/ll$ could be combined with data in non-leptonic decays $B \to PP,PV,VV$ to constrain four Fermi operators of $b s(d) qq$-type more effectively.
On the theoretical side the SM isospin prediction would benefit from an evaluation at ${\cal O}(\alpha_s)$ of the WA contribution. This computation would also be beneficial to understand $D^0 \to V ll/\gamma$ decays [@LZ12]. For the BSM analysis a computation of QLSS within LCSR would be desirable for the reasons mentioned at the beginning of the section \[sec:QLSS\].
We explained why the $K$ and the $K^*_\parallel$ contribution are linked at leading twist and for left-handed currents only. Thus the relation between the $Kll$- and $K^*ll$-asymmetry is therefore already only approximate in the SM and lost entirely should there be sizeable [$V$+$A$]{} structures. In view of the experimental results we therefore conclude: whereas it is very plausible that the $K$ isospin asymmetry is larger or very different from the $K^*$ isospin asymmetry, it remains mysterious at this moment why it would be sizeable at high $q^2$ at all. In fact, in view of this and the smallness of the prediction in the low $q^2$-region, c.f. Fig. \[fig:1\] (top,right), the measured deviation of the integrated isospin asymmetry in $B \to Kll$ of the LHCb collaboration [@Aaij:2012cq] away from zero by four standard deviations is somewhat puzzling. More statistics, especially in the neutral channel, is therefore eagerly awaited.\
Acknowledgements {#acknowledgements .unnumbered}
================
This work has benefited from discussion and or correspondence with Christoph Bobeth, Greig Cowan, Ulrik Egede, Thorsten Feldmann, Uli Haisch, Gudrun Hiller, Franz Muheim, Leonardo Vernazza and especially Steve Playfer. Part of the computations in this paper were performed by the help of FeynCalc [@Mertig:1990an]. RZ gratefully acknowledges the support of an advanced STFC fellowship.
${\cal B}(B^0 \to K^{*0}\gamma)/{\cal B}(B_s \to \phi \gamma)$ {#app:update}
==============================================================
The LHCb collaboration has recently measured [@Aaij:2012ita] the ratio of branching fractions of $B^0 \to K^{*0}\gamma$ to $B_s \to \phi \gamma$ to be $$\label{eq:Rbr}
R_{K^*\phi} \equiv \frac{\mathcal B (B^0\to K^{*0}\gamma)}{\mathcal B (B^0_s\to\phi\gamma)} = 1.23(6)_{\rm stat} (4)_{\rm syst} (10)_{f_s/f_d} \;,$$ where the uncertainties are statistical, systematic and due to $s,d$-fragmentation.
In the SM the difference to unity of is mainly due to the ratio of form factors. Generically a difference can arise from WA and this where it connects to the rest of this work. We shall give an update of the form factor ratio below, discuss an example of how an enhancement of one of the operators in can lead to sizeable deviations from the SM-value.
Form factor ratio update
------------------------
We present a phenominological update of the form factor ratio, $$\label{eq:r}
r_{K^*\phi} = \frac{T_1^{B \to K^* \gamma}(0)}{T_1^{B_s \to \phi \gamma}(0)} = 0.89(10)\% \;,$$ using the results in [@Ball:2004rg] with the same hadronic input as in [@DLZ12]. The uncertainty consists of an estimate of violation of semi-global quark hadron duality as well as a parametric error. The first uncertainty is obtained by varying the continuum thresholds $s_0^{B \to K^*,B_s \to \phi}$ separately and adding them in quadrature. It leads to an $\Delta_{s_0} \approx 4\%$ uncertainty. We fix $s_0^{B \to K^*},s_0^{B_s \to \phi} = 35(1),36(1){\,{\rm GeV}}^2$ which is consistent with $s_0^{B \to K^*}-s_0^{B_s \to \phi} \approx m_{B_s}^2 - m_{B_d}^2$. The second uncertainty is obtained by varying all other parameters and adding them in quadrature which leads to a $\Delta_{\rm para} \approx 6\%$-uncertainty. Possibly we should add that we vary the $K^*$ and $\phi$ decay constants separately but vary $f^\perp$ and $f^\parallel$ in a correlated way as the ratio is known from lattice QCD to a high precision. This leads to either a $(\Delta_{\rm para}^2+ \Delta_{s_0}^2)^{1/2} = 7\%$ or $\Delta_{\rm para} + \Delta_{s_0} = 10\%$ error depending on whether the two uncertainties are added in quadrature or linearly. We chose to quote the more conservative error in Eq. above.
It would seem worthwhile to compare the central value with previous determinations. Taking the ratio of the individual form factor predictions in [@Ball:2004rg] we get $r_{K^*\phi} = 0.95 + 0.93 (a_1(K^*)-0.1)$. In this formula $a^\perp_1(K^*) = a_1^\parallel(K^*)$ was assumed which is still a reasonable rule in view of current determinations $a^\perp_1(K^*) = 0.04(3)$ and $a_1^\parallel (K^*)=0.06(4)$ as used in [@Ball:2004rg]. Taking the average value of the two Gegenbauer moments one gets, $r_{K^*\phi} = 0.91$, a value rather close to [^21].
One might further wonder why $r_{K^*\phi}$ is about $18\%$ lower than a naive estimate $f_{K^*}^\perp/f_\phi^\perp$. We identify four main effects: 1) $-6\%$ due to $m_\phi \neq m_{K^*}$ 2) $-3\%$ $s_0^{B \to K^*}\neq s_0^{B_s \to \phi}$, 3) $-5\%$ due to $a_1(K^*) \neq a_1(\phi)=0$ and 4) $-2\%$ due to $a_2(K^*) \neq a_2(\phi)$ which adds up to $16\%$ and consists of the bulk effect.
Prediction of ${\cal B}(B^0 \to K^{*0}\gamma)/{\cal B}(B_s \to \phi \gamma)$ & BSM-effect of WA
-----------------------------------------------------------------------------------------------
The theoretical prediction in the SM is proportional to the form factor ratio $$\label{eq:Rschema}
R_{K^*\phi} = |r_{K^*\phi}|^2 c_{K^*\phi}(1+\delta_{WA})$$ times a phase space factor (whose uncertainty is almost entirely from to the uncertainty in $\tau_{B_s}$) $$c_{K^*\gamma} = \frac{\tau_{B^0}}{\tau_{B_s}}\left(\frac{m_{B^0}}{m_{B_s}}\right)^3 \left(\frac{1-m_{K^{*0}}^2/m_{B^0}^2}{1-m_\phi^2/m_{B_s}^2}\right)^3 = 1.01(2)\,;$$ and a small correction for WA: $\delta_{WA} = -0.02(2)$. Thus essentially $R_{K^*\phi}|_{\rm SM} \approx |r_{K^*\phi}|^2$ Finally we shall requote experimental ratio besides our prediction assembling all three quantities in : $$\begin{aligned}
R_{K^*\phi}|_{\rm LHCb} = 1.23(6)_{\rm stat} (4)_{\rm syst} (10)_{f_s/f_d} \;, \qquad \quad
R_{K^*\phi}|_{\rm LZ} = 0.78(18) \;.\end{aligned}$$ The theory uncertainty is almost entirely due to the form factor ratio uncertainty which is after all not small. Thus new physics would need to manifest itself rather prominently[^22] in order to surface above the form factor uncertainty. The possibility of which we shall illustrate just below.
The WA processes in $B_s\to\phi$ decay couples to a unique set of operators, and so we can modify the WCs in such a way as to shift this amplitude without affecting any other process considered in this work. By way of example, making the shift $a^{u,d,s}_7\to a^{u,d,s}_7 - 0.5$ leads to $\delta_{WA} \to 0.5(3)$, and therefore $R_{K^*\phi}\to1.2(3)$, without affecting any other FCNC process we are considering. This result cannot be derived by a simple rescaling of the results in Tab. \[tab:1\] because the effect of Gegenbauer moments in the $B_s\to\phi$ WA amplitudes are significant.
An extension of this analysis to the differential branching fractions $(B^0)B_s \to K^{*0}(\phi) \mu^+\mu^-$, which have recently been measured by the LHCb collaboration [@Aaij:2013aln], would be interesting and is deferred to later work.
Distribution amplitudes {#app:DA}
=======================
Light meson DA {#app:light-DA}
--------------
We shall briefly summarise and define the DA used throughout this paper. For further references we refer the reader to the classic review [@Chernyak:1983ej], the LCSR review [@Colangelo:2000dp] and the thorough paper on higher twist DA [@Ball:1998sk]. The $2$-particle DA for the pseudoscalar at twist-2 ($\phi_K$) and -3 ($\phi_{p,\sigma}$) (e.g. [@Ball:2004ye]) is given by $$\begin{split}
\label{eq:KDA}
\Braket{K(p)|\bar s(x)_a [x,z] q(z)_b|0} =&
\int_0^1 du e^{i(up\cdot x+\bar up\cdot z)} \Bigg[i\frac{f_K}{4 N_c}[\slashed p\gamma_5]_{ba}\phi_K(u) \\
- i\frac{\mu_K^2}{4 N_c} [\gamma_5]_{ba} \phi_p(u)
& - i\frac{\mu_K^2}{24 N_c} p_\mu (x-z)_\nu [\sigma^{\mu\nu}\gamma_5]_{ba} \phi_\sigma(u) \Bigg] + \text{higher twist} \;,
\end{split}$$ where $a,b$ are Dirac indices, $\bar u\equiv 1-u$, $\mu_K^2 \equiv f_K m_K^2/(m_s+m_q)$ and the $[x,z]$, here and hereafter, represent a QCD Wilson line to make the matrix element gauge invariant. The asymptotic forms[^23] of the DA functions are $$\begin{aligned}
\phi_K(u) &= \phi_\sigma(u) = 6\bar uu & \phi_p(u) &= 1\end{aligned}$$ From the appendix of [@Ball:2004ye] we see that upon neglecting quark masses and 3-particle DAs, equations of motion constrain $\phi_{p,\sigma}(u)$ to their asymptotic forms. $\phi_K(u)$ is expanded in Gegenbauer moments as usual.
The $2$-particle DA for the vector meson at twist-2 ($\phi_{\parallel,\perp}$) and -3 ($g^{(v,a)}_{\perp}$) (e.g. [@Ball:2004rg]) is $$\begin{split}
\Braket{K^*(p,\eta)|\bar s(x)_a [x,z] q(z)_b|0}
= \int_0^1 du\,e^{i(up\cdot x+\bar up\cdot z)}\Bigg\{\frac{f^\perp_{K^*}}{4 N_c}\Bigg[(\slashed\eta\slashed p)_{ba}\phi_\perp(u) \\
- \frac{i}{2}(1)_{ba}(\eta\cdot(x-z)) m_{K^*}^2 h^{(s)}_\parallel(u)
-i ( \sigma_{\mu \nu})_{ba} p^\mu (x- z)^\nu \frac{\eta\cdot (x-z)}{(p\cdot (x-z))^2} m_{K^*}^2 h^{(t)}_\parallel(u) \Bigg]\\
+ \frac{m_{K^*}f_{K^*}}{4 N_c}\Bigg[(\slashed p)_{ba} \frac{\eta\cdot (x-z)}{p\cdot (x-z)} \phi_\parallel(u)
+ \left(\slashed\eta - \slashed p \frac{\eta\cdot(x-z)}{p\cdot(x-z)}\right)_{ba} g^{(v)}_\perp(u) \\
+ \frac{1}{4}\epsilon_{\mu\nu\rho\sigma}\eta^\nu p^\rho (x-z)^\sigma \left(\gamma^\mu\gamma_5\right)_{ba} g^{(a)}_\perp(u)\Bigg]\Bigg\} + \text{higher twist} \;.
\end{split}
\label{eq:vector-da}$$ The asymptotic DAs are $$\begin{gathered}
\phi_\perp(u) = \phi_\parallel(u) = g^{(a)}_\perp(u) = h_\parallel^{(s)}(u) = 6\bar uu \nonumber \\
\begin{align}
g^{(v)}_\perp(u) &= \frac{3}{4}\left(1 + (u-\bar u)^2\right) &
h^{(t)}_\parallel(u) &= 3(u-\bar u)^2 \;.
\end{align}\end{gathered}$$ In fact, these functions overparametrise the $K^*$ state and are related by QCD equations of motion [@Ball:1998sk]. In the limit of three massless quark flavours, the relevant constraint for QLSS reads[@Kagan:2001zk][^24] $$\label{eq:WW}
\int_0^u dv \left[\phi_\parallel(v) - g^{(v)}_\perp(v)\right] = \bar u\left(g^{(v)}_\perp(u) - \frac{g^{(a)'}_\perp(u)}{4}\right) - \frac{g_\perp^{(a)}(u)}{4}\;,$$ which is used to eliminate the integral from . We also require the identity $$\label{eq:WW2}
u h_\parallel^{(t)}(u) + \frac{u}{2} h_\parallel^{(s)'}(u) = 2\int_0^u \left(h_\parallel^{(t)}(v) - \phi_\perp(v)\right) dv$$ in order to show gauge invariance in in $O^{\rm WA}_2$ results in appendix \[app:wa-formulae\]. To this end we note that Eqs.(\[eq:WW\],\[eq:WW2\]) follow from equations (4.15/16) and (3.21/22) in [@Ball:1998sk].
Photon DA {#app:photon-DA}
---------
The leading twist $2$ photon DA [@Ball:2002ps] is: $$\begin{aligned}
{2}
& \Braket{\gamma(q,\epsilon)|\bar q_a(x) [x,z] q_b(z)|0} = i e \int_0^1 d^4 y
\epsilon^*_\mu e^{i q \cdot y} {\Braket{0|T \bar q_a(x) [x,z] q_b(z) j_{\rm em}^\mu(y)|0}} =
\nonumber \\[0.1cm]
& \qquad \frac{iQ_q\Braket{\bar qq}}{4 N_c}\int_0^1 du e^{i(uq\cdot x + \bar uq\cdot z)}\big(
\phi_\gamma(u) \sigma^{\alpha \beta} \epsilon_\alpha q_\beta+ (x-z) \!\cdot\! \epsilon \big)_{ba} + \text{higher twist}\;.
\label{eq:photon-da}\end{aligned}$$ The first and second term on the last line correspond to the LHS of equation (2.7) in [@Ball:2002ps] and second term on the RHS of the same equation. The reason Eq. is not gauge invariant is that $[x,z]$ does not contain the QED (quantum electrodynamical) Wilson line as we expand in the external field to first order. Furthermore we have assumed the Lorentz gauge $\partial \cdot A =0$ through $A_\mu \to \epsilon_\mu e^{i q \cdot x}\;$[^25]. Note that the perturbative photon contribution has to be included separately. The asymptotic photon DA is given by $$\phi_\gamma(u) = 6\chi\bar uu \;,$$ where $\chi$ is the magnetic susceptibility of the quark condensate, calculated to be $\chi=-3.15(10){\,{\rm GeV}}^{-2}$ at $\mu=1{\,{\rm GeV}}$ in [@Ball:2002ps] (the sign is adjusted to our convention of the covariant derivative).
$B$-meson DA {#app:B-DA}
------------
The $B$-meson DA used in the QLSS diagrams is given in [@Beneke:2000wa; @Beneke:2000ry], $$\label{eq:fuller-BDA}
\begin{split}
{\Braket{0|\bar q_a(x) [x,z] b_b(0) |B(p_B)}}
&= \frac{-i f_B m_B}{4 N_c}\int_0^\infty dl_+ e^{-il\cdot x} \\
\times &\left.\left[
\frac{1+\slashed v}{2}\left\{\phi_+(l_+)\slashed n_+ + \phi_-(l_+)\left(\slashed n_- - l_+\gamma^\nu_\perp\frac{\partial}{\partial l^\nu_\perp}\right)\right\}\gamma_5
\right]_{ba}\right|_{l=\frac{l_+ n_+}{2}}
\end{split}$$ where $p_B=m_B v$ and $n_+$ and $n_-$ are light-like vectors $$\begin{aligned}
n_+^2 &= n_-^2 = 0 \;, &
n_+\cdot n_- &= 2 \;,\end{aligned}$$ for which $n_\pm = (1,0,0,\pm1)$ is a possible parametrisation. This allows an arbitrary vector $x$ to be written as $$\label{eq:lc-dec}
x^\mu = \frac{x_+ n_+^\mu + x_- n_-^\mu}{2} + x_\perp^\mu\;$$ and the scalar product of two such vectors reads: $$\label{eq:lc-SP}
x \cdot y = \frac{1}{2}(x_+ y_- + x_- y_+) + x_\perp
\cdot y_\perp \;.$$ The kinematics required for $B\to K^{(*)}(\gamma^* \to ll)$ are $$\begin{aligned}
\label{eq:lc-dynamics}
p_+ &= m_B - \frac{q^2}{m_B} \;, & p_- &= 0 \;, &
q_+ &= \frac{q^2}{m_B} \;, & q_- &= m_B\;,\end{aligned}$$ with $p_\perp = q_\perp = 0$.
Furthermore we take $\phi_+$ and $\phi_-$ to be the model functions defined in [@Grozin:1996pq] $$\begin{aligned}
\phi_+(\omega) &= \frac{\omega}{\omega_0^2}e^{-\omega/\omega_0} \;,&
\phi_-(\omega) &= \frac{1}{\omega_0}e^{-\omega/\omega_0} \;,\end{aligned}$$ with $\omega_0=2\Lambda_{\text{HQET}}/3 \simeq 0.4 {\,{\rm GeV}}$. Our results contain the moment functions $$\lambda_\pm^{-1}(q^2) = \int_0^\infty dl_+ \frac{\phi_\pm(\omega)}{l_+ - q^2/m_B - i\epsilon}$$ which evaluate to $$\begin{aligned}
\lambda_+^{-1}(q^2) &= \frac{1}{\omega_0}\left[1 + ye^{-y}(i\pi - \mathrm{Ei}(y))\right] \;, &
\lambda_-^{-1}(q^2) &= \frac{e^{-y}}{\omega_0}(i\pi - \mathrm{Ei}(y)) \;,\end{aligned}$$ where $y=q^2/\omega_0 m_B$ and the function $\mathrm{Ei}$ is the exponential integral.
### On corrections for QLSS within QCDF {#app:O(q2/mB2)}
We would like to discuss the origin of the ${\cal O}(q^2/m_B^2)$-corrections due to neglecting the $l_-$-direction and the $l_\perp$-derivative alluded to in section \[sec:quark-loop-spectator\]. Further comments can be found in that section.
- *Neglecting the $l_-$-direction:* We wish to stress a particular feature of the $B$-meson DA: it takes the form of a function of a light-cone coordinate. In the $B$-meson rest frame all components of the spectator quark momentum are expected to be of comparable magnitude ${{\cal O}}(\Lambda_{\mathrm{QCD}})$ and thus the special rôle of $l_+$ originates from the dynamics. It turns out that to leading order in $1/m_B$ the short distance part of the matrix element is only sensitive to the $l_+$ component of the light quark momentum[^26], and hence a light-cone DA is what is required [@Beneke:2000ry]. The next-leading order diagram in Fig. \[fig:quark-loop-spectator\] with photon emission next to the $B$-meson is sensitive to $(q-l)^2 = q^2 + l^2 - q_+ l_- - q_- l_+$ ($q_\perp =0$ in the notation of ) with $q_- = m_B$ and $q_+ = m_B (q^2/m_B^2)$. Thus at $q^2=0$ the process depends only on the $l_+$ direction but becomes increasingly sensitive to $l_-$ direction as $q^2$ rises. At $q^2 = 4 m_c^2$ this amounts to about a $30\%$-effect ($q_+/q_- \simeq 0.3$).
- *Neglecting the $l_\perp$ derivative:* The derivative w.r.t. $l_\perp$ will be $1/m_B$ suppressed, as compared to the other term coupling to $\phi_-(l_+)$, except for the case where the photon is emitted from the light quark originating from the $B$-meson (same diagram as discussed in the previous point). The effect on the corresponding light quark propagator $S_F$ is $$l_+ \gamma_\perp^\rho \frac{\partial}{\partial l_\perp^\rho}\gamma_5\gamma^\mu S_F(q-l)
= i l_+ \gamma_5 \gamma_\perp^\rho \gamma^\mu \left(\frac{\gamma^\rho_\perp}{(q-l)^2} + 2\frac{\slashed q-\slashed l}{(q-l)^4} l^\rho_\perp\right) = {\cal O}(\Lambda_{\mathrm{QCD}}/m_B) \;.$$ This comes about as follows: the second term vanishes by setting $l_\perp=0$ after taking the derivative. To analyse the first term we contract $\gamma^\rho_\perp \slashed\epsilon \gamma_{\perp,\rho}$ with a polarisation vector $\epsilon_\mu$, using the light-cone decomposition , $$l_+ \gamma^\rho_\perp \slashed \epsilon \gamma_{\perp,\rho}
= -l_+\left[\slashed n_+\epsilon_+ + \slashed n_-\epsilon_-\right] + l_+ \underbrace{\gamma^\rho_\perp \slashed\epsilon_\perp \gamma_{\perp,\rho}}_{=0} \;,$$ where the first part must be compared with the other structure coupling to $\phi_-(l_+)$: $$i \slashed n_- \slashed \epsilon (\slashed q-\slashed l) =
\frac{i}{4} \slashed n_-\left[\epsilon_+ q_- + \slashed \epsilon_\perp \slashed n_+ (q_+ + l_+)\right]$$ We therefore see that the derivative term is subleading in the $\epsilon_+$ coefficient by $l_+/q_-={\cal O}(\Lambda_{\mathrm{QCD}}/m_B)$. The $\epsilon_-$ coefficient must be related by gauge invariance; see appendix \[app:QL-GI\] for further discussion. At last we would like to mention that it would be interesting to study whether there is any significant change for $0 < q^2 < 4 m_c^2$.
Helicity projectors {#app:decay-width-tensors}
===================
As hinted in the main text the basis ${\cal T}_{1,2,3}$, or more precisely ${\cal T}_{2,3}$, is not ideal for addressing physical quantities. In the decay rate this emerges in two ways. First a particular direction namely zero helicity has to be ${\cal O}(m_V)$ and furthermore the directions ${\cal T}_{2,3}$ are not orthogonal to each other. In the main text we have given the transformation to the helicity basis $h_{0,\pm}$ in Eq. . We shall give the Lorentz structures for the latter and discuss a few more details. As in we define:
$$\begin{aligned}
_{\rm out}\left\langle V(p,\eta) l^+(l_1) l^-(l_2)\mid B(p+q)\right\rangle_{\rm in} &= \frac{G_F}{\sqrt 2}\lambda_t \frac{\alpha}{q^2\pi}
\left({\mathcal{T}}^{V\mu}\bar u(l_1)\gamma_\mu v(l_2) + {\mathcal{T}}^{A\mu}\bar u(l_1)\gamma_\mu\gamma_5 v(l_2)\right) \;, \nonumber \end{aligned}$$
where $${\mathcal{T}}^{(V,A)\mu} = \sum_{i = \pm,0} {h}^{(V,A)} P_i^\mu \;,$$ and the helicity basis tensors are given by $$\begin{aligned}
P^\mu_\pm &=
\frac{1}{\sqrt{2}}\left[2\epsilon^{\mu\nu\rho\sigma}\eta_\nu p_\rho q_\sigma \mp \frac{i}{\sqrt{\lambda_V}}
\left(\lambda_{V} m_B^2 \eta^\mu -
2(\eta\cdot q)\left((1-\hat m_V^2-\hat q^2)p^\mu - 2\hat m_V^2 q^\mu\right) \right)\right]
\;, \nonumber \\
P_0^\mu &= \frac{4 i \hat m_V}{ \sqrt{2\hat q^2 \lambda_{V}}}(\eta\cdot q) \left[2 \hat q^2 p^\mu - (1- \hat m_V^2-\hat q^2) q^\mu \right] \;. \nonumber\end{aligned}$$ Writing $\vec{P}_h = (P_0,P_+,P_-)$ and $\vec{P} = (P_1,P_2,P_3)$, suppressing a Lorentz index for the time being, the transformation follows from the transformation through $\vec{P}_h = (B^T)^{-1} \vec{P}$. The Lorentz structures have the following properties: $q \cdot P_{\pm,0} = 0$ and $p \cdot P_{\pm} = 0$. It seems worthwhile to mention that the $m_V$-factor in $P_0^\mu$ cancels against the $1/m_V^2$ originating from the polarisation sum: $\sum_{\text{pol.}} = \eta_\mu \eta_\nu = (p_\mu p_\nu/m_V^2-g_{\mu\nu})$. This assures finiteness of the rate as $m_V$ approaches zero, provided that ${h}_0 = {\cal O}(m_V^0)$.
Gauge invariance {#app:gauge-invariance}
================
WA contact terms and gauge invariance {#app:wa-gauge-invariance}
-------------------------------------
Before discussing the problem in more detail let us state a few general facts, some of which have already been stated in the main text.
- GI is satisfied in $Q_b$ and $Q_q$ terms separately.
- When there is ISR as well as FSR then one needs to approximate ISR and FSR consistently in order for (i) to be true.
- In the neutral case (i.e. $Q_b = Q_q$), (ii) can be circumvented, at the cost of (i), as ISR and FSR are separately gauge invariant.
- Statement (ii) can be circumvented in the case when the four quark operator is of the current-current type (${\cal O}^{{\rm WA}}_{5-8}$ ). In this case FSR corresponds to a contact term, up to corrections ${\cal O}(m_{q,s})$, which is easily computed using the weak WI.
In previous computations [@Ali:1995uy; @Khodjamirian:1995uc], as discussed in [@Khodjamirian:2001ga] in more clarity, (iv) applied as in the SM only ${\cal O}^{{\rm WA}}_{5-8}$-type are significant in the absence of CKM suppression; then (ii) does not apply as there is either only ISR or FSR c.f.Tab. \[tab:OWA\]. Inspecting Tab. \[tab:OWA\] we see that ${\cal O}^{{\rm WA}}_4$ for the $K$ is the only problematic case which we shall discuss in some more detail in subsection \[app:wa-contact-terms\] below. Furthermore statement (iv) is explained in section \[app:vector-current\]. The modification of the issue of contact terms for $q^2 =0$, which implies substituting the quark condensate terms ${\Braket{qq}}/q^2$ for the the photon DA, is outlined in appendix \[app:qq-photonDA\].
### Eliminating parasitic cuts - spurious momentum $k$ {#app:wa-contact-terms}
It is at this point we must point out that factorising the WA matrix elements conceals a problem in constructing sum rules: the problem of parasitic cuts. As shown in Fig. \[fig:wa-k-extended\](left) a naïvely constructed sum rule will receive contributions from cuts which do not have the same quantum numbers as the $B$-meson. A solution to this problem was introduced in [@Khodjamirian:2000mi] where spurious momentum $k$ is introduced at the weak vertex, which gives the second cut in Fig. \[fig:wa-k-extended\](left) momentum $(p_B-k)^2$ which is distinct from $p_B^2$ of the first cut. How the effect of the momentum $k$ is eliminated from the final result is to be discussed shortly below. We use the momentum assignments shown in Fig. \[fig:wa-k-extended\](right) and reuse the modified basis tensors from [@DLZ12], which are given by $$p_T^\rho = i \left[Q^\rho - \frac{q^2}{Q \cdot (p_B+p)} (p_B + p)^\rho\right] \;, \quad
\bar p_{\bar T}^\rho = i \left[k^\rho - \frac{k \cdot Q}{Q \cdot (p_B+p)} (p_B + p)^\rho\right]
\;,
\label{eq:ps-extended-basis}$$ where $Q \equiv q - k$. Amongst the possible six invariants four are fixed as $$\begin{aligned}
p^2 &= m_{V,P}^2 = 0 &
k^2 &= 0 &
Q^2 &= q^2\end{aligned}$$ and the remaining two invariants $p_B^2$ and $P^2 = (p_B -k)^2$ correspond to the two cuts shown in Fig. \[fig:wa-k-extended\](left). $p_B^2$ is the dispersion variable and the second cut variable $P^2 = (p_B -k)^2$, is the only trace of the spurious momentum. This is eliminated by setting $P^2 = m_B^2$ as $p_B^2 \simeq m_B^2$ by virtue of Eq. . After projection onto this extended basis, the coefficient of $p_T^\rho$ corresponds to the coefficient of $P_T^\rho$ which appears in the decay rate.
![(left) Momentum assignments for $B\to K\gamma^*$ including an additional momentum at the weak vertex. (right) Dashed lines denote possible cuts with momentum $(p+q)^2$ flowing through them, which contribute to a naïve sum rule. The right hand cut is a parasite because the lines it cuts do not have the quantum numbers of the $B$-meson so should not contribute to a dispersion relation for the $B$-meson current current $J_B$.[]{data-label="fig:wa-k-extended"}](wa-parasite "fig:"){width="44.00000%"} ![(left) Momentum assignments for $B\to K\gamma^*$ including an additional momentum at the weak vertex. (right) Dashed lines denote possible cuts with momentum $(p+q)^2$ flowing through them, which contribute to a naïve sum rule. The right hand cut is a parasite because the lines it cuts do not have the quantum numbers of the $B$-meson so should not contribute to a dispersion relation for the $B$-meson current current $J_B$.[]{data-label="fig:wa-k-extended"}](wa-k-extended "fig:"){width="51.00000%"}
### Vector & axial $4$-quark operators and the weak WI {#app:vector-current}
In this subsection we dwell in more detail on how point (iv) at the beginning of this appendix unfolds. According to statement (ii) ISR and FSR then ought to be treated consistently, as for instance outlined in the previous subsection, in order to maintain GI. The problem in distinguishing the two cuts shown in Fig.\[fig:wa-k-extended\](right) applies only to the FSR diagram[^27]. We shall see just below that in the case where the current with kaon quantum numbers is of the vector and axial type the diagram is a pure contact term by virtue of the weak WI and only produces a gauge variant part. This means that it does not carry any non-trivial dynamics and that its sole purpose is to render the matrix element gauge invariant. Furthermore we note that adding a spurious momentum does not have any impact on the diagram. In two subsequent paragraphs we are going to show this through the weak WI and infer the same result by sketching an explicit computation.
#### Weak WI {#app:weakWI}
Consider the FSR for the operator ${\cal O}_6^{{\rm WA}}$ at leading order ${\cal O}(\alpha_s^0)$, $$\begin{aligned}
{\Braket{K^* \gamma|\bar s\gamma^\mu q|0}} {\Braket{0|\bar q\gamma_\mu\gamma_5 b|B}}
&=& -e f_B (p_B)_\mu \epsilon_\nu \int_x e^{-ip_B \cdot x} {\Braket{K^*|T \bar s\gamma^\mu q(x) J^\nu_{\text{em}}(0)|0}} \nonumber \\[0.1cm]
&=& - e f_B \epsilon_\nu \int_x e^{-ip_B \cdot x} {\Braket{K^*| i \partial_\mu \left\{ T \bar s\gamma^\mu q(x) J^\nu_{\text{em}}(0) \right\} |0}} \nonumber \\[0.1cm]
&=& ie(Q_q-Q_s) f_B \epsilon_\nu {\Braket{K^*(p,\eta)|\bar s\gamma^\nu q(0)|0}} \nonumber \\[0.1cm] &=& ie (Q_q-Q_s) f_B f_{K^*}m_{K^*}(\eta\cdot\epsilon)
\label{eq:wa-by-wti}\end{aligned}$$ where we have used ${\Braket{0|\bar q\gamma_\mu\gamma_5 b(0)|B(p+q)}} = if_B(p+q)_\mu$ in the first equality, $$\label{eq:weakWI}
\text{weak WI:} \quad \partial_\mu \bar s\gamma^\mu q(x) = {\cal O}(m_s-m_q) \to 0$$ in the second equality and $[Q, {\cal O}] = Q_{\cal O} {\cal O}$ ($Q=\int d^3 x J_{\rm em}^0$) in the third equality. The last step is due to the definition of the $K^*$ decay constant: ${\Braket{K^*(p,\eta)|\bar s\gamma^\nu q(0)|0}}=m_{K^*}f_{K^*}\eta^\nu$. As stated previously this contribution is a pure gauge variant term. Adding a spurious momentum $p_B \to p_B -k$ would not change anything in the derivation. Similarly we find for the $K$: $$\label{eq:seconds}
{\Braket{K \gamma |\bar s\gamma^\mu\gamma_5 q|0}} {\Braket{0|\bar q\gamma_\mu\gamma_5 b|B}} = e (Q_q-Q_s)f_B f_K (p\cdot\epsilon)$$ We would like to remark that the results in (\[eq:wa-by-wti\],\[eq:seconds\]) are correct to all orders in QCD (with $m_q = 0$).
In summary the weak WI replaces the computation. In the next paragraph we shall outline the main points of the explicit LC-OPE computation which comes to the same conclusion.
#### Explicit computation {#app:explicit}
We would like to mention one additional point: the reader may wonder whether we could have simply used the $K^*$ DAs in , worked out the result and not had to concern ourselves with arguments based on WIs. It turns out that is in fact insufficient for this purpose and the Wandzura–Wilczek type relation has to be used. We have checked that this leads to the same result up to $O(m_{K^*}^2)$ terms. The latter are of twist-$4$ and expected to be there as we have consistently neglected them throughout this work.
### Remarks on gauge invariance and contact terms at $q^2 =0$. {#app:qq-photonDA}
At $q^2 =0$ the ${\Braket{\bar q q}}$-term from the light quark propagator, originating from the interpolating current $J_B$, have to replaced by the photon DA. This gives rise to a puzzle as the former are gauge variant whereas DA are usually GI. The resolution is, as we shall see, that the photon DA is QED gauge variant.
Generally for $q^2 \neq 0$ and for ${\cal O}^{{\rm WA}}_{5-8}$ the term with FSR produces solely a gauge variant contact term proportional to $Q_q-Q_b$ c.f. as discussed in subsection \[app:weakWI\]. GI is restored by a gauge variant term coming from ISR. As discussed in the main text section \[sec:WAq2eq0\] for $q^2 =0$ the the $Q_q {\Braket{\bar qq}}$ is replaced by a photon DA term as depicted in Fig. \[fig:wa-diagram-lcope\]. This means that the ISR and FSR cancellation of gauge non-invariant terms at the $(Q_q - Q_b) {\Braket{\bar q q}}$-level implies that the matrix element used for the photon DA, which is usually gauge invariant, is gauge variant! This is indeed the case as the QED Wilson line is absent in the matrix element as we expand in the external electromagnetic field. This can be seen explicitly from the corresponding matrix element which is the sum of an explicit gauge invariant plus a gauge variant term. We have checked that, by working in the Lorentz gauge $\partial \cdot A =0$[^28], which is consistent with $A_\mu \to \epsilon_\mu e^{i q \cdot x}$, that the gauge variant term (corresponding to the second term on the RHS of ) conspires with the gauge variant terms from the other diagram in Fig. \[fig:wa-diagram-ope\](right) to produce a term proportional to $Q_q-Q_b$ which combines with the contact term Eq. \[eq:wa-by-wti\] and leads to a gauge invariant result.
QLSS and gauge invariance {#app:QL-GI}
-------------------------
The issue of GI for spectator scattering, in section \[sec:quark-loop-spectator\], at $q^2 \neq 0$ is not straightforward. In principle we would expect the two diagrams, by which we mean photon emission form the spectator quark, in Fig. \[fig:quark-loop-spectator\] to be GI. The computation used in [@Feldmann:2002iw][^29], which we reproduced in this paper for non-SM operators, can only be expected to respect GI at leading order. Yet, since GI mixes different orders a rigourous test cannot be expected. The recipe of the pragmatist is then subtract the amount of next leading term that renders the leading term GI. We shall discuss it in more detail below and see that a pole in $1/q^2$ supports our argumentation from another point of view.
In full generality, the $B\to K^* l^+l^-$ decay may be parametrised: $$\begin{split}
& {\Braket{K^*(\eta,p) \gamma^*(q,\mu)|\mathcal H_{\mathrm{eff}}|B(p+q)}} \\
& \equiv U^\mu(q^2) = (\eta\cdot q)p^\mu U_p(q^2) + (\eta\cdot q) q^\mu U_q(q^2) + \eta^\mu (p\cdot q) U_\eta(q^2) + i\epsilon^{\mu\nu\rho\sigma} \eta_\nu p_\rho q_\sigma U_\epsilon(q^2) \;.
\end{split}$$ QED GI requires the following WI to hold: $$\label{eq:WIx}
0 = q_\mu U^\mu(q^2) = (\eta\cdot q)\left[(p\cdot q) U_p(q^2) + q^2 U_q(q^2) + (p\cdot q) U_\eta(q^2)\right] \;.$$ In best of all worlds, where GI is obeyed exactly, we may choose to eliminate any function by virtue of the equation above. For example we could solve for either $$\begin{aligned}
{2}
\label{eq:failure}
& \text{{\ding{55}}} \qquad &U_q(q^2) \to& -\frac{p\cdot q}{q^2} \left[U_p(q^2) + U_\eta(q^2)\right] \;, \\
\label{eq:procedure}
& \text{{\ding{51}}} &U_p(q^2) \to& -U_\eta(q^2) - \frac{q^2}{p\cdot q}U_q(q^2)\; .\end{aligned}$$ For to be well defined the following relation must hold: $$\label{eq:lacondition}
U_p(0) + U_\eta(0) = 0 \;,$$ or $U_q(q^2) $ behaves as $1/q^2$, which is not acceptable.[^30] Since $U_p p_\mu$ is power suppressed with respect to $U_q q_\mu$, c.f. , we cannot expect to hold, however applying does work since in contrast to it does not contain any $m_B^2/q^2$ enhancement. Note for the $K$-meson the same discussion applies with $U_\eta|_{K} = 0$ from the start. The term $U_\epsilon$ is of no relevance for the discussion here.
We will illustrate this procedure in the case of $B\to K l^+ l^-$. The result in this case is $$U^\mu \propto \frac{(l_+ m_B - 2q^2)p^\mu + 2(p \cdot q) q^\mu}{l_+ m_B - q^2}
= 2\frac{(p\cdot q) q^\mu - q^2 p^\mu}{l_+ m_B - q^2} + \frac{l_+ m_B p^\mu}{l_+ m_B - q^2} \;.$$ Our procedure ($U_{\eta}|_{K}=0$) demands that $U_p = -(q^2/(p \cdot q)) \, 2 (p \cdot q) (l_+m_B -q^2)$, which amounts to dropping the second term on the RHS. This ensures GI. We reemphasize that if the $1/m_b$-expansion was implemented to all orders GI would have been automatic.
Details of calculation
======================
Input values {#app:inputvalues}
------------
Here we summarise the numerical input to our calculation for convenience of the reader. We compute $\alpha_s$ using 2-loop running with 4 or 5 active flavours, with $M_Z=91.1876(21){\,{\rm GeV}}$, $\alpha_s(M_Z)=0.1184(7)$ and $m_b(m_b)=4.18(3){\,{\rm GeV}}$ in the $\overline{\rm MS}$ scheme [@Beringer:1900zz]. We use $b$ and $c$ quark masses adapted for the pole mass scheme $m_c = 1.4(1)$ and $m_b=4.7(1){\,{\rm GeV}}$ in all other cases. We use a lattice average $f_B=191(5)$ [@Bazavov:2011aa; @Na:2012kp] when not calculating sum rules, i.e. in the computation of $F_{(2,4),i}$ . Inputs used to compute WCs are given below Table. \[tbl:wilson-coefficient-example\]. We compute the CKM matrix elements using a Wolfenstein parametrisation expanding up to ${{\cal O}}(\lambda^2)$ [@Wolfenstein:1983yz; @Buras:1994ec] with the parameters $\lambda=0.2254(7)$, $A=0.81(2)$, $\bar\rho=0.131(26)$ and $\bar\eta=0.345(14)$ [@Beringer:1900zz]. For the $\alpha_{\rm CKM}$ dependence of $\delta_{a_I}$ , we fix the magnitude $|\lambda_u/\lambda_t|$ from the Wolfenstein parametrisation. All hadronic inputs for the light mesons are as given in our previous paper [@DLZ12]. The new input $\mu_K^2=f_K m_K^2/m_s$ is computed using $m_s(2{\,{\rm GeV}})=95(5){\,{\rm MeV}}$ [@Beringer:1900zz]. The condensates ${\Braket{\bar qq}}$ and ${\Braket{\bar qGq}}$ are taken to be ${\Braket{\bar qq}}(1{\,{\rm GeV}})=(-0.24(1){\,{\rm GeV}})^3$ and ${\Braket{\bar qGq}}(1{\,{\rm GeV}})=(0.8(1) {\,{\rm GeV}})^2 {\Braket{\bar qq}}$ [@DLZ12].
Error estimation {#app:uncertainty}
----------------
We compute error estimates in the following way: the central value of a result is computed using the central values of all inputs. To compute the error, we then generate a list of pseudo-random sample points from the probability distributions of the input parameters, and compute the result for each sample point.
For a function $f(x)$, where $x$ represents all $N$ input parameters and is thus $N$-dimensional, the variance is estimated as $$\sigma^2 = \frac{1}{n-1}\sum_{i=1}^n (f(x_i) - f(x_c))^2 \;,$$ where $x_c$ is the central values of the input parameters, and not included in $x_i$, and $n$ is the number of sample points used to compute an error estimate, excluding the central value $x_c$. The points $x_i$ are generated from the $N$-dimensional probability distribution of input parameters; note that $x_i$ is varied for all parameters simultaneously, so *none* of its elements are equal to the central value of any input parameter. In effect, this is a primitive Monte Carlo integration over the input parameter distribution space. All input parameters are assumed to be Gaussian distributed with standard deviation equal to their quoted error, except for the renormalisation scale, to be discussed below. We assign the functions $h_{0,\pm}$ and $h_T$ an error of 20%, which arises from the uncertainty in the form factors $T_i$, $A_{1,3}$, $V$ and $f_{+,T}$ and non form factor corrections. We impose this at the level of the $h$ functions so that constraints such as and $h_+\sim{{\cal O}}(1/m_B)$ are maintained.
To compute the scale uncertainty only 3 points are sampled: $\mu$, $\mu/2$ and $2\mu$. The renormalisation scale is set to $\mu$ to compute the central value of a result. The error is computed as $$\sigma^2_\mu = \frac{1}{2n-1}\sum_{i=1}^{n}\left[\left(f\left(\frac{\mu}{2}\right) - f(\mu)\right)^2 + \left(f(2\mu) - f(\mu)\right)^2\right] \;,$$ although in practice this is implemented by generating a $2n$ pseudo-random numbers $y_i$ in $[0,1]$ and selecting $\mu/2$ or $2\mu$ depending on whether $y>0.5$. This may then be incorporated into the same procedure as sampling all other input parameters. We take the central renormalisation scale $\mu=m_b=4.7 {\,{\rm GeV}}$ for all processes except QLSS and ${{\cal O}}_8$, which we take to be $\mu'=\sqrt{\Lambda_H\mu}$, where $\Lambda_H=0.5(2){\,{\rm GeV}}$ as in [@DLZ12].
Wilson coefficients {#app:wilson-coefficients}
-------------------
Although we specify our results in the BBL basis [@Buchalla:1995vs] our calculation is carried out in the CMM basis [@Chetyrkin:1996vx] $$\mathcal H_{\mathrm{eff}} = \frac{G_F}{\sqrt 2}\left( \sum_{i=1}^2
(\lambda_u C^{\rm CMM}_i \mathcal Q_i^u + \lambda_c C^{\rm CMM}_i \mathcal Q_i^c ) - \lambda_t \sum_{i=3}^{10} C^{\rm CMM}_i \mathcal Q_i \right) \;,$$ where $\mathcal Q_{7-10}=\mathcal O_{7-10}$ and the four quark operators are given by $$\begin{aligned}
\mathcal Q_1^q &= 4(\bar s_L\gamma_\mu T^a q_L)(\bar q\gamma^\mu T^a b_L) &
\mathcal Q_2^q &= 4(\bar s_L\gamma_\mu q_L)(\bar q\gamma^\mu b_L) \nonumber \\
\mathcal Q_3 &= 4(\bar s_L\gamma_\mu b_L) \sum_q (\bar q\gamma^\mu q) &
\mathcal Q_4 &= 4(\bar s_L\gamma_\mu T^a b_L) \sum_q (\bar q\gamma^\mu T^a q) \nonumber \\
\mathcal Q_5 &= 4(\bar s_L\gamma_\mu\gamma_\nu\gamma_\rho b_L) \sum_q (\bar q\gamma^\mu\gamma^\nu\gamma^\rho q) &
\mathcal Q_6 &= 4(\bar s_L\gamma_\mu\gamma_\nu\gamma_\rho T^a b_L) \sum_q (\bar q\gamma^\mu\gamma^\nu\gamma^\rho T^a q) \;,\end{aligned}$$ with $2q_L = (1-\gamma_5)q$. We transform into the BBL basis following the recipe in appendix A of [@Beneke:2001at]; our $C_i$ are equivalent to the $\bar C_i$ in [@Beneke:2001at] and are *defined* by a linear transform from $C^{\rm CMM}_i$. This linear transform reproduces BBL WCs at $O(\alpha_s^0)$.
We calculate the WCs to NNLL order. The calculation is carried out as described in the appendix of [@Beneke:2001at] using the full anomalous dimension matrix computed in [@Czakon:2006ss], at fixed $N_f=5$, and initial conditions are computed at $\mu=M_W$ as described therein using the NNLO expressions in [@Bobeth:1999mk] for $C_{1-6}$ and $C_{9,10}$ and those in [@Misiak:2004ew] for $C_{7,8}^{\mathrm{eff}}$. An example of the result of this calculation is given in Tab. \[tbl:wilson-coefficient-example\].
-- --------- --------- --------- ---------
CMM BBL CMM BBL
-0.2622 -0.1311 -0.5636 -0.2818
1.0087 1.0524 1.0299 1.1238
-0.0051 0.0110 -0.0175 0.0194
-0.0778 -0.0316 -0.1718 -0.0524
0.0003 0.0087 0.0012 0.0132
0.0009 -0.0371 0.0042 -0.0775
-- --------- --------- --------- ---------
: WCs at $\mu=m_b$ and $\mu=\sqrt{m_b\Lambda_H}$ at NNLL order for $m_b=4.7 \mathrm{GeV}$, $M_W=80.4 {\,{\rm GeV}}$, $\sin^2\theta_W=0.23$, $m_t=177 \mathrm{GeV}$, $\Lambda_H=0.5 \mathrm{GeV}$ and $\Lambda^{(5)}_{\mathrm{QCD}}=214 \mathrm{MeV}$ in two different bases. Three loop running for $\alpha_s$ is used. The BBL basis we use is that defined in [@Beneke:2001at]; it is equivalent to the traditional basis defined in [@Buchalla:1995vs] at leading order. We use the CMM basis [@Chetyrkin:1996vx] for loop calculations. The BBL coefficients presented here are defined in terms of a linear transform of the CMM coefficients as explained in the text. []{data-label="tbl:wilson-coefficient-example"}
Numerical evaluation of $\delta_{a_I}$ from PDG values {#app:delta-ai-calc}
------------------------------------------------------
In terms of experimentally measured quantities, $\delta_{a_I}$ is $$\delta_{a_I} = 1 -
\left|\frac{V_{\rm ts}}{V_{\rm td}}\right|
\frac{2\frac{\tau_{B^+}}{\tau_{B^0}} \mathcal B(B^0\to\rho^0\gamma) - \mathcal B(B^+\to\rho^+\gamma)}{\frac{\tau_{B^+}}{\tau_{B^0}}\mathcal B(B^0\to K^{*0}\gamma) - \mathcal B(B^+\to K^{*+}\gamma)}
\sqrt{\frac{\frac{\tau_{B^+}}{\tau_{B^0}}\mathcal B(B^0\to K^{*0}\gamma) + \mathcal B(B^+\to K^{*+}\gamma)}{2\frac{\tau_{B^+}}{\tau_{B^0}} \mathcal B(B^0\to\rho^0\gamma) + \mathcal B(B^+\to\rho^+\gamma)}}$$ We use the values [@Beringer:1900zz] $$\begin{aligned}
\frac{\tau_{B^+}}{\tau_{B^0}} &= 1.079(7) &
\left|\frac{V_{\rm td}}{V_{\rm ts}}\right| &= 0.211(7) \nonumber \\
\mathcal B(B^+\to\rho^+\gamma) &= 9.8(2.5)\times10^{-7} &
\mathcal B(B^0\to\rho^0\gamma) &= 8.6(1.5)\times10^{-7} \\
\mathcal B(B^+\to K^{*+}\gamma) &= 4.21(18)\times10^{-5} &
\mathcal B(B^0\to K^{*0}\gamma) &= 4.33(15)\times10^{-5} \nonumber\end{aligned}$$ and combine all errors in quadrature to get the result . The main error comes from the ratio of differences, that is to say the isospin asymetries themselves, with approximately equal parts from the numerator and the denominator.
Results {#app:results}
=======
Tabulated results for four Fermi operators {#app:tables}
------------------------------------------
We provide numerical data corresponding to Figs. \[fig:1\] and \[fig:2\] in Tabs. \[tab:1\] and \[tab:2\], at $1 {\,{\rm GeV}}^2$ intervals in $q^2$. Data for Figs. \[fig:1rho\] and \[fig:2rho\] are given in Tab. \[tab:1rho\]. We also provide data for $B\rightarrow (K^*,\rho)\gamma$, denoted by $q^2=0$ in Tabs. \[tab:1\] and \[tab:1rho\] respectively.
--------------------------------------------------- -------- -------- -------- -------- -------- -------- -------- --------
$B\rightarrow Kll$ 1 2 3 4 5 6 7 8
$a^u_{4} = 0.1$ 0.35% 0.14% -0.03% -0.15% -0.23% -0.27% -0.28% -0.25%
$a^u_{8}$ 0.68% 0.60% 0.63% 0.64% 0.62% 0.58% 0.53% 0.47%
$a^d_{4}$ -0.10% -0.13% -0.18% -0.21% -0.22% -0.23% -0.22% -0.20%
$a^d_{8}$ 0.35% 0.31% 0.33% 0.33% 0.32% 0.30% 0.27% 0.24%
$s^{SU(3)}_{1(R,L)}$ = 1 1.28% 0.68% 0.35% 0.18% 0.08% 0.04% 0.01% -0.01%
$s^{c}_{1(R,L)}$ 0.88% 0.60% 0.39% 0.25% 0.16% 0.11% 0.07% 0.04%
$s^{b}_{1(R,L)}$ -0.20% -0.34% -0.31% -0.25% -0.20% -0.15% -0.12% -0.09%
$s^{c}_{2(R,L)}$ -4.68% -3.94% -3.13% -2.46% -1.96% -1.57% -1.25% -0.91%
$s^{b}_{2(R,L)}$ 5.03% 1.75% 0.03% -1.04% -1.76% -2.25% -2.51% -2.44%
${C}_{1}$ Tab. \[tbl:wilson-coefficient-example\] -0.00% -0.00% -0.00% -0.00% -0.00% -0.00% -0.00% -0.00%
${C}_{2}$ -0.84% -0.45% -0.22% -0.10% -0.03% 0.01% 0.03% 0.04%
${C}_{3}$ 0.02% 0.04% 0.04% 0.04% 0.04% 0.04% 0.03% 0.03%
${C}_{4}$ -0.11% -0.21% -0.28% -0.31% -0.31% -0.29% -0.27% -0.24%
${C}_{5}$ 0.01% -0.00% -0.01% -0.02% -0.03% -0.03% -0.03% -0.03%
${C}_{6}$ 0.20% 0.23% 0.30% 0.35% 0.39% 0.41% 0.39% 0.34%
${C}_8^{\rm eff}$ -0.22% -0.09% -0.02% 0.02% 0.05% 0.08% 0.09% 0.09%
SM total -0.93% -0.48% -0.20% -0.01% 0.12% 0.20% 0.24% 0.24%
--------------------------------------------------- -------- -------- -------- -------- -------- -------- -------- --------
: Breakdown of contributions to $B\rightarrow Kll$ isospin asymmetry in SM operator coefficients ${C}_i$, and in a generalised basis of four quark WA operators with coefficients $a_i$ and QLSS contributions with coefficients $s^q_{x\chi}$. We use $a^q_i=0.1$ and $s^q_{x,\chi}=1$ to produce these values.[]{data-label="tab:2"}
--------------------------------------------------- -------- -------- -------- -------- -------- -------- -------- -------- --------
$B\rightarrow K^*ll$ 0 1 2 3 4 5 6 7 8
$a^u_{2} = 0.1$ -1.55% -0.22% -0.00% 0.06% 0.08% 0.08% 0.07% 0.06% 0.06%
$a^u_{4}$ -1.58% -0.33% -0.09% -0.00% 0.02% 0.03% 0.04% 0.03% 0.03%
$a^u_{5}$ 1.29% -0.07% 0.02% 0.00% -0.00% 0.00% 0.01% 0.02% 0.03%
$a^u_{6}$ -0.84% -0.53% -0.64% -0.67% -0.65% -0.60% -0.54% -0.47% -0.42%
$a^u_{9}$ 10.3% -0.20% 0.23% 0.03% -0.02% 0.02% 0.10% 0.17% 0.26%
$a^u_{10}$ 10.5% 0.43% 0.40% 0.13% 0.08% 0.14% 0.24% 0.34% 0.47%
$a^d_{2} = 0.1$ -2.85% -0.40% -0.00% 0.12% 0.15% 0.15% 0.14% 0.12% 0.11%
$a^d_{4}$ -2.91% -0.61% -0.17% -0.01% 0.05% 0.07% 0.07% 0.07% 0.06%
$a^d_{5}$ 0.78% 0.00% 0.02% 0.00% -0.00% -0.00% -0.00% 0.00% 0.01%
$a^d_{6}$ -0.50% -0.30% -0.34% -0.35% -0.33% -0.31% -0.27% -0.24% -0.21%
$a^d_{9}$ 6.23% 0.18% 0.20% 0.02% -0.04% -0.03% 0.00% 0.04% 0.08%
$a^d_{10}$ 6.29% 0.45% 0.24% 0.03% -0.03% -0.01% 0.04% 0.09% 0.16%
$s^{SU(3)}_{1R} = 1$ 0.00% -1.26% -0.75% -0.38% -0.18% -0.08% -0.03% -0.01% 0.00%
$s^{c}_{1R}$ 0.00% -0.90% -0.67% -0.43% -0.26% -0.16% -0.10% -0.06% -0.03%
$s^{b}_{1R}$ 0.01% 0.20% 0.38% 0.34% 0.26% 0.19% 0.14% 0.10% 0.08%
$s^{SU(3)}_{1L}$ -0.28% 0.81% 0.58% 0.36% 0.21% 0.12% 0.06% 0.03% -0.00%
$s^{c}_{1L}$ -0.40% 0.67% 0.57% 0.42% 0.30% 0.22% 0.16% 0.11% 0.07%
$s^{b}_{1L}$ 0.95% -0.00% -0.28% -0.33% -0.31% -0.26% -0.22% -0.18% -0.14%
$s^{c}_{2R}$ 1.59% -1.82% -1.96% -1.64% -1.27% -0.97% -0.73% -0.54% -0.36%
$s^{b}_{2R}$ 5.03% 8.33% 3.25% 0.12% -1.56% -2.38% -2.67% -2.62% -2.28%
$s^{c}_{2L}$ 0.02% 2.43% 2.21% 1.66% 1.19% 0.85% 0.61% 0.44% 0.29%
$s^{b}_{2L}$ 0.05% -4.60% -1.84% -0.05% 0.98% 1.56% 1.83% 1.88% 1.69%
${C}_{1}$ Tab. \[tbl:wilson-coefficient-example\] -0.01% -0.00% -0.00% -0.00% -0.00% -0.00% -0.00% -0.00% -0.00%
${C}_{2}$ 0.11% -0.71% -0.44% -0.24% -0.12% -0.06% -0.02% 0.01% 0.03%
${C}_{3}$ 0.09% 0.01% 0.04% 0.04% 0.05% 0.04% 0.04% 0.03% 0.03%
${C}_{4}$ -0.98% -0.08% -0.25% -0.30% -0.31% -0.30% -0.28% -0.26% -0.24%
${C}_{5}$ -0.51% -0.09% -0.02% 0.01% 0.02% 0.02% 0.02% 0.02% 0.01%
${C}_{6}$ 6.41% 1.40% 0.40% 0.03% -0.11% -0.17% -0.18% -0.18% -0.17%
${C}_8^{\rm eff}$ -0.19% -0.34% -0.14% -0.02% 0.05% 0.09% 0.10% 0.10% 0.09%
SM total 4.92% 0.18% -0.42% -0.48% -0.44% -0.38% -0.33% -0.28% -0.24%
--------------------------------------------------- -------- -------- -------- -------- -------- -------- -------- -------- --------
: Breakdown of contributions to $B\rightarrow K^*ll$ isospin asymmetry in SM operator coefficients ${C}_i$, and in a generalised basis of four quark WA operators with coefficients $a_i$ and QLSS contributions with coefficients $s^q_{x\chi}$. We use $a^q_i=0.1$ and $s^q_{x,\chi}=1$ to produce these values. The $q^2=0$ value corresponds to the process $B\rightarrow K^*\gamma$ and is computed slightly differently to $B\rightarrow K^*ll$ as described in section \[sec:WAq2eq0\]. The value for $s^f_{1R}$ and $s^f_{2L}$ are zero at $q^2 = 0$ as a consequence of $h_+(0) = 0$ in our approximation.[]{data-label="tab:1"}
--------------------------------------------------- -------- -------- -------- -------- -------- -------- -------- -------- --------
$B\rightarrow \rho ll$ 0 1 2 3 4 5 6 7 8
$a^u_{2} = 0.1$ -1.55% -0.23% -0.01% 0.05% 0.07% 0.07% 0.07% 0.06% 0.06%
$a^u_{4}$ -1.59% -0.33% -0.09% -0.01% 0.02% 0.04% 0.04% 0.04% 0.03%
$a^u_{5}$ 1.25% -0.06% 0.02% 0.00% -0.00% 0.00% 0.01% 0.02% 0.03%
$a^u_{6}$ -0.81% -0.62% -0.72% -0.74% -0.71% -0.66% -0.59% -0.52% -0.46%
$a^u_{9}$ 11.0% -0.20% 0.26% 0.04% -0.02% 0.03% 0.11% 0.19% 0.28%
$a^u_{10}$ 11.1% 0.45% 0.43% 0.14% 0.07% 0.12% 0.23% 0.33% 0.47%
$\tilde{a}^d_{2} = 0.1$ -3.10% -0.46% -0.03% 0.11% 0.14% 0.15% 0.14% 0.12% 0.11%
$\tilde{a}^d_{4}$ -3.17% -0.65% -0.18% -0.01% 0.05% 0.07% 0.07% 0.07% 0.07%
$\tilde{a}^d_{5}$ 0.76% 0.00% 0.02% 0.00% -0.00% -0.00% -0.00% 0.00% 0.01%
$\tilde{a}^d_{6}$ -0.48% -0.34% -0.38% -0.38% -0.37% -0.34% -0.30% -0.26% -0.23%
$\tilde{a}^d_{9}$ 6.62% 0.19% 0.22% 0.03% -0.04% -0.03% 0.00% 0.04% 0.09%
$\tilde{a}^d_{10}$ 6.68% 0.48% 0.27% 0.04% -0.03% -0.01% 0.03% 0.09% 0.16%
$s^{SU(3)}_{1R} = 1$ 0.00% -1.39% -0.81% -0.41% -0.19% -0.08% -0.03% -0.01% 0.00%
$s^{c}_{1R}$ 0.00% -1.01% -0.74% -0.47% -0.28% -0.17% -0.10% -0.06% -0.03%
$s^{b}_{1R}$ 0.01% 0.22% 0.42% 0.37% 0.29% 0.21% 0.15% 0.11% 0.08%
$s^{SU(3)}_{1L}$ -0.40% 0.94% 0.64% 0.39% 0.22% 0.12% 0.06% 0.03% -0.00%
$s^{c}_{1L}$ -0.44% 0.77% 0.64% 0.45% 0.32% 0.23% 0.16% 0.12% 0.07%
$s^{b}_{1L}$ 1.12% 0.00% -0.31% -0.36% -0.33% -0.28% -0.23% -0.19% -0.15%
$s^{c}_{2R}$ 1.76% -2.05% -2.13% -1.74% -1.34% -1.01% -0.76% -0.57% -0.38%
$s^{b}_{2R}$ 4.02% 8.46% 3.29% 0.06% -1.70% -2.55% -2.86% -2.82% -2.47%
$s^{c}_{2L}$ 0.02% 2.69% 2.38% 1.76% 1.26% 0.89% 0.64% 0.46% 0.30%
$s^{b}_{2L}$ 0.05% -4.81% -1.85% 0.03% 1.11% 1.70% 1.99% 2.04% 1.83%
${C}_{1}$ Tab. \[tbl:wilson-coefficient-example\] 0.01% 0.02% 0.01% 0.01% 0.00% 0.00% -0.00% -0.00% -0.00%
${C}_{2}$ 0.01% -1.46% -1.00% -0.65% -0.40% -0.23% -0.11% -0.02% 0.09%
${C}_{3}$ 0.08% 0.01% 0.04% 0.05% 0.05% 0.05% 0.04% 0.04% 0.03%
${C}_{4}$ -0.93% -0.09% -0.28% -0.34% -0.35% -0.33% -0.31% -0.28% -0.26%
${C}_{5}$ -0.54% -0.10% -0.02% 0.01% 0.02% 0.02% 0.02% 0.02% 0.01%
${C}_{6}$ 6.74% 1.51% 0.46% 0.06% -0.10% -0.16% -0.18% -0.18% -0.18%
${C}_8^{\rm eff}$ -0.14% -0.35% -0.14% -0.01% 0.06% 0.09% 0.11% 0.11% 0.09%
SM total 5.22% -0.45% -0.93% -0.87% -0.72% -0.57% -0.43% -0.32% -0.21%
--------------------------------------------------- -------- -------- -------- -------- -------- -------- -------- -------- --------
: Breakdown of contributions to $B\rightarrow \rho ll$ isospin asymmetry in SM operator coefficients ${C}_i$, and in a generalised basis of four quark WA operators with coefficients $a_i$ and QLSS contributions with coefficients $s^q_{x\chi}$. We use $a^u_i=0.1$, $\tilde a^d_i=0.1$ and $s^q_{x,\chi}=1$ to produce these values. The modified four quark coefficients $\tilde a_i$ are explained in section \[sec:rho-meson\]. The $q^2=0$ value corresponds to the process $B\rightarrow \rho\gamma$ and is computed slightly differently to $B\rightarrow \rho ll$ as described in section \[sec:WAq2eq0\]. The value for $s^f_{1R}$ and $s^f_{2L}$ are zero at $q^2 = 0$ as a consequence of $h_+(0) = 0$ in our approximation.[]{data-label="tab:1rho"}
Effective coefficients in $B^0\to \rho^0$ decay {#app:rho0-effective-coefficients}
-----------------------------------------------
Here we collect the formulae for $\tilde a_i^d$ omitted from section \[sec:rho-meson\].
$$\begin{aligned}
\begin{split}
\tilde a_2^d =& a_2^d
+ \frac{1}{6}(-a_2^u - a_3^u + 4a_6^u - 4a_7^u + 3a_{10}^u) + \frac{2}{9}(-a_2^{8u} - a_3^{8u} + 4a_6^{8u} - 4a_7^{8u} + 3a_{10}^{8u}) \\
& + \frac{1}{12}(-a_2^d - a_3^d + 4a_6^d - 4a_7^d + 3a_{10}^d) + \frac{1}{9}(-a_2^{8d} - a_3^{8d} + 4a_6^{8d} - 4a_7^{8d} + 3a_{10}^{8d})
\end{split} \\
\begin{split}
\tilde a_4^d =& a_4^d
+ \frac{1}{6}(-a_1^u - a_4^u + 4a_5^u - 4a_8^u + 3a_9^u) + \frac{2}{9}(-a_1^{8u} - a_4^{8u} + 4a_5^{8u} - 4a_8^{8u} + 3a_9^{8u}) \\
& + \frac{1}{12}(-a_1^d - a_4^d + 4a_5^d - 4a_8^d + 3a_9^d) + \frac{1}{9}(-a_1^{8d} - a_4^{8d} + 4a_5^{8d} - 4a_8^{8d} + 3a_9^{8d})
\end{split} \displaybreak[0] \\
\begin{split}
\tilde a_5^d =& a_5^d + \frac{1}{12}\left(2(a_5^d - a_5^u) + 2(a_8^d-a_8^u) + (a_4^d-a_4^u) - (a_1^d-a_1^u)\right) \\
& + \frac{1}{9}\left(2(a_5^{8d}-a_5^{8u}) + 2(a_8^{8d}-a_8^{8u}) + (a_4^{8d}-a_4^{8u}) - (a_1^{8d}-a_1^{8u})\right)
\end{split} \\
\begin{split}
\tilde a_6^d =& a_6^d + \frac{1}{12}\left(2(a_6^d - a_6^u) + 2(a_7^d-a_7^u) + (a_2^d-a_2^u) - (a_3^d-a_3^u)\right) \\
& + \frac{1}{9}\left(2(a_6^{8d}-a_6^{8u}) + 2(a_7^{8d}-a_7^{8u}) + (a_2^{8d}-a_2^{8u}) - (a_3^{8d}-a_3^{8u})\right)
\end{split} \displaybreak[0] \\
\tilde a_9^d =& a_9^d + \frac{1}{6}(a_9^d-a_9^u) + \frac{1}{12}((a_1^d-a_1^u)+(a_4^d-a_4^u)) + \frac{1}{9}((a_1^{8d}-a_1^{8u})+(a_4^{8d}-a_4^{8u})) \\
\tilde a_{10}^d =& a_{10}^d + \frac{1}{6}(a_{10}^d-a_{10}^u) + \frac{1}{12}((a_2^d-a_2^u)+(a_3^d-a_3^u)) + \frac{1}{9}((a_2^{8d}-a_2^{8u})+(a_3^{8d}-a_3^{8u}))\end{aligned}$$
### Effective coefficients in $B^0\to \rho^0$ decay in the SM {#app:rho0-effective-coefficientsSM}
The effective coefficients in $B^0\to \rho^0$ decay in the SM for $B^0\to\rho^0$ are $$\begin{aligned}
\tilde a_2^d &= \tilde a_4^d = 2\left(\frac{C_5}{N_c} + C_6\right) \nonumber \\
\tilde a_5^d &= -\tilde a_6^d = \left(\frac{C_3}{N_c} + C_4\right) + \frac{\lambda_u}{\lambda_t}\left(C_1 + \frac{C_2}{N_c}\right) \\
\tilde a_9^d &= \tilde a_{10}^d = 0 \;, \nonumber\end{aligned}$$ where we have used the formulae of the previous section and Eqs. (\[eq:aSM\],\[eq:a8SM\]). Note, we recognise the well known colour suppressed tree-level combination $C_1 + C_2/N_c$ in the formula above.
Weak annihilation formulae {#app:wa-formulae}
--------------------------
We list the functions defined on the RHS of . Any function not listed is zero and there are many as can be inferred from Tab. \[tab:OWA\]. The functions $\rho_{C_b}$ an $\rho_{C_d}$ are derived from the dispersion representation of the Passarino-Veltman functions $$\begin{aligned}
C_b &= C_0(p_B^2,p_B^2-m_B^2,q^2,0,m_b^2,0) &
C_d &= C_0(p_B^2,p_B^2-m_B^2,q^2,m_b^2,0,m_b^2)\end{aligned}$$ which are given in appendix H of [@DLZ12] (note that $C_b=C_a|_{u=1}$ and $C_d=C_c|_{u=1}$).
The functions in which apply at $|q^2|>1{\,{\rm GeV}}^2$ are given in subsection \[app:q2neq0\], and the funtions in which apply at $q^2=0$ are given in subsection \[app:q2eq0\].
### WA formulae $|q^2| > 1 {\,{\rm GeV}}^2$ {#app:q2neq0}
Deinfing, as before, $d \equiv -\frac{\sqrt{2} m_B m_V}{\sqrt{q^2} E}$. we get:
f\_[2,A]{}\^q(q\^2,u)=2 \^2 \_(u) (-)
d f\^q\_[2,0]{}(q\^2,u) = h\_\^[(s)’]{}(u)
f\_[4,V]{}\^q(q\^2,u)=-2 \^2 \_(u) (+)
\_[5,V]{}\^q(q\^2,s)= m\_b f\_[K\^\*]{} m\_[K\^\*]{} (s (s-q\^2)\^3)\^[-1]{} ((m\_b\^2-s) (Q\_b-Q\_q) (s\^2-(q\^2)\^2)-s Q\_b (2 m\_b\^2 q\^2-s q\^2+s\^2) ()+s Q\_q q\^2 (2 m\_b\^2+q\^2-s) ())
V\_[5,V]{}\^q(q\^2)=
\_[6,A]{}\^q(q\^2,s)= m\_b f\_[K\^\*]{} m\_[K\^\*]{} (s\^2 (s-q\^2)\^3 (q\^2-m\_B\^2))\^[-1]{} ((m\_b\^2-s) (s-q\^2) (m\_b\^2 (Q\_b-Q\_q) (-s q\^2+(q\^2)\^2+2 s\^2)-s (s-q\^2) (s (Q\_b-Q\_q)-2 Q\_b q\^2))+s\^2 Q\_q q\^2 (-2 m\_b\^2 (s-q\^2)+2 m\_b\^4+(s-q\^2)\^2) ()+s\^2 Q\_b (-2 s m\_b\^2 (s-q\^2)-2 m\_b\^4 q\^2+s (s-q\^2)\^2) ())
V\_[6,A]{}\^q(q\^2)=-
d \_[6,0]{}\^q(q\^2,s)=3 m\_b m\_B\^2 f\_[K\^\*]{} m\_[K\^\*]{} (s\^2 (s-q\^2)\^3 (m\_B\^2-q\^2))\^[-1]{} (2 s\^2 m\_b\^4 Q\_b ()-2 s\^2 m\_b\^2 Q\_q (m\_b\^2+q\^2-s) ()+(m\_b\^2-s) (Q\_b-Q\_q) (s-q\^2) (m\_b\^2 (q\^2-3 s)+s (s-q\^2)))
d V\_[6,0]{}\^q(q\^2)=
\_[9,V]{}\^q(q\^2,s)= (s (s-q\^2)\^3)\^[-1]{} f\_[K\^\*]{}\^ (-2 s m\_b\^4 Q\_b q\^2 ()+(m\_b\^2-s) (s-q\^2) (m\_b\^2 (Q\_b-Q\_q) (q\^2+s)-s (Q\_b+Q\_q) (s-q\^2))+2 s m\_b\^4 Q\_q q\^2 ())
V\_[9,V]{}\^q(q\^2)=
\_[10,A]{}\^q(q\^2,s)=- f\_[K\^\*]{}\^ (s (s-q\^2)\^2 (q\^2-m\_B\^2))\^[-1]{} (-2 s m\_b\^4 Q\_b q\^2 ()+(m\_b\^2-s) (s-q\^2) (m\_b\^2 (Q\_b-Q\_q) (q\^2+s)-s (Q\_b+Q\_q) (s-q\^2))+2 s m\_b\^4 Q\_q q\^2 ())
V\_[10,A]{}\^q(q\^2)=
d \_[10,0]{}\^q(q\^2,s)=-12 m\_B\^2 m\_[K\^\*]{}\^2 f\_[K\^\*]{}\^ ((q\^2-s)\^2 (m\_B\^2-q\^2)\^3)\^[-1]{} (m\_b\^2 Q\_b (m\_b\^2 (q\^2+s)+2 s (s-q\^2)) ()-(m\_b\^2-s) (s-q\^2) (2 m\_b\^2 (Q\_b-Q\_q)+(Q\_b+Q\_q) (s-q\^2))+m\_b\^2 Q\_q (q\^2+s) (m\_b\^2+q\^2-s) (-()))
d V\_[10,0]{}\^q(q\^2)=
\_[4,T]{}\^q(q\^2,s)=- \_K\^2 (m\_B+m\_K) (s m\_B\^2 (2 m\_B\^2 q\^2+m\_B\^4-4 s q\^2+(q\^2)\^2))\^[-1]{} (2 s Q\_b m\_B\^2 (m\_b\^4+s (m\_B\^2-s)) \_[C\_d]{}(s)+2 s m\_B\^2 Q\_q \_[C\_b]{}(s) (m\_b\^2 (m\_B\^2+q\^2-2 s)+m\_b\^4+s (s-m\_B\^2))+(m\_b\^2-s) (Q\_b-Q\_q) (m\_b\^2 (m\_B\^2+q\^2-4 s)+s (-3 m\_B\^2-q\^2+4 s)))
V\_[4,T]{}\^q(q\^2)=-
f\^[q]{}\_[4,T]{}(q\^2,u) = (m\_B+m\_K)
\_[8,T]{}\^q(q\^2,s)= m\_b f\_K (m\_B+m\_K) (s\^2 (s-q\^2)\^3)\^[-1]{} (2 s\^2 m\_b\^4 Q\_b ()-2 s\^2 m\_b\^2 Q\_q (m\_b\^2+q\^2-s) ()+(m\_b\^2-s) (Q\_b-Q\_q) (s-q\^2) (m\_b\^2 (q\^2-3 s)+s (s-q\^2)))
V\_[8,T]{}\^q(q\^2)=
### WA formulae $q^2 = 0$ {#app:q2eq0}
$$\begin{aligned}
\widetilde{\rho}_{5,V}^{q,\gamma}(s) &=\frac{2 \pi ^2 f_{K^*} m_{K^*} Q_q \phi _{\gamma }\left(\frac{m_b^2}{s}\right)}{s}&
V_{5,V}^{q,\gamma} &=-\frac{2 \pi ^2 Q_b f_{K^*} m_{K^*}}{m_b^2}\end{aligned}$$
$$\begin{aligned}
\widetilde{\rho}_{6,A}^{q,\gamma}(s) &=-\frac{2 \pi ^2 f_{K^*} m_{K^*} Q_q \left(s \phi _{\gamma }\left(\frac{m_b^2}{s}\right)-2\right)}{s m_B^2}&
V_{6,A}^{q,\gamma} &=\frac{2 \pi ^2 f_{K^*} m_{K^*} \left(Q_b-2 Q_q\right)}{m_B^2}\end{aligned}$$
$$\begin{aligned}
\widetilde{\rho}_{9,V}^{q,\gamma}(s) &=\frac{4 \pi ^2 m_b Q_q f_{K^*}^{\perp} \phi _{\gamma }\left(\frac{m_b^2}{s}\right)}{s}&
V_{9,V}^{q,\gamma} &=-\frac{4 \pi ^2 Q_b f_{K^*}^{\perp}}{m_b}\end{aligned}$$
$$\begin{aligned}
\widetilde{\rho}_{10,A}^{q,\gamma}(s) &=\frac{4 \pi ^2 m_b Q_q f_{K^*}^{\perp} \phi _{\gamma }\left(\frac{m_b^2}{s}\right)}{m_B^2}&
V_{10,A}^{q,\gamma} &=-\frac{4 \pi ^2 m_b Q_b f_{K^*}^{\perp}}{m_B^2}\end{aligned}$$
[^1]: Roman.Zwicky@ed.ac.uk
[^2]: This corresponds to a covariant derivative $D_\mu = \partial_\mu - i Q e A_\mu - i g_s A_\mu$ and interaction vertex $+i( Qe + g_s\frac{\lambda^a}{2}) \gamma^\mu$ in agreement with [@Beneke:2001at] but differing from [@Ali:1995uy; @Khodjamirian:1995uc; @Buchalla:1995vs; @Chetyrkin:1996vx].
[^3]: The ${\mathcal{T}}^V_i$ differ from the ones [@Beneke:2001at] in that we include the contributions of $C_9$ as well.
[^4]: The direction $0$ and $\pm$ are also known as the longitudinal and transversal polarisation directions.
[^5]: The IR sensitive $1/q^2$ factor in the $B \to V ll$ rate for $m_l\to 0$ is compensated by a virtual lepton loop in the limit $q^2 \to 0$ as the collinear lepton pair is indistinguishable from a photon. This corresponds to the famous Bloch-Nordsieck cancellation mechanism. Furthermore we note that $|h_0|^2 \sim q^2$ by virtue of and and corresponds to the well-known decoupling of the zero helicity mode towards $q^2 \to 0$. In the differential rate into the pseudoscalar the $q^2$ has been factored out from $|h_T|^2$ to cancel the explicit pole.
[^6]: Note we do not want to invoke the $m_V \to 0$ limit per se as it is well known that massless and massive representations differ in a discontinuous fashion.
[^7]: For the $K^*$ this merely doubles the statistics and reduces experimental uncertainties in the production. For the pseudoscalar $K$ this is essential as the $K_S^0$ is detected in experiment which is a linear superposition of $|s \bar d \rangle$ and $|d \bar s \rangle$ eigenstates which implies averaging.
[^8]: This accounts for $\rho^0\sim(\bar uu-\bar dd)/\sqrt{2}$ since the leading decay amplitude only couples to the $\bar dd$ component of the $\rho^0$.
[^9]: The mass difference between the two neutral kaons is about one percent and relatively large and rather exceptional as a result of the Gell-Mann–Oakes–Renner relation $m_K^2 = -2 (m_q+m_s) {\Braket{\bar q q}}/f_K^2 + ..$.
[^10]: As we shall see shortly there are further selection rules e.g. parity at ${\cal O}(\alpha_s)$ and Lorentz covariance to all orders for the $K$.
[^11]: One might also pose the problem the other way around, starting from the photon DA at $q^2=0$ and asking how the latter is to be modified when $q^2 > 0$. The primary effect can be covered by the quark condensate contribution.
[^12]: This statement is only corrected by UV isospin violating effects in WA at ${\cal O}(\alpha_s)$.
[^13]: We differ from these references in that we compute WA and ${\cal O}_8$ in LCSR which includes LD contributions as argued at the beginning of section \[sec:QLSS\]. Moreover we include twist-3 contributions for WA for the reasons mentioned in section \[sec:comment\]. The QLSS contributions are effectively treated in the same way. Whereas their result is small it differs from ours quantitatively which is explained by the differences mentioned above.
[^14]: For $D \to V \gamma$ and decays such as $D_s^+ \to \rho^+ \gamma$ there is no CKM suppression at all and since all other subprocesses are small, WA dominates these decays as we have argued in [@LZ12] in appendix A.
[^15]: In this work we refrain from including the isospin asymmetry $B \to \pi ll$. $B^+ \to \pi^+ ll$, but not the neutral mode, has only been observed recently by the LHCb collaboration [@LHCb:2012de]. Another logical extension would be to consider a $\rho$-$\omega$ asymmetry as in [@Ball:2006eu]. We refrain from doing so mainly because the latter suffers from a large theoretical uncertainty in the actual difference, not to be confused with the separate values, of the $\rho$ and $\omega$ form factors. This situation could be improved considerably through a dedicated study of the respective ratio of decay constants; both transversal and longitudinal.
[^16]: Note that [@Ball:2006eu] uses the opposite sign convention for $\Delta(\rho\gamma)$.
[^17]: $\Delta F=2$-constraints from neutral meson oscillations, usually rather severe, are presumably not very strong. More precisely if we are to compare SM/MFV type operator ${{\cal O}}^{\rm MFV}_{\Delta B = 2} \approx |\lambda_t|^2 G_F/16\pi^2(\bar b \Gamma_1 s_L)(\bar b \Gamma_2 s_L)$ (with $\Gamma_{1,2}$ specific Dirac structures) then integrating out either $b$-quarks or saturating light quarks with intermediate hadronic states one would expect to get a $ G_F \times (m_b^2, \Lambda_{\rm QCD}^2) \approx (10^{-4},10^{-6})$ suppression in each case.
[^18]: An extension to $q^2 > 0$ is not straightforward as the isospin asymmetries of the $K^*$ and $\rho^*$ do differ qualitatively: $C_9^{\rm eff}(q^2)$ contributes a small weak phase to the leading amplitude which partially alleviates the $\cos\alpha_{\rm CKM}$ suppression.
[^19]: For the $\rho$-meson this implies $\bar \Gamma(B\to\rho\gamma)=\frac{1}{2}\bar \Gamma(B^+\to\rho^+\gamma) + \bar \Gamma(B^0\to\rho^0\gamma)$ due to $\rho^0\sim (\bar uu-\bar dd)/\sqrt{2}$ as discussed previously.
[^20]: The tables \[tab:2\],\[tab:1\] and \[tab:1rho\] can be obtained from the authors on request.
[^21]: In [@Ball:2006eu] $r_{K^*\phi} = 0.99(13)$ was quoted based on some input from lattice QCD on the ratio of $f_{B_s}/f_{B_d}$ for which there is no reason if the $f_{B_{d,s}}$ are taken from sum rules to the same order which is a consistent procedure.
[^22]: Similar remarks would apply to ratio of the kind ${\cal B}(B^0 \to \rho^{*0}\gamma)/{\cal B}(B^0 \to \omega\gamma)$, as discussed in a previous footnote.
[^23]: By asymptotic we mean, as usual, for $\mu_F \to \infty$. All DA depend on the factorisation scale $\mu_F$ of the LC-OPE which we do not indicate explicitly.
[^24]: This may be obtained from the equation in [@Kagan:2001zk eq.8] assuming that $\phi_\parallel(u)=\phi_\parallel(\bar u)$ and likewise for $g^{(v)}_\perp$ and $g^{(a)}_\perp$ which is valid up to small isospin violating terms. It may more properly be derived directly from the equation of motion in [@Ball:1998sk]
[^25]: By working with a plane wave the Lorentz gauge is a natural choice. Note still adhering to the plane wave picture the axial gauge $n \cdot A=0$ with $A_\mu \to ( \epsilon_\mu - (n \cdot \epsilon)/(n \cdot q) q_\mu) e^{i q \cdot x}$ is an alternative. It would amount to replacing the polarisation vector accordingly in the formulae above.
[^26]: This is the component in the light-like direction which is parallel to the final state light meson.
[^27]: For ISR radiation the second cut corresponds to the kaon as the momentum flowing into $4$ quark operator is the kaon final state momentum.
[^28]: Note, the Lorentz gauge does still allow for residual gauge transformations of the form $\epsilon_\mu \to \epsilon_\mu + q_\mu$ for example.
[^29]: These authors do not discuss the QED GI.
[^30]: More precisely integrability of the rate, which we expect, is incompatible with $1/q^2$-behaviour. Note this pole cannot be compensated by virtual correction as in $\gamma
\to ll$ which leads to $1/q^2$ in $|h_\pm|^2$ .
|
/*==LICENSE==*
CyanWorlds.com Engine - MMOG client, server and tools
Copyright (C) 2011 Cyan Worlds, Inc.
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Additional permissions under GNU GPL version 3 section 7
If you modify this Program, or any covered work, by linking or
combining it with any of RAD Game Tools Bink SDK, Autodesk 3ds Max SDK,
NVIDIA PhysX SDK, Microsoft DirectX SDK, OpenSSL library, Independent
JPEG Group JPEG library, Microsoft Windows Media SDK, or Apple QuickTime SDK
(or a modified version of those libraries),
containing parts covered by the terms of the Bink SDK EULA, 3ds Max EULA,
PhysX SDK EULA, DirectX SDK EULA, OpenSSL and SSLeay licenses, IJG
JPEG Library README, Windows Media SDK EULA, or QuickTime SDK EULA, the
licensors of this Program grant you additional
permission to convey the resulting work. Corresponding Source for a
non-source form of such a combination shall include the source code for
the parts of OpenSSL and IJG JPEG Library used as well as that of the covered
work.
You can contact Cyan Worlds, Inc. by email legal@cyan.com
or by snail mail at:
Cyan Worlds, Inc.
14617 N Newport Hwy
Mead, WA 99021
*==LICENSE==*/
#ifndef plDynaRippleMgr_inc
#define plDynaRippleMgr_inc
#include "plDynaDecalMgr.h"
class plArmatureUpdateMsg;
class plDynaRippleMgr : public plDynaDecalMgr
{
protected:
hsVector3 fInitUVW;
hsVector3 fFinalUVW;
virtual bool IRippleFromShape(const plPrintShape* shape, bool force=false);
virtual int INewDecal();
public:
plDynaRippleMgr();
virtual ~plDynaRippleMgr();
CLASSNAME_REGISTER( plDynaRippleMgr );
GETINTERFACE_ANY( plDynaRippleMgr, plDynaDecalMgr );
virtual void Read(hsStream* stream, hsResMgr* mgr);
virtual void Write(hsStream* stream, hsResMgr* mgr);
virtual bool MsgReceive(plMessage* msg);
void SetUVWAnim(const hsVector3& init, const hsVector3& final) { fInitUVW = init; fFinalUVW = final; }
const hsVector3& GetInitUVW() const { return fInitUVW; }
const hsVector3& GetFinalUVW() const { return fFinalUVW; }
};
#endif // plDynaRippleMgr_inc
|
Varun Agarwal
Varun Agarwal (born December 6, 1987) is an Indian entrepreneur, film maker and author. He has co-founded three companies and authored a national bestseller, How I Braved Anu Aunty and Co-Founded a Million Dollar Company.
Early life
Brought up in Bangalore, Varun did his schooling from Bishop Cotton Boys' School and studied engineering at CMR Institute of Technology.
Entrepreneur
Varun has co-founded three startups, Alma Mater, an online store for merchandise especially for students of colleges and schools which was started in 2009, Reticular, a social media marketing company started in 2010, and Last minute Films, a production company for online video content which was started in 2005.
Alma Mater
Varun says that the current aim of the company is to become profitable as well as more responsible.
Alma Mater has also launched a customised online Do-It-Yourself (DIY) online T-shirt maker tool called PLAY. The user can join or create a group, make custom T-shirts with an online editing tool, share it with friends and group members and invite others to join.
Grades don't matter
Varun Agarwal also founded an online learning platform name Grades don't matter which is a platform that provides educational courses taught by professionals.
Author
How I Braved Anu Aunty and Co-Founded a Million Dollar Company was rolled out in 2012 by Rupa publishers and is a national bestseller. ‘How I Braved Anu Aunty & Co-founded A Million Dollar Company’ had already hit the number 5 spot on the Amazon India bestsellers list.
Music Video
He has teamed up with a Bangalore-based stand-up comedian Sanjay Manaktala to make a music video called ‘Anu Aunty, Engineering Anthem’ based on his book. This video, which went viral, was featured on The Enthu Cutlets, a channel promoted by Varun in 2014 to showcase Bengaluru's comedians.
The Movie
Siddarth Roy Kapur and Ronnie Screwvala will be making a movie which is an adaptation of Varun's book ‘How I Braved Anu Aunty and Co-founded A Million Dollar Company’. Nitesh Tiwari, who directed the Bollywood movie Dangal, is working on this new film.
Motivational Speaker
Varun is one of the prominent storytellers and motivational speakers in India. Varun has also given INK talks, the Indian version of TED, where he shares his story. His first INKTalk's speech has marked more than 7,50,000 views on YouTube and is constantly increasing. He has given talks to executives at Unilever in London, college students in Pune and to employees of tobacco firm Philip Morris in Macau.
References
External links
Book Review: How I Braved Anu Aunty and Co-founded a Million Dollar Company
Category:1987 births
Category:Bishop Cotton Boys' School alumni
Category:Living people
Category:Indian filmmakers |
In the related art, motors (three-phase motors) that are driven in three phases have been widely used. In general three-phase motors, coils of respective phases are connected to each other at neutral positions thereof, and electric currents are not independently applied to the coils of the respective phases.
In contrast, an invention of an electric power steering apparatus equipped with a motor having a connection relationship in which coils of respective phases can be independently driven is disclosed (for example, refer to Patent Document 1). If the coils of the respective phases can be independently driven, a larger torque can be output as compared to the case where the coils of the respective phases are connected to each other.
On the other hand, the applicability of motors has also increased. For example, an invention of a motor generator that functions as a starter motor at the time of starting an engine and functions as a generator after the engine is started is disclosed (refer to Patent Document 2). The motor generator of such an aspect may be referred to as an alternating current generator (ACG) starter. By using the ACG starter, the need for including a related-art cell motor type starter disappears. For this reason, weight and costs can be reduced, and generation of noise caused by a reduction gear that couples a cell motor type starter and a crankshaft together can be eliminated. Particularly, in vehicles that perform idling stop, which have recently become more common, the ACG starter is preferably used because mechanical noise at the time of the starting of the engine is suppressed. |
You followers of the constitution, have you forgotten what you said in your constitution when we were preaching in Maiduguri town? In your constitution, you cite section 8 verse 1, 2 to 3 in that your cursed document referred to as the constitution, that it is a law and not reversible. You came out in your radio and newspapers and say we are fighting for Islamic Caliphate, it is that constitution that stops us preaching in Maiduguri, and we move out because of exile Allah tasked us to embark.
Have you also forgotten? And you are now seating down and say you have reached ceasefire with us, with who? That your infidel Danladi Ahmadu, if he is in our hands today he will not pass the day because we will slice his throat. When did we even know him? Who is Danladi in this world? Allah is the knower of everything.
Because of this, there is no any ceasefire or dialogue with anyone instead it is a war with beating and killings, and guns that we are hungry for like food with Maggi cubes. We are on course; our focus and determination is to see that only Quran is being use in running the world, with Allah this is what we put ahead of us.
ADVERTISEMENT
That President Idris Deby of Chad and one Ambassador of Nigeria, with Cameroon that we are doing ceasefire, where did they see us? Your white man from Germany is with us presently, he is crying and if we like we will cut him into pieces, or gun him down. We are not afraid of anyone except Allah; this is our job.
Who have freed girls from Chibok whom we abducted in their school? Those girls that Shekau abducted and took them to place of his choice about six months today. Allah passed infidels; Allah is ahead of America, Allah is ahead of a plane called drone, nonsense, Allah is supreme ahead of everyone.
If parents of Chibok girls will know the condition of their children, they will not be worry; it is either to be with their conversion to Islam or you die with pains. You don’t know that the over 200 Chibok girls have convert to Islam, they have memorized several sections of Quran, they have finished in the midst of John, Luka and others, they have realized that Christians have filled old testament with lies.
Small girl from Chibok insisting that Islam is the true religion, just form six. We have married them off, and they are in the house of their husbands. To hurt people is Shekau, they are saying Shekau is a throne; it is me Shekau whose father is
Muhammadu, Shekau the man that hurts infidels, staying in the world will be difficult for you, you are just misbehaving in the world. Who created you? We have not done any ceasefire with anyone; we did not, we did not do ceasefire with Chad, we did not do same with Cameroon and we did not do same with Niger and Nigeria. We did not do same with Ambassador of Chad, and we did not do any dialogue with Africa. We did not do same with Europe and Asia; we did not do with America and the useless United Nations of nonsense.
We did not, who is dialogue? It is a lie; it is a lie, we will not do it, Allah said no to it. We are working with Quran, and no infidel will threaten us. You lacked what to do; you want to please your leaders, and you are lying, the likes of Solomon Darlung, Abdullahi Wase, the likes of Senator Ndume. The people are tired, whether you like it or not we are working for others to convert Islam.
What is my business with you? Me that left my parents in our house; I left my mother and father. I came out to team up with those that want to promote Islam; you are just deceiving people with ceasefire.
It is with a single knife that I started and today with more than 20 vehicles I ceased from you, and they are saying Shekau is not a person but a special name. I greet you SSS; I greet you that went to study in Israel, I greet you a member of psychology origin; I greet you descendants of biology. I greet you fools that pledge to Nigeria. You pledge to Nigeria your country, I Shekau pledge to Allah my God. If you don’t know, today you will know, I pledge to Allah to be faithful. This is Shekau, nonsense like you people. This is my brief talk; this one is okay for you, and you should convert to Allah and follow Quran. You are unlucky to have missed Quran and stopping those doing it; it is a lie anyone that refuse will see. Thanks. |
reftype: Web Page
publication_journal: None
title: None
publication_year: None
conference: None
key: guido
authors: []
source_url: http://www.network-theory.co.uk/docs/pytut/
id: 4981 |
import Foundation
class CircleAPI: MixinAPI {
private enum Path {
static func circle(id: String) -> String {
"/circles/\(id)"
}
}
static func circle(id: String) -> MixinAPI.Result<CircleResponse> {
return request(method: .get, path: Path.circle(id: id))
}
static func circle(id: String, completion: @escaping (MixinAPI.Result<CircleResponse>) -> Void) {
request(method: .get, path: Path.circle(id: id), completion: completion)
}
}
|
Q:
Can the manifest file be dynamic in Chrome Apps?
I am writing a Chrome App that communicate with a web page. For that I have added something similar in my manifest file.
"externally_connectable": {
"matches": ["*://*.example.com/*"]
}
But the "example.com" has to be dynamic as individual customers has their one web server.
Is there any possibility, user(who install the app) can change the externally_connectable site/s.
A:
There is an alternative way a web page can communicate with extension through content script. This approach can be used if both web page and extension are done by you.
E.g.
web page <--> content script of extension <--> background script of
extension <--> native application
For web page to content script of extension communication use window.postMessage and window.addEventListener
For Google Chrome browser,
For content script of extension to background script of extension communication use chrome.runtime.sendMessage and chrome.runtime.onMessage.addListener
For background script of extension to native application communication use chrome.runtime.sendNativeMessage
Please make sure your code has necessary security in place.
|
Prevalence of occult hepatitis C virus infection in Iranian patients with lymphoproliferative disorders.
Occult HCV infection is a form of chronic HCV infection characterized by absence of detectable anti-HCV antibodies or plasma HCV-RNA but presence of HCV-RNA in liver biopsy and/or peripheral blood mononuclear cells (PBMCs). The aim of this study was to determine the presence of HCV-RNA in PBMCs of patients with lymphoproliferative disorders. One hundred and four consecutive patients with lymphoproliferative disorders admitted to Firouzgar Hospital from January 2010 to March 2011 were recruited in this cross-sectional study. A 6-ml sample of whole blood was taken from the patients, the total RNA was extracted from the samples after the separation of plasma and PBMCs. The HCV-RNA of the samples was amplified by reverse transcriptase-nested polymerase chain reaction (RT-nested PCR). The HCV genotypes of the positive samples were tested using the INNO-LiPA™ HCV II kit, and the HCV genotypes were then confirmed by sequencing of the 5'-UTR fragments after the PCR products were cloned into a pJET1.2/blunt cloning vector. The mean age of the patients was 48.3 ± 1.76 years (range: 16-83). HCV-RNA was found in PBMCs from 2 (1.9%) of the 104 patients. Genotyping showed that the patients were infected with HCV subtype 1a. One patient suffered non-Hodgkin's lymphoma and the other suffered chronic lymphocytic leukemia. Patients with lymphoproliferative disorders with negative anti-HCV antibodies and negative plasma HCV-RNA may have occult HCV infection. Therefore, in the absence of a liver biopsy, the testing of PBMCs for the detection of genomic HCV-RNA may be beneficial. |
Thursday, December 22, 2011
Mr. Plinkett's next review trailer...IJ4 Coming soon
Mr. Plinkett'snext review trailer...IJ4 Coming soon
Explain why I really like this trailer?
I will neverlook at Follow That Bird thesame way again. I want to know who that girl is in the video though.
Anyway,I think I am going to love Red Letter Media ripping into IndianaJones and the Kingdom of the Crystal Skull. I let IJ4 off the hookwith my review and I would probably review the movie more harshlynow. There are way too many George Lucas flaws in the script to giveit pass today, because clearly the movie doesn't hold up like thelast three movies.
Iremember Lucas coming out and warning people that the movie wouldn'tbe as good as the last movies. |
12 Cal.App.4th 1094 (1993)
16 Cal. Rptr.2d 52
THE PEOPLE, Plaintiff and Respondent,
v.
ANTHONY HOLMES, Defendant and Appellant.
Docket No. A054687.
Court of Appeals of California, First District, Division Five.
January 26, 1993.
*1096 COUNSEL
Richard I. Targow, under appointment by the Court of Appeal, for Defendant and Appellant.
Daniel E. Lungren, Attorney General, George Williamson, Chief Assistant Attorney General, Ronald A. Bass, Assistant Attorney General, Ronald S. Matthias and Aileen Bunney, Deputy Attorneys General, for Plaintiff and Respondent.
[Opinion certified for partial publication.[*]]
OPINION
HANING, J.
Anthony Holmes appeals his conviction by jury trial of first degree murder (Pen. Code, § 187), second degree robbery (Pen. Code, § 211) and a finding of firearm use. (Pen Code, § 12022.5). He raises instructional and identification error. We affirm.
*1097 FACTS
(1) In resolving this appeal we are required by established rules of appellate procedure to view the evidence in the light most favorable to respondent, and presume in support of the judgment the existence of every fact the jury could reasonably deduce from the evidence. (People v. Johnson (1980) 26 Cal.3d 557, 576 [162 Cal. Rptr. 431, 606 P.2d 738, 16 A.L.R.4th 1255].) Since appellant does not challenge the sufficiency of the evidence per se, only those facts necessary for resolution of appellant's assignment of errors need recitation, and they are provided in accordance with the stated established rules. The record reveals that appellant conspired with one Kimberly Hutchinson to rob the victim, who had arranged with Hutchinson to purchase cocaine from her. Appellant shot and killed the victim during the course of the robbery.
DISCUSSION
I
(2a) Appellant contends the court erred by failing to instruct sua sponte that the testimony of a witness to whom he confessed required independent corroboration, in light of the witness's testimony that her pretrial statements to the police were fabricated. Jessica Hawley told the investigating police sergeant that appellant was at her home when he was called by Hutchinson on the day of the murder. Appellant told Hawley of the plan to rob the victim, left the house with his gun and a ski mask, and was driving a car he had stolen. When appellant returned he told Hawley that the robbery had been accomplished and that he had shot the victim.
Hawley changed her story at the preliminary hearing and trial. She testified at trial that she fabricated her statement to the police because appellant had told her two days earlier that he preferred another woman to her, and she felt vindictive toward him. She said she had learned the details of the shooting from Hutchinson and another person during the week after it occurred, and did not speak with appellant about it.
(3) The rules governing admission and use of evidence are contained principally in the Evidence Code, and the statutes therein govern all criminal proceedings unless overridden by constitutional concerns of specific provisions of the Penal Code. (Evid. Code, §§ 300; 1102; 1204; see also 1 Witkin, Cal. Evidence (3d ed. 1986) Introduction, § 12, p. 14.) The statutes are not the exclusive source of evidentiary rules, however; they are supplemented by judicial decisions that answer questions on which the Legislature has been silent or inexplicit. (See 1 Witkin, Cal. Evidence, op. cit. supra, § 14, p. 16.)
*1098 Appellant does not dispute that his statement to Hawley that he shot the victim was admissible as an admission (Evid. Code, § 1220), a declaration against his penal interest (Evid. Code, § 1230), and as a component of Hawley's prior inconsistent statement. (Evid. Code, § 1235.) (4) He bases his contention on the requirement for independent corroboration of her repudiated statement on a line of cases beginning with People v. Gould (1960) 54 Cal.2d 621 [7 Cal. Rptr. 273, 354 P.2d 865], which holds: "An extrajudicial identification that cannot be confirmed by an identification at the trial is insufficient to sustain a conviction in the absence of other evidence tending to connect the defendant with the crime. [Citation.]" (Id., at p. 631; see also People v. Lucky (1988) 45 Cal.3d 259, 288 [247 Cal. Rptr. 1, 753 P.2d 1052]; In re Miguel L. (1982) 32 Cal.3d 100, 106 [185 Cal. Rptr. 120, 649 P.2d 703]; People v. Ford (1981) 30 Cal.3d 209, 212 [178 Cal. Rptr. 196, 635 P.2d 1176]; People v. Chavez (1980) 26 Cal.3d 334, 361 [161 Cal. Rptr. 762, 605 P.2d 401]; In re Johnny G. (1979) 25 Cal.3d 543, 547 [159 Cal. Rptr. 180, 601 P.2d 196].)
A review of Gould and its progeny reveals that the Gould rule comes into play when a nonaccomplice witness to a criminal offense victim or bystander makes an out-of-court identification of the defendant and subsequently fails to identify him at trial. It is related in principle to the requirement that an accomplice's testimony is insufficient for conviction unless it is corroborated by other evidence connecting the defendant with the offense. (Pen. Code, § 1111; see also People v. Belton (1979) 23 Cal.3d 516, 535 [153 Cal. Rptr. 195, 591 P.2d 485] (conc. opn. of Jefferson, J.); CALJIC No. 3.11) Such an identification or testimony, standing alone, is deemed to lack sufficient indicia of accuracy and trustworthiness. (See In re Miguel L., supra, 32 Cal.3d at p. 107; People v. Ford, supra, 30 Cal.3d at p. 215; People v. Armijo (1990) 221 Cal. App.3d 271, 278-279 [270 Cal. Rptr. 496]; In re Eugene M. (1976) 55 Cal. App.3d 650, 657-658 [127 Cal. Rptr. 851].) (2b) Here, Hawley was not a witness or accomplice to the crime, made no extrajudicial statement that she witnessed its commission, and her identification or misidentification of appellant as the perpetrator was not in issue. She simply recited the events of the day of the shooting, including appellant's admission to her that he had participated in a robbery during which he shot the victim. She then testified at trial that her statement to the police was not true.
Appellant has not cited, and we have not located, any cases where the Gould rule was applied to a situation in which a trial witness who was not present during the commission of the crime recants an extrajudicial statement concerning a defendant's admission against penal interest. Nor has *1099 the Gould rule been applied to an extrajudicial admission of a party. (5) Unlike an out-of-court identification or accomplice testimony, extrajudicial admissions do not require corroboration with other evidence tending to connect the defendant with the offense as long as the corpus delicti of the crime has been established independently of the admissions. (See People v. Mattson (1990) 50 Cal.3d 826, 873-874 [268 Cal. Rptr. 802, 789 P.2d 983]; People v. Alcala (1984) 36 Cal.3d 604, 624-625 [205 Cal. Rptr. 775, 685 P.2d 1126]; People v. Cooper (1960) 53 Cal.2d 755, 765 [3 Cal. Rptr. 148, 349 P.2d 964]; People v. McMonigle (1947) 29 Cal.2d 730, 738-739 [177 P.2d 745]; People v. Mills (1991) 1 Cal. App.4th 898, 921 [2 Cal. Rptr.2d 614].)
(6) To establish the corpus delicti of a murder charge the People must make a prima facie showing of a death caused by a criminal agency. (People v. Mattson, supra, 50 Cal.3d at p. 874.) Proof of the corpus delicti does not require proof that the accused committed the crime. Once the corpus delicti is established, the defendant's admissions and confessions are admissible and may suffice by themselves to establish the defendant's connection with the crime. (People v. Manson (1977) 71 Cal. App.3d 1, 42-43 [139 Cal. Rptr. 275]; see also People v. Cantrell (1973) 8 Cal.3d 672, 679-681 [105 Cal. Rptr. 792, 504 P.2d 1256].) (2c) There is no dispute that in this case the People established the corpus delicti independently of any admissions appellant made to Hawley: A witness testified he saw one man threatening another man with a pistol; while the witness was inside telephoning the police he heard a gunshot; he returned outside to see the threatened man bleeding; and the victim was pronounced dead from a gunshot wound approximately one and one-half hours later.
The court properly instructed that an out-of-court admission by a defendant was to be viewed with caution, that evidence of prior inconsistent statements could be considered for both the credibility of the declarant and the truth of the facts in the prior statement, and that the jurors were the sole judges of the credibility of a witness. It was not required to instruct sua sponte that Hawley's statement to the police detailing the events of the day of the shooting had to be corroborated by independent evidence.[1]
*1100 II[*]
.... .... .... .... .... .... .... .
Affirmed.
Peterson, P.J., and King, J., concurred.
NOTES
[*] Pursuant to California Rules of Court, rules 976 and 976.1, this opinion is certified for publication with the exception of part II.
[1] In a footnote of his opening brief, appellant comments that the court's procedure for giving an omitted instruction after jury deliberations commenced reading the instruction to the jurors in the jury room instead of calling them to the courtroom was error. However, he neither asserts nor argues this procedure as an assignment of error, so we need not consider it. (People v. Scott (1944) 24 Cal.2d 774, 783 [151 P.2d 517]; People v. Doolittle (1972) 23 Cal. App.3d 14, 16, fn. 1 [99 Cal. Rptr. 810].)
[*] See footnote, ante, page 1094.
|
1. Field
Example embodiments relate to a flash memory device and a method for programming/erasing the same.
2. Description of the Related Art
Non-volatile memory devices, e.g., flash memory devices, may be electrically erasable and programmable memory devices. The non-volatile memory devices may maintain data even when power is not supplied. For example, a flash memory device may be a NAND-type non-volatile memory device having memory transistors arranged on NAND strings. |
# Firebase SDK for Cloud Functions Quickstart - Cloud Storage trigger
This quickstart demonstrates using **Firebase SDK for Cloud Functions** setup with a Cloud Storage trigger.
## Introduction
This sample automatically generates thumbnails for images that are uploaded to Cloud Storage.
## Functions Code
See file [functions/index.js](functions/index.js) for the thumbnail generation code.
The thumbnail generation is performed using ImageMagick which is installed by default on all Cloud Functions instances. This is a CLI so we execute the command from node using the [child-process-promise](https://www.npmjs.com/package/child-process-promise) package. The image is first downloaded locally from the Cloud Storage bucket to the `tmp` folder using the [google-cloud](https://github.com/GoogleCloudPlatform/google-cloud-node) SDK.
The dependencies are listed in [functions/package.json](functions/package.json).
## Trigger rules
The function triggers on upload of any file to your Firebase project's default Cloud Storage bucket.
## Deploy and test
To deploy and test the sample:
- Create a Firebase project on the [Firebase Console](https://console.firebase.google.com) and visit the **Storage** tab.
- Get the code, for instance using `git clone https://github.com/firebase/functions-samples`
- Enter the correct directory `cd functions-samples/quickstarts/thumbnails`
- Setup the CLI to use your Firebase project using `firebase use --add` and select your Firebase project
- Deploy your project's code using `firebase deploy`
- Go to the Firebase Console **Storage** tab and upload an image. After a short time a thumbnail image with the same name but a `thumb_` prefix will be created in the same folder (make sure you refresh the UI to see the new file).
## Contributing
We'd love that you contribute to the project. Before doing so please read our [Contributor guide](../../CONTRIBUTING.md).
## License
© Google, 2016. Licensed under an [Apache-2](../../LICENSE) license.
|
‘Supergirl’ and ‘Arrow’ Stars Speak Out on Producer’s Sexual Harassment
Late Friday saw Supergirl and Flash fans taken aback with word that producer Andrew Kreisberg had his own streak of sexual harassment. That put the stars in a difficult position, but Melissa Benoist herself has now spoken up about “refusing to accept an environment that is anything less than a safe, respectful and collaborative space,” as have other Arrow cast.
Kreisberg has since been suspended in his capacity as executive producer, following a Variety report that at least nineteen staffers had complained about the Arrow-verse boss’ history of lewd comments and inappropriate touching. It isn’t entirely clear what Kreisberg’s role might be going forward, but Benoist took it on her super-shoulders to become the first franchise star with indirect comments on the matter:
Benoist wasn’t the only star willing to speak out, however, as Arrow vet Emily Bett Rickards took a sharper line against those who perpetuate rape culture:
That line about “reverse sexism” seems particularly charged, as Arrow’s own executive producer Marc Guggenheim took flack on Twitter for invoking reverse sexism in a response to Conan O’Brien:
Other stars like David Ramsey, Chyler Leigh and Caity Lotz also offered platitudes in support of Benoist and Rickards:
UPDATE: Stephen Amell released his own video statement, having spoken to the Arrow cast and crew first:
Kreisberg had been serving in a more overall producer capacity to Flash and Supergirl, but we’ll see if his suspension has any noticeable effect on the franchise, or if other stars speak out. Stay tuned for the latest in the meantime. |
Majority of the teams that we tend to struggle against have speed. It's why we stuggle against Colorado; it's part of the reason Winnipeg had a lot of shots; the last game against Chicago, they were flying, and we lost. We have trouble with teams that combine speed with skill. We should be going after a defenseman that can skate. They should be at least 6 foot, but they don't necessarily have to be a big crease clearer.
Majority of the teams that we tend to struggle against have speed. It's why we stuggle against Colorado; it's part of the reason Winnipeg had a lot of shots; the last game against Chicago, they were flying, and we lost. We have trouble with teams that combine speed with skill. We should be going after a defenseman that can skate. They should be at least 6 foot, but they don't necessarily have to be a big crease clearer.
Again; I don't see it.
The majority of the Blues' Losses have come against teams that out muscle us in the defensive zone(Nashville, Detroit, Minnesota), not against teams that are speed oriented.
I want an answer to guys like Franzen, Clowe, Lucic, Iginla and Fisher.
We're doing a good enough job containing speed guys.
I don't think it's a matter of crease clearing vs. speed, I think they just need someone who has playoff experience, can play 20ish minutes and take some pressure off Pietrangelo and Shattenkirk.
The "crease-clearer" needs to be physical enough to stop forwards from "camping out" near the crease and to impede opponents from getting off a clean shot near the net. He doesn't have to be a giant, but can't be small. A big reach would help (but not be completely necessary). The D-man would have to be good positionally, and able to skate decently (not be as immobile as some of the huge monsters). He should have good playoff experience. Someone who won't get bowled over, or shy away from contact, or allow the opponent to stay near the cease, and just try to poke-check the puck away. He must be a decent passer, and be able to skate the puck out of danger if necessary. He won't have to be a big asset on offence.
We need a RWer as weird as that sounds. With Dags and Steen potentially out for the year, we will need some depth there. I also think we should try to upgrade our D, but that won't be cheap or easy to swing.
The money factor is going to be a huge hurdle to overcome, because most sellers are not going to want to take much salary on and we can afford to take it on either.
Eh, I voted for yes because that would be the prudent thing to do if they're truly pushing for the division title/#1 seed.
Having an entire top 9 line out for an extended period is going leave our top forwards overplayed, and our defense exposed. If everyone's healthy by the playoffs, it's not that big of a deal (again, unless you're serious about pushing for the #1 overall)...but that's not a given either. This team is based on holding top talent in check and exploiting depth/system advantages. That advantage dissipates with each additional injury.
I would also like to see a smidge of remodeling done on defense. I've always leaned towards a combination of mobility/puck-moving ability/poise/intelligence/positioning over brute physicality at the expense of those attributes in my preference for defensemen, but physicality definitely has its place in the game.
I would like to see someone a bit more well-rounded brought in on defense than what Colaiacovo or Huskins brings to the table. Physicality would be a nice attribute, but only if the defender is mobile enough and has good enough puck skills to key the transition play well if the puck is consistently funnelled in his direction (as opposed to, say, Pietrangelo's) by other teams. We're playing right into their hands if every reverse from Pietrangelo to his partner leads to an icing, a turnover, or a bank out of the zone/missed breakout pass to the other team's defense. The Blues want to play in the offensive zone...they can't do that if they can't get there with the puck.
I think the Blues can afford to move anybody not named Tarasenko, Schwartz or Rattie to make to deep playoff run this year. I would even trade this years 1st,2nd and both 3rd's if needed. We have plenty of prospects.
I think the Blues can afford to move anybody not named Tarasenko, Schwartz or Rattie to make to deep playoff run this year. I would even trade this years 1st,2nd and both 3rd's if needed. We have plenty of prospects.
I would be very hesitant to move either Fairchild or Cole. We just don't have anything in the AHL level after those to. Everybody else is atleast 2-3 years away, and I am not sold on Ponich making the transitition.
The more I think about it the more I could see McRae moved or Bishop. Personally, I think Bishop will be moved to someone else - like Tampa or CBJ. And I also think the price could be pretty steep.
Finally, I don't see all that many teams willing to sell anything unless it is at a steep price.
I believe the Blues are legitimately a top 6 team in the enitre league this year, but lets be honest we don't have the financial resources to bring someone in to make a huge impact at the trade deadline. Therefore I say lets role with what we got and take our chances this year. It kinda seems like one of those special years like the Cardianls had where things are falling into place for us. In my opinion we should save our resources and cap space for an offseason move for Parise or Weber. If we get a new owner there is no doubt we will be signing a big time free agent in the offseason with the year we are having this year. Give Perron, Oshie, Bergulnd, Petro, and Stewart one more year to develop, plus add a big time free agent and I believe next year could be our year. That being said, Im curious if you could choose what would you rather have, a big time d-man like Weber or an imapct forward like Parise?
I would be very hesitant to move either Fairchild or Cole. We just don't have anything in the AHL level after those to. Everybody else is atleast 2-3 years away, and I am not sold on Ponich making the transition.
I'm not as doubtful about Ponich as you are, but I agree that he still needs a lot of polishing and refining before he's ready to bring his big frame to the NHL.
For an organization that had one of the best stables of defense prospects just a few years ago, the cupboard is starting to look a little bare for the Blues.
They only have five legitimate prospects on defense in Peoria - Cole, Fairchild, Ponich, Shields and Cundari. And I doubt either Shields or Cundari ever gets more than a cup of coffee or an emergency call-up to the NHL.
They have just two d-prospects in major junior - Beukeboom, who should turn pro next year, and Edmundson, who has another year of junior eligibility left after this year.
They have two decent prospects in Finland in Hakanpaa and Teemu Eronen, both of whom could turn pro next year. Both would be most welcome in Peoria, but Hakanpaa just went down for the remainder of the season with a knee injury, and there's no way to tell just yet how that will affect his development, and it's likely 50/50 at best if Eronen ever comes over at all.
This draft is deep in defense prospects, especially at the top, and I would not be averse to seeing the Blues trade up in the first round so they could draft a Griffin Reinhart or an Olli Maatta or a Jacob Trouba or a Cody Ceci. Give me another blue-chipper on defense, with a couple of years to play him in junior or college and develop him on someone else's dime.
...if you could choose what would you rather have, a big time d-man like Weber or an impact forward like Parise?
If the choice was literally between those two, I'd take Weber every day of the week and twice on Sunday.
No disrespect intended to Parise, whom I love as a player and would be overjoyed to see him in the 'Note, but Weber is the bomb. How good would a top four on defense of Pietrangelo, Shattenkirk, Polak and Weber be for the next ten years?
I agree, we either need to draft a defenseman or an actual center in the 1st round.
Of the centers in the organization, only McRae and Lehtera have NHL potential IMO. Lehtera might never come over, and McRae might only be a bottom 6 player. We could really some more depth in the prospect pool at center. |
D.C. Ban on Pavement Sealants Helps Clean Waterways
Dec 22, 2008
The District of Columbia City Council voted Dec. 16 to ban the use of harmful coal tar sealants on paved surfaces. Runoff from the sealants carries toxic chemicals into the metro-area’s stormwater system, harming fish and posing health risks to people.
“Every time it rains, stormwater gushes through the streets and alleys of D.C., carrying trash, fertilizer, animal droppings, and a fetid mix of toxic pollutants into our nearby waterways. On top of that, sewage pipes overflow and dump bacteria, viruses, and other dangerous pollutants into the water," said Nancy Stoner, director of the Clean Water Project at the Natural Resources Defense Council.
“This [Comprehensive Stormwater Management Enhancement Amendment Act of 2008] will reduce contaminated stormwater, one of the major sources of pollution that pours into the Anacostia River, the Potomac River and Rock Creek, and the Chesapeake Bay. The ban helps reverse the degradation of metro-area waterways to make them safer for our kids to swim and for fish to live.”
Coal tar sealants contain high levels of polycyclic aromatic hydrocarbons, known as PAHs, which can significantly harm waterways. The U.S. Fish and Wildlife Service has determined that the unusually high levels of PAHs in contaminated sediments in the Anacostia River is one of the causes of the high incidence of cancer and tumors in fish in the river. Studies by the U.S. Geological Survey have also demonstrated that runoff from coal tar sealants carries toxins into waterways that can cause cancer in fish.
In addition to banning the sealants, the legislation helps pay for cleanup and provides a credit for city property owners who help restore metro waterways by installing rain gardens, green roofs, or permeable pavement.
This bill was the result of a collaborative effort, known as the D.C. Stormwater Task Force, which was chaired by Councilmember Jim Graham and D.C. Department of the Environment Director George Hawkins, and included the participation of the D.C. Building Industry Association and the D.C. Apartment and Office Building Association. Councilmember Mary Cheh also championed a ban on the toxic sealants. |
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This new instalment in the critically-acclaimed franchise marks the return to the Prince of Persia Sands of Time storyline. Prince of Persia: The Forgotten Sands will feature many of the fan-favorite elements from the original series as well as new gameplay innovations that gamers have come to expect from the Prince of Persia brand. |
[Risks and health problems caused by the use of video terminals].
To evaluate the association between video display terminal (VDT) use and health hazards, occupational risks, and psychosocial factors, in newspaper workers. A cross-sectional study was conducted in 1998 in a representative sample (n = 68) drawn from a population of 218 VDT operators in Mexico City. Data were collected using a self-administered questionnaire. Data were confirmed by performing physical examinations. The research hypothesis was that both the current and cumulative use of VDT are associated with visual, musculoskeletal system, and skin illnesses, as well as with fatigue and mental or psychosomatic disorders. Occupational health hazards were assessed (visual problems, postural risks, sedentary work, computer mouse use, excessive heat, and overcrowding), as well as psychosocial factors related to work organization (psychological demands, work control, and social support). Prevalence ratios were adjusted for confounding variables like age, sex and schooling. Women were more likely than men to have upper extremity musculoskeletal disorders (MSD), dermatitis, and seborrheic eczema. VDT use was associated with neuro-visual fatigue, upper extremity MSD, dermatitis, and seborrheic eczema. Computer mouse use and postural risks were significantly associated with health problems. Psychosocial factors were mainly associated with mental problems, psychosomatic disorders, and fatigue. Intense use of video screens has been found to cause musculoskeletal disorders of the hand. The diversification of tasks and control of labor processes itself had a protective effect against psychosomatic disorders and pathological fatigue. |
'Straight Outta Compton' Shoot Marred By Fatal Hit-and-Run; Suge Knight Driver, Attorney Confirms
The incident occurred near a promotional shoot for the Universal biopic of rap group NWA.
Police were called to Compton on Thursday in response to a fatal hit-and-run near the set of a promotional shoot for Straight Outta Compton, an upcoming biopic about the rap group NWA. The driver was rap mogul Suge Knight, his attorney James Blatt confirmed.
Blatt told NBC News that Knight was driving the truck and called it a "tragic accident," adding that Knight was making arrangements to surrender to authorities. Detectives are investigating the incident as a homicide. Knight's attorney had earlier confirmed the incident to Billboard and said, "facts all over the place right now" and he is waiting for a preliminary investigation to learn more.
Universal declined to comment, but sources tell The Hollywood Reporter that the incident occurred on or near the set of a promo shoot associated with the film.
Sources say the incident occurred after shooting had wrapped for the day. Dr. Dre and Ice Cube, who were present during the shoot, were not present at the time of the incident.
The film Straight Outta Compton has wrapped production.
John Corina of the Los Angeles Sheriff's Department detective's unit, told the Lt.of the Los Angeles Sheriff's Department detective's unit, told the LA Times that the confrontation began around 3 p.m. when Knight and two unidentified men began arguing on the set and that at least one of the victims was a member of the film crew.
Corina said that about 20 minutes after the alleged argument on set, the victims visited Tam's Burgers near Central and East Rosecrans avenues. Knight, 49, is believed to have followed the men in his truck before running them over the parking lot before leaving the scene.
"They obviously knew each other," Corina told the Times. "They got into some kind of verbal altercation and it escalated. So far the people we talked to said it looked like an intentional act so we are handling it like a homicide."
Terry Carter, a friend of Knight's. Actor Cle "Bone" Sloan was also reportedly struck with the vehicle, and received non-life threatening injuries. LASD confirmed that one of the victims, a 55-year-old man, died. The other, a 51-year-old man, sustained undisclosed injuries. According to TMZ , the dead victim was, a friend of Knight's. Actorwas also reportedly struck with the vehicle, and received non-life threatening injuries.
Knight is known as the co-founder of Death Row Records and currently serves as CEO of Black Kapital Records. He has had multiple run-ins with the law over the years. He was the victim of a shooting in August at a pre MTV Video Music Awards party.
Straight Outta Compton is being directed by F. Gary Gray and is set for an Aug. 14 release. The film is set in the1980s and tells the story of the group's rise to fame.
O’Shea Jackson Jr., Corey Hawkins and Jason Mitchell are starring as Ice Cube, Dr. Dre and Eazy-E, respectively.
Jan. 29, 8:05 p.m. Updated with news of Knight preparing to surrender to authorities.
Jan. 29, 9:20 p.m. Updated with information from Lt. John Corina, LASD, cited by LA Times. |
[Current situation and reflection on the treatment of relative low-heat burns].
Relative low-heat burn can cause primary and secondary damage, and its basic research and clinical studies need to be carried out urgently. In this article, we review content related to relative low-heat burn, including pathogenesis, epidemiological characteristics, and prevention and treatment based on retrieving relevant domestic literature. |
Bug Description
I ran into this bug while trying to deploy a power8 (powerVM) LPAR via MAAS. I was using Trusty with hwe-v kernel. Most of the time, using the same images, I never have issues but I have seen this panic happen randomly. |
Tuesday, September 13, 2011
Oh, fall. The time of year where the leaves are changing, Halloween is right around the corner, and people are obsessing over football. With women putting back on the baggy sweaters and nary a short skirt or cleavage to be seen, where else can a man's mind turn other than the wonders of college basketball. With college basketball preview magazines starting to hit your local newsstand, I figured it's time to get to moving. Right around the corner we'll start up some of the award winning conference previews I do here every year, but before we look ahead let's look further ahead. The Gophers are still in the hunt for some interesting players for 2012-2013, including a few who have visited or will visit in this key early signing period. Let's talk about a few. All player rankings from Rivals.com because that's where I have a membership.
- C Adam Woodbury (Sioux City, IA); 7-0, 230 lbs; #7 center, #42 overall. The highest ranked recruit left the Gophers have offered (and third highest overall), Woodbury would be an incredible coup if Tubby could snag him. Not just because of his talent, which is considerable, but because of the competition for it. Not only would he be battling some top clubs (Ohio State, North Carolina, possibly Kansas and Duke as well), but he'd also be going against Woodbury's home town team (Iowa) who has only one scholarship remaining and can really focus on him, as well as recruiting nemesis Bo Ryan and Wisconsin.
The good news, however, is that there a few reasons for optimism. The first is that Woodbury is from Iowa, and everybody knows that people from Iowa are afraid of the city and anywhere that isn't the midwest, so Minnesota, Wisconsin, and Iowa definitely have the advantage here. I also found an interview with him where he specifically calls out the Gophers (along with Ohio State, Stanford, and Iowa) as having been recruiting him the longest - not his favorites, although he doesn't claim any favorites right now - but those who have been after him for awhile. That's a nice positive. The Buckeyes also seem like they've put him on the back burner a bit - another positive.
If I had to bet money, and I probably would if I could find a site with this bet, I'd guess he's either heading to North Carolina (small townish and his AAU teammate Marcus Paige is already heading there) or Iowa (home town team). But, if he wants to break away from home, but not too far away from home, and thinks about his midwest roots and which teams have shown him loyalty and love from the beginning, he'll probably go to Wisconsin. But if they pull their offer or run out of schollys then the Gophers have a chance.
- C A.J. Hammons (Mouth of Wilson, VA); 7-0, 260 lbs.; #18 center, #123 overall. This is the guy I'd call the most important name of this group, mainly because I think he's the guy they have the best shot at snagging. He's a midwestern kid from Indiana who is playing out in Virginia after transferring to Oak Hill Basketball Factory Academy, but who had said at one point that he wanted to play in the Big 10. The Gophers have stiff competition here because Indiana and Illinois have both offered and Purdue is in the mix, but I'm giving the Gophers a very slight edge because Hammons has mentioned the Gophers specifically in an interview as a team that's been in the mix for a while and also because he counts his mom as helping him to make his decision, and you know Tubby kills it with moms.
Personally, I'd love to get this kid because he's 6-11 or seven feet tall but has measured at a 7-3 wingspan and is generally regarded as one of the best defensive centers in this class with good strength and excellent rebounding and defensive instincts who can score in the post from either block. That's just an awesome description. Of course, since he's not ranked #1 there are some negatives which include conditioning (can be mixed) and motivation (a bit nervous here thanks to 3 years of Ralph). I figure his downside is pretty much Ralph Sampson, so let's get this get on board. According to Chris Monter at gopherhole.com he's visiting this weekend, so let's hope we hear some really good news soon.
- SF Andrew White (Chester, VA); 6-6, 210 lbs; #12 SF, #56 overall. Probably the least likely get on this list, but I'm including him because there's nothing out there to say the Gophers are out of the picture. There's no real good news here either. White has 25 offers, including Texas, Kansas, Maryland, Louisville and like everybody. He's also already visited (unofficially) 5-6 schools and has officials setup to 3 more, none of which are the Gophers. I can't come up with a single reason this guy would end up at a Gopher, but he mentions his dad as an integral part of making his decision, and, as I mentioned earlier Tubby is great with parents. Moreso with Moms, but if you get the crazy involved dad who really wants his kid to grow up to be a man and get an education Tubby could sway him. If you get the crazy dad whose looking to maximize his son as an asset to get his payday Tubby doesn't have a chance, but we already did that dance with the Kardashian kid, and I'm not interested in an encore anyway. Unless of course we get Kim here somehow. I could get down with that.
- SG Sherron Dorsey-Walker (Detroit, MI); 6-4, 175 lbs.; #24 SG, #122 overall. Another guy who fits the combo-guard mold that Tubby seems to be after these days, another guy like White who has been collecting offers because he's up to 16. Even though I prefer a pure point guard and thena couple wings, Memphis under Calipari and Huggins' WVU teams intrigued me with their collection of interchangeable parts, and I think if they get this guy they are pretty much going to be doing that, at least with the perimeter players.
From the sounds of things his upside is pretty huge. I can't find any references to weakness and at some pint in the various articles I've seen shooting, ball-handling, passing, and driving and scoring at the rim listed as strengths which I guess probably means he isn't the best defender since I can't find any reference to that but whatever since that's the only thing Tubby really truly knows how to teach and with his athleticism I'm sure he could be a capable defender in no time. Well lookit here, I've apparently talked myself right into this kid.
He says he's planning to commit sometime in October and the Gophers are very much in the mix. He has visits planned already for B.C., Temple, and Iowa State (damn you Hoiberg! :shakesfist:), but lists the Gophers amongst the teams he's considering for his final two visits (along with VA Tech, Florida State, and Baylor). Maybe I'm crazy at this point, but I still believe whenever Tubby gets this close he's got a chance. He mentions Tubby and his respect and good feeling about him in one of his interviews. Of course he also said he was planning on making his decision in August and yet here we are so maybe he's just a pathological liar.
- PF Chad Rykhoek (Fort Worth, TX); 6-9, 215 lbs.; #39 PF, #135 overall. He could be the first one to sign somewhere, whether with the Gophers or elsewhere, since he's already said he's planning to commit during the early period which ends in November. That's bad news for the Gophers because he's already set up four official campus visits for the coming months (Missouri, Rice, Colorado, and Nebraska) and is trying to decide which school he wants to make his fifth official - SMU, North Texas, TCU, Drake, or the Gophers. SMU is his home town school and he mentions Drake as having been after him the longest, so they have the inside track, but Minnesota is the highest profile program of those five so who knows. I'd probably write the kid off as the Gophers not having a shot, but that seems like a fairly underwhelming list of offers, no? And in the few interviews I read he doesn't seem like he's exactly chomping at the bit to sign with any of them, so I'll give Tubby and the Gophers an outside shot here.
I didn't bother discussing Jevontae Hawkins because he seems like he's practically a done deal for West Virginia and even if he isn't I don't think the Gophers can steal him away. I also didn't include Jodan Price who dropped the Gophers from consideration after they signed Wally Ellenson or Demarquise Johnson who looks like he's going to stay somewhere out west.
As far as a list of target's for the spring session I think it's solid. The team will probably have two scholarships or so, so you don't want to overextend yourself if these are the guys you want. Keep in mind the three guys I didn't include plus Ellenson mean they've offered nine guys and that doesn't include guys who they offered who signed elsewhere (including recent losses Brandon Taylor to Penn State (ouch) and Nick Banyard to New Mexico (double outch)).
I like the quality here as well. Outside of home town kids I think if Tubby focuses on the players in the #50-#150 range that's how he can build up the program. Getting kids of that caliber (AND KEEPING THEM, DAMMIT) can help create a winning program that will allow him to sweet talk some top 50 types once in a while. Plus, since he's allegedly a good coach who can coach players up, that level of player should be perfect - talented enough to develop into a great player, but not so talented they already think they can't really be coached - not that that stops Calipari. I'm just afraid that if they whiff on all these kids or get strung out too long they're going to end up in a scramble situation again and end up with lower tier talent again. Self-perpetuating and self-defeated cycle, and I think they're already scrambling on the edge to stay off that ride.
One guy I wish they'd offer is PG Ray Lee from Michigan, who has already said he wants to play out of state so that takes Izzo (and Beilein) out of the running. He's a big kid at 6-3 and ranked #142 overall in the country. His number 1 priority is playing time, and with the Gophers absolutely refusing to address their PG problem he'd be perfect. The problem? Priority #2 is "an offense that is fast paced and allows the freedom to drive and create while being allowed to play through mistakes." |
If some people are going to say that INTJs bump into walls, don’t pay attention, doze off, and aren’t athletic as S-types, wouldn’t this mean that INTJs are “less predacious” than say ISTJs? If ISTJs have a closer relationship to the empirical, reality, and concrete, wouldn’t that also mean that they’re likely to make better hunters, killers, or predators? Is it possible that a lot of INTJs with a death stare or death glare are mistyped and are actually ISTJs? Is it possible to argue a case saying that ISTJs might actually make better surgeons than INTJs? Could some general evolutionary theory somehow be connected to everything that has been said?
"So all that was great in the past was ridiculed, condemned, combatted, suppressed — only to emerge all the more powerfully, all the more triumphantly from the struggle." – Nikola Tesla
Do immigrants, refugees, or migrants take away jobs? Of course they do. Ever rode the public bus and see some people where it’s pretty obvious they’re wearing a job uniform but appear as if they might not speak adequate English or would have a hard time understanding big words? There you go.
"So all that was great in the past was ridiculed, condemned, combatted, suppressed — only to emerge all the more powerfully, all the more triumphantly from the struggle." – Nikola Tesla
After browsing through the Google search engines typing in various phrases, I can’t believe some people actually believe Elon Musk to be an ENTJ. Check out the following:
When Musk was a child, he would often gaze into the distance while his parents were speaking to him, which led them to believe that he might be hard of hearing. Doctors removed his adenoids, but it made no difference. It turned out he was just daydreaming. His mother, Maye, told biographer Ashlee Vance, “He goes into his brain, and then you just see he is in another world. … Now I just leave him be because I know he is designing a new rocket or something.”
"Every ENTJ I’ve ever met has this slightly vague look in their eyes, like they see you but at the same time they don’t. I’ve been told that I do this and that it’s mildly unsettling at times." - Kathleen-June Horne
"Every ENTJ I’ve ever met has this slightly vague look in their eyes, like they see you but at the same time they don’t. I’ve been told that I do this and that it’s mildly unsettling at times." - Kathleen-June Horne
"Every ENTJ I’ve ever met has this slightly vague look in their eyes, like they see you but at the same time they don’t. I’ve been told that I do this and that it’s mildly unsettling at times." - Kathleen-June Horne
I just remembered I had a strange dream a while ago about some ENTJ chick I became friends with and realized that every now and then, she noted on social media that she travels internationally for work or her job. In my mind in that dream, I guess I never really made much of it but then one day, I started to think about how limited jobs/professions like that really are. I started to have all kinds of conspiracy theories about what she really does for a living but then I woke up so oh well.
"So all that was great in the past was ridiculed, condemned, combatted, suppressed — only to emerge all the more powerfully, all the more triumphantly from the struggle." – Nikola Tesla |
Left-Sided Complete Revascularization With Bilateral Internal Thoracic Arteries in Patients With Diabetes.
Reports are few on the long-term patency of bilateral internal thoracic artery (BITA) grafts in patients with diabetes. We evaluated the relationship between the long-term patency of BITAs and the clinical outcomes in diabetes. We retrospectively identified 569 patients (321 with diabetes, 248 without diabetes) who underwent isolated BITA grafting for left-sided complete revascularization at our institution from 2000 to 2015. The primary end point was the incidence of major adverse cardiovascular events comprising death, re-revascularization, and myocardial infarction. The secondary end point was the patency of the BITAs. No differences were found in the major adverse cardiovascular event rate (10-year: diabetic group, 33.7%; nondiabetic group, 22.3%; p = 0.15) or overall mortality rate (24.0% versus 12.2%, p = 0.066) between the patients with and without diabetes. The incidence of cardiac death (3.3% versus 1.8%, p = 0.80) or re-revascularization and myocardial infarction (11.4% versus 11.8%, p = 0.67) was similar between the groups. The patency of free internal thoracic artery (ITA) grafts to the left circumflex artery was associated with greater patency in patients with diabetes than in patients without diabetes (4 years: 99.3% versus 95.5%, p = 0.049); the patency of other ITA grafts did not differ between the groups. All-cause death, re-revascularization, and myocardial infarction showed no differences between patients with and without diabetes who underwent left-sided revascularization with the BITAs. Although diabetes did not affect the patency of the ITA, free ITA grafts to the left circumflex artery showed good long-term patency in patients with diabetes. |
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<distance name="right_titlebar_edge" value="6"/>
<distance name="button_width" value="20"/>
<distance name="button_height" value="20"/>
<distance name="title_vertical_pad" value="8"/>
<border name="title_border" left="2" right="2" top="0" bottom="0"/>
<border name="button_border" left="1" right="1" top="1" bottom="1"/>
</frame_geometry>
<frame_geometry name="shaded" parent="normal" rounded_top_left="false" rounded_top_right="false" rounded_bottom_left="false" rounded_bottom_right="false"/>
<frame_geometry name="normal_maximized" parent="normal" rounded_top_left="false" rounded_top_right="false" rounded_bottom_left="false" rounded_bottom_right="false">
<distance name="left_width" value="0"/>
<distance name="right_width" value="0"/>
<distance name="bottom_height" value="0"/>
<distance name="left_titlebar_edge" value="6"/>
<distance name="right_titlebar_edge" value="6"/>
<distance name="button_width" value="20"/>
<distance name="button_height" value="20"/>
<distance name="title_vertical_pad" value="8"/>
<border name="title_border" left="2" right="2" top="0" bottom="0"/>
<border name="button_border" left="1" right="1" top="1" bottom="1"/>
</frame_geometry>
<frame_geometry name="utility" title_scale="small" rounded_top_left="false" rounded_top_right="false" rounded_bottom_left="false" rounded_bottom_right="false">
<distance name="left_width" value="2"/>
<distance name="right_width" value="2"/>
<distance name="bottom_height" value="2"/>
<distance name="left_titlebar_edge" value="3"/>
<distance name="right_titlebar_edge" value="3"/>
<distance name="title_vertical_pad" value="0"/>
<border name="title_border" left="2" right="2" top="0" bottom="0"/>
<border name="button_border" left="1" right="1" top="1" bottom="1"/>
<aspect_ratio name="button" value="1"/>
</frame_geometry>
<frame_geometry name="border" has_title="false">
<distance name="left_width" value="2"/>
<distance name="right_width" value="2"/>
<distance name="bottom_height" value="2"/>
<distance name="left_titlebar_edge" value="0"/>
<distance name="right_titlebar_edge" value="0"/>
<distance name="button_width" value="0"/>
<distance name="button_height" value="0"/>
<distance name="title_vertical_pad" value="4"/>
<border name="title_border" left="0" right="0" top="0" bottom="0"/>
<border name="button_border" left="0" right="0" top="0" bottom="0"/>
</frame_geometry>
<!-- button minimum size -->
<constant name="Bmin" value="7"/>
<!-- button inside padding -->
<constant name="Bpad" value="6"/>
<!-- ::: BORDER ::: -->
<draw_ops name="border">
<rectangle color="shade/gtk:bg[NORMAL]/1.00" filled="false" x="0" y="0" width="width-1" height="height-1"/>
</draw_ops>
<draw_ops name="border_unfocused">
<rectangle color="shade/gtk:bg[NORMAL]/0.95" filled="false" x="0" y="0" width="width-1" height="height-1"/>
</draw_ops>
<draw_ops name="maxed_border">
<line color="shade/gtk:bg[NORMAL]/1.00" x1="0" y1="0" x2="width" y2="0"/>
<line color="shade/gtk:bg[NORMAL]/1.00" x1="0" y1="height-1" x2="width" y2="height-1"/>
</draw_ops>
<!-- ::: TITLEBAR ::: -->
<draw_ops name="titlebar_gradient">
<gradient type="vertical" x="0" y="0" width="width" height="top_height">
<color value="shade/gtk:bg[NORMAL]/0.97"/>
<color value="shade/gtk:bg[NORMAL]/1.00"/>
<color value="shade/gtk:bg[NORMAL]/1.00"/>
</gradient>
</draw_ops>
<draw_ops name="titlebar_gradient_unfocused">
<gradient type="vertical" x="0" y="0" width="width" height="top_height">
<color value="shade/gtk:bg[NORMAL]/1.00"/>
<color value="shade/gtk:bg[NORMAL]/1.00"/>
</gradient>
</draw_ops>
<!-- ::: TITLEBAR DIALOG ::: -->
<draw_ops name="titlebar_dialog">
<gradient type="vertical" x="0" y="0" width="width" height="top_height">
<color value="shade/gtk:bg[NORMAL]/0.97"/>
<color value="shade/gtk:bg[NORMAL]/1.00"/>
<color value="shade/gtk:bg[NORMAL]/1.00"/>
</gradient>
<!-- <line color="shade/gtk:bg[NORMAL]/0.60" x1="0" y1="title_height + 6" x2="width" y2="title_height + 6"/> -->
</draw_ops>
<draw_ops name="titlebar_maximized">
<include name="titlebar_gradient"/>
<include name="maxed_border"/>
</draw_ops>
<draw_ops name="round_titlebar">
<include name="titlebar_gradient"/>
<include name="border"/>
</draw_ops>
<draw_ops name="round_titlebar_unfocused">
<include name="titlebar_gradient_unfocused"/>
<include name="border_unfocused"/>
</draw_ops>
<draw_ops name="dialog_round_titlebar">
<include name="titlebar_dialog"/>
<include name="border"/>
</draw_ops>
<draw_ops name="titlebar_shaded">
<include name="titlebar_gradient_unfocused"/>
<include name="border_unfocused"/>
</draw_ops>
<draw_ops name="round_titlebar_shaded">
<include name="titlebar_gradient_unfocused"/>
<include name="border"/>
<line color="shade/gtk:bg[NORMAL]/0.85" x1="5" y1="height-1" x2="width-6" y2="height-1"/>
</draw_ops>
<!-- ::: TITLES ::: -->
<draw_ops name="title">
<title color="shade/gtk:bg[NORMAL]/0.85" x="((width - title_width) / 2) -36 `max` 0" y="1 `max` ((height-title_height)/2)+1"/>
<title color="shade/gtk:text[NORMAL]/1.10" x="((width - title_width) / 2) -36 `max` 0" y="0 `max` ((height-title_height)/2)"/>
</draw_ops>
<draw_ops name="title_unfocused">
<title color="shade/gtk:fg[NORMAL]/0.85" x="((width - title_width) / 2) -36 `max` 0" y="0 `max` ((height-title_height)/2)"/>
</draw_ops>
<!-- menu icon -->
<draw_ops name="menu_button_normal">
<image filename="menu-focus-normal.svg"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="menu_button_prelight">
<image filename="menu-focus.svg"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="menu_button_pressed">
<image filename="menu-pressed.svg"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"
colorize="shade/gtk:bg[SELECTED]/0.85"/>
</draw_ops>
<draw_ops name="menu_button_unfocused">
<image filename="menu-focus-none.svg"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<!-- close icon -->
<draw_ops name="close_button_normal">
<image filename="close_focused_normal.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="close_button_prelight">
<image filename="close_focused_prelight.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="close_button_pressed">
<image filename="close_focused_pressed.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="close_button_unfocused">
<image filename="close_unfocused.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<!-- maximize icon -->
<draw_ops name="maximize_button_normal">
<image filename="maximize_focused_normal.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="maximize_button_prelight">
<image filename="maximize_focused_prelight.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="maximize_button_pressed">
<image filename="maximize_focused_pressed.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="maximize_button_unfocused">
<image filename="maximize_unfocused.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<!-- minimize icon -->
<draw_ops name="minimize_button_normal">
<image filename="minimize_focused_normal.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="minimize_button_prelight">
<image filename="minimize_focused_prelight.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="minimize_button_pressed">
<image filename="minimize_focused_pressed.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="minimize_button_unfocused">
<image filename="minimize_unfocused.png"
x="(width - object_width) / 2"
y="(height - object_height) / 2"
width="object_width"
height="object_height"/>
</draw_ops>
<draw_ops name="blank">
<!-- nothing -->
</draw_ops>
<!-- ::: FRAME STYLES ::: -->
<frame_style name="normal" geometry="normal">
<piece position="entire_background" draw_ops="round_titlebar_unfocused"/>
<piece position="title" draw_ops="title_unfocused"/>
<button function="close" state="normal" draw_ops="close_button_unfocused"/>
<button function="close" state="pressed" draw_ops="close_button_pressed"/>
<button function="close" state="prelight" draw_ops="close_button_prelight"/>
<button function="maximize" state="normal" draw_ops="maximize_button_unfocused"/>
<button function="maximize" state="pressed" draw_ops="maximize_button_pressed"/>
<button function="maximize" state="prelight" draw_ops="maximize_button_prelight"/>
<button function="minimize" state="normal" draw_ops="minimize_button_unfocused"/>
<button function="minimize" state="pressed" draw_ops="minimize_button_pressed"/>
<button function="minimize" state="prelight" draw_ops="minimize_button_prelight"/>
<button function="menu" state="normal" draw_ops="menu_button_unfocused"/>
<button function="menu" state="pressed" draw_ops="menu_button_pressed"/>
<button function="menu" state="prelight" draw_ops="menu_button_prelight"/>
</frame_style>
<frame_style name="normal_shaded" geometry="shaded" parent="normal">
<piece position="entire_background" draw_ops="round_titlebar_shaded"/>
</frame_style>
<frame_style name="focused" geometry="normal" parent="normal">
<piece position="entire_background" draw_ops="round_titlebar"/>
<piece position="title" draw_ops="title"/>
<button function="close" state="normal" draw_ops="close_button_normal"/>
<button function="close" state="pressed" draw_ops="close_button_pressed"/>
<button function="close" state="prelight" draw_ops="close_button_prelight"/>
<button function="maximize" state="normal" draw_ops="maximize_button_normal"/>
<button function="maximize" state="pressed" draw_ops="maximize_button_pressed"/>
<button function="maximize" state="prelight" draw_ops="maximize_button_prelight"/>
<button function="minimize" state="normal" draw_ops="minimize_button_normal"/>
<button function="minimize" state="pressed" draw_ops="minimize_button_pressed"/>
<button function="minimize" state="prelight" draw_ops="minimize_button_prelight"/>
<button function="menu" state="normal" draw_ops="menu_button_normal"/>
<button function="menu" state="pressed" draw_ops="menu_button_pressed"/>
<button function="menu" state="prelight" draw_ops="menu_button_prelight"/>
</frame_style>
<frame_style name="focused_shaded" geometry="shaded" parent="focused">
<piece position="entire_background" draw_ops="round_titlebar_unfocused"/>
</frame_style>
<frame_style name="dialog_focused" geometry="normal" parent="normal">
<piece position="entire_background" draw_ops="dialog_round_titlebar"/>
<piece position="title" draw_ops="title"/>
<button function="close" state="normal" draw_ops="close_button_normal"/>
<button function="close" state="pressed" draw_ops="close_button_pressed"/>
<button function="close" state="prelight" draw_ops="close_button_prelight"/>
<button function="maximize" state="normal" draw_ops="maximize_button_normal"/>
<button function="maximize" state="pressed" draw_ops="maximize_button_pressed"/>
<button function="maximize" state="prelight" draw_ops="maximize_button_prelight"/>
<button function="minimize" state="normal" draw_ops="minimize_button_normal"/>
<button function="minimize" state="pressed" draw_ops="minimize_button_pressed"/>
<button function="minimize" state="prelight" draw_ops="minimize_button_prelight"/>
<button function="menu" state="normal" draw_ops="menu_button_normal"/>
<button function="menu" state="pressed" draw_ops="menu_button_pressed"/>
<button function="menu" state="prelight" draw_ops="menu_button_prelight"/>
</frame_style>
<frame_style name="normal_maximized" geometry="normal_maximized" parent="normal">
<piece position="entire_background" draw_ops="titlebar_maximized"/>
<button function="maximize" state="normal" draw_ops="maximize_button_unfocused"/>
<button function="maximize" state="pressed" draw_ops="maximize_button_pressed"/>
<button function="maximize" state="prelight" draw_ops="maximize_button_prelight"/>
</frame_style>
<frame_style name="focused_maximized" geometry="normal_maximized" parent="focused">
<piece position="entire_background" draw_ops="titlebar_maximized"/>
<button function="maximize" state="normal" draw_ops="maximize_button_normal"/>
<button function="maximize" state="pressed" draw_ops="maximize_button_pressed"/>
<button function="maximize" state="prelight" draw_ops="maximize_button_prelight"/>
</frame_style>
<frame_style name="border" geometry="border" parent="normal">
<piece position="entire_background" draw_ops="border"/>
<piece position="title" draw_ops="blank"/>
</frame_style>
<frame_style name="utility_normal" geometry="utility" parent="normal">
</frame_style>
<frame_style name="utility_focused" geometry="utility" parent="focused">
</frame_style>
<frame_style name="utility_focused_shaded" geometry="utility" parent="focused_shaded">
<piece position="entire_background" draw_ops="titlebar_shaded"/>
</frame_style>
<frame_style_set name="normal">
<frame focus="yes" state="normal" resize="both" style="focused"/>
<frame focus="no" state="normal" resize="both" style="normal"/>
<frame focus="yes" state="maximized" style="focused_maximized"/>
<frame focus="no" state="maximized" style="normal_maximized"/>
<frame focus="yes" state="shaded" style="focused_shaded"/>
<frame focus="no" state="shaded" style="normal_shaded"/>
<frame focus="yes" state="maximized_and_shaded" style="focused_maximized"/>
<frame focus="no" state="maximized_and_shaded" style="normal_maximized"/>
</frame_style_set>
<frame_style_set name="dialog">
<frame focus="yes" state="normal" resize="both" style="dialog_focused"/>
<frame focus="no" state="normal" resize="both" style="dialog_focused"/>
<frame focus="yes" state="maximized" style="focused_maximized"/>
<frame focus="no" state="maximized" style="normal_maximized"/>
<frame focus="yes" state="shaded" style="focused_shaded"/>
<frame focus="no" state="shaded" style="normal_shaded"/>
<frame focus="yes" state="maximized_and_shaded" style="focused_maximized"/>
<frame focus="no" state="maximized_and_shaded" style="normal_maximized"/>
</frame_style_set>
<frame_style_set name="utility" parent="normal">
<frame focus="yes" state="normal" resize="both" style="utility_focused"/>
<frame focus="no" state="normal" resize="both" style="utility_normal"/>
<!-- this is a bunch of crack since utility windows shouldn't be maximized -->
<frame focus="yes" state="maximized" style="focused"/>
<frame focus="no" state="maximized" style="normal"/>
<frame focus="yes" state="shaded" style="utility_focused_shaded"/>
<frame focus="no" state="shaded" style="utility_normal"/>
<frame focus="yes" state="maximized_and_shaded" style="focused_shaded"/>
<frame focus="no" state="maximized_and_shaded" style="normal"/>
</frame_style_set>
<frame_style_set name="border">
<frame focus="yes" state="normal" resize="both" style="border"/>
<frame focus="no" state="normal" resize="both" style="border"/>
<frame focus="yes" state="maximized" style="border"/>
<frame focus="no" state="maximized" style="border"/>
<frame focus="yes" state="shaded" style="border"/>
<frame focus="no" state="shaded" style="border"/>
<frame focus="yes" state="maximized_and_shaded" style="border"/>
<frame focus="no" state="maximized_and_shaded" style="border"/>
</frame_style_set>
<window type="normal" style_set="normal"/>
<window type="dialog" style_set="dialog"/>
<window type="modal_dialog" style_set="dialog"/>
<window type="menu" style_set="utility"/>
<window type="utility" style_set="utility"/>
<window type="border" style_set="border"/>
<menu_icon function="close" state="normal" draw_ops="close_button_icon_unfocused"/>
<menu_icon function="maximize" state="normal" draw_ops="maximize_button_icon_unfocused"/>
<menu_icon function="unmaximize" state="normal" draw_ops="maximize_button_icon_unfocused"/>
<menu_icon function="minimize" state="normal" draw_ops="minimize_button_icon_unfocused"/>
</metacity_theme>
|
Ajike Ogunoye
Ajike Ogunoye was a paramount ruler of Owo Kingdom, Ondo state, southwestern Nigeria who reigned between 1938 and 1941. He was the son of Olagbegi Atanneye I and immediate brother of Olowo Ajaka.
References
Category:Yoruba monarchs
Category:Nigerian traditional rulers
Category:People from Owo
Category:Olagbegi family |
A church warden has been jailed for life after being found guilty of murdering a university lecturer following a sustained campaign of physical and mental abuse.
Benjamin Field, 28, was convicted in August of killing Peter Farquhar, 69, a retired teacher and part-time university lecturer, to inherit his house and money, and then trying to make his death look like an accident or suicide.
Field was given life imprisonment with a minimum term of 36 years by Mr Justice Sweeney at Oxford crown court on Friday.
Detectives branded Field a psychopath and said he would have posed an “ongoing danger to society” had he not been stopped.
After Farquhar’s death in October 2015, Field, a Baptist minister’s son, began targeting Farquhar’s neighbour, 83-year-old Ann Moore-Martin, a deeply religious retired headteacher. He wrote messages on her mirrors purporting to be from God.
After protracted deliberations, Field was cleared of charges of conspiracy to murder and the attempted murder of Moore-Martin, who lived a few doors away from Farquhar in the village of Maids Moreton. Moore-Martin died from natural causes in May 2017.
The judge Mr Justice Sweeney said Field “lived by deception and deceit and had been a well-practised and able liar”.
He added: “The evidence at trial clearly demonstrated grandiosity, a sense of superiority towards others, the exploitation of others to achieve personal gain, the need to belittle and humiliate others, fixation on fantasies of power and success, intelligence, a need for admiration from others and a sense of entitlement, together with an unwillingness to empathise with the feelings, needs and wishes of others.”
David Jeremy QC, the defence lawyer, said two psychiatrists had said Field had either a narcissistic personality disorder or a psychopathic personality disorder. “He was and is an intelligent and educated man and chose to apply those gifts towards the manipulation and humiliation of his victims, leading to the murder of Peter Farquhar and the degradation of Ann Moore-Martin and the causing of irreparable harm to their families and those close to them,” he said.
Prosecutors said Field had a “profound fascination in controlling and manipulating and humiliating and killing”, and they alleged he had plotted his crimes with a friend, Martyn Smith.
Smith, 32, a failed magician, was cleared of murdering Farquhar and of conspiracy to murder and the attempted murder of Moore-Martin.
During the trial, jurors were told of Field’s elaborate project of befriending elderly individuals who were vulnerable and lonely and then defrauding them by allowing them to think he was in a loving relationship with them. He encouraged them to change their will to benefit him and then began a devastating campaign of physical and mental torture.
Facebook Twitter Pinterest Ann Moore-Martin. Field was cleared of charges of conspiracy to murder and attempted murder. Photograph: Thames Valley police/PA
Field admitted to poisoning, gaslighting and defrauding Farquhar in order to get a better job and inherit his wealth when he died, and he told the court he had also deceived and manipulated Moore-Martin in a similar way. He accepted he had “psychologically manipulated” the pair but he denied any involvement in their deaths.
Field drew up a list of 100 future “targets”, including his own parents and grandparents, the court heard. He told the jury the “100 clients” file was not just a list of future targets but of people who could help him. The Crown Prosecution Service said the case was like a “plot from a novel”.
Field and Smith met Farquhar when they were students at Buckingham University. Field struck up a friendship with the university lecturer and began lodging with him. Oliver Saxby QC, the lead prosecutor, told the jury that Field saw that Farquhar was vulnerable, “and this was something from the very outset he decided to exploit”.
Field and Farquhar soon entered into a relationship and had a formal ceremony, which they called a betrothal ceremony. Like Farquhar, Moore-Martin was unmarried and had no children. Saxby told the court she was “fundamentally lonely”.
In a statement, the Church of England diocese of Oxford said: “The sentencing of Ben Field marks the conclusion of a long, complex and disturbing case. It’s clear that Ben Field manipulated everyone he came into contact with. We’re determined to learn what we can from this extraordinary case. The church and wider society needs to be ever more vigilant of those who can be made vulnerable by the likes of Ben Field simply because they are elderly or lonely.” |
Total blood washout and exchange. A valuable tool in acute hepatic coma and Reye's syndrome.
Total body washout (TBW) was accomplished thirteen times in twelve patients, with response in five and survival in three. TBW can be done without apparent harm to patients and is less laborious and more rapidly effective than repeated exchange transfusion. Early application of TBW in stage III to stage IV hepatic coma may increase survival and possibly prevent progression of metabolic derangements. Patients with stage III to IV Reye's syndrome probably should have TBW promptly, without time-consuming attempts at exchange transfusion. Based on our experience, further application of TBW is warranted in coma due to acute hepatic failure and stage III to IV Reye's syndrome. |
<#include "/public/macro.html">
<form class="layui-form" action="/apps/report/design/values.html" id="selcubelevel">
<input type="hidden" name="t" value="${t!''}" id="t">
<#if dtype??><input type="hidden" name="dtype" value="${dtype!''}"></#if>
<input type="hidden" name="tabid" value="${tabid!''}">
<input type="hidden" name="dsid" value="<#if cube??>${cube.id!''}</#if>" >
<input type="hidden" name="mid" value="<#if reportModel?? && reportModel.id??>${reportModel.id!''}</#if>" />
<#if t?? && t=='dim'>
<div class="layui-form-item">
<label class="layui-form-label">选择维度</label>
<div class="layui-input-inline">
<select id="dimensionselect" name="dimension" lay-filter="dimensionselect">
<option value="">选择维度</option>
<#if cube?? && cube.cube?? && cube.cube.dimension??>
<#list cube.cube.dimension as thisdim>
<option value="${thisdim.id!''}" <#if dim?? && dim == thisdim.id>selected</#if> >${thisdim.name!''}</option>
</#list>
</#if>
</select>
</div>
</div>
<div class="layui-form-item" >
<label class="layui-form-label">维度成员：</label>
<div class="layui-input-inline">
<select name="d" id="levelid" lay-verify="required">
<option value="">请选择维度成员</option>
<#if cube?? && cube.cube?? && cube.cube.dimension??>
<#list cube.cube.dimension as thisdim>
<#if dim?? && dim == thisdim.id && thisdim.cubeLevel??>
<#list thisdim.cubeLevel as cubelevel>
<option value="${cubelevel.id!''}" >${cubelevel.name!''}</option>
</#list>
</#if>
</#list>
</#if>
</select>
</div>
</div>
<#elseif t?? && t=='measure'>
<div class="layui-form-item">
<label class="layui-form-label">选择指标</label>
<div class="layui-input-inline">
<select name="m" lay-verify="required">
<option value="">选择指标</option>
<#if cube?? && cube.cube?? && cube.cube.measure??>
<#list cube.cube.measure as measure>
<option value="${measure.id!''}" >${measure.name!''}</option>
</#list>
</#if>
</select>
</div>
</div>
<#elseif t?? && t=='filter'>
<div class="layui-form-item">
<label class="layui-form-label">选择维度</label>
<div class="layui-input-inline">
<select id="dimensionselect" name="dimension" lay-filter="dimensionselect">
<option value="">选择维度</option>
<#if cube?? && cube.cube?? && cube.cube.dimension??>
<#list cube.cube.dimension as thisdim>
<option value="${thisdim.id!''}" <#if dim?? && dim == thisdim.id>selected</#if> >${thisdim.name!''}</option>
</#list>
</#if>
</select>
</div>
</div>
<div class="layui-form-item" >
<label class="layui-form-label">维度成员：</label>
<div class="layui-input-inline">
<select name="f" id="levelid" lay-verify="required">
<option value="">请选择维度成员</option>
<#if cube?? && cube.cube?? && cube.cube.dimension??>
<#list cube.cube.dimension as thisdim>
<#if dim?? && dim == thisdim.id && thisdim.cubeLevel??>
<#list thisdim.cubeLevel as cubelevel>
<option value="${cubelevel.id!''}" >${cubelevel.name!''}</option>
</#list>
</#if>
</#list>
</#if>
</select>
</div>
</div>
</#if>
<div class="layui-form-button" >
<div class="layui-button-block">
<button class="layui-btn layui-btn-normal" lay-submit>立即提交</button>
</div>
</div>
</form>
<script>
layui.use('form', function(){
var form = layui.form;
form.render();
<#if t?? && (t=='dim'|| t=='filter') >
form.on('select(dimensionselect)', function(data){
loadURL('/apps/report/design/adddata.html?<#if dtype??>dtype=${dtype!''}&</#if>tabid=${tabid!''}&t=${t!''}&cubeid=<#if cube??>${cube.id!''}</#if>&mid=<#if reportModel??>${reportModel.id!''}</#if>&dim='+data.value, '#selcubelevel');
});
</#if>
});
</script>
|
FILED
NOT FOR PUBLICATION
SEP 13 2016
UNITED STATES COURT OF APPEALS MOLLY C. DWYER, CLERK
U.S. COURT OF APPEALS
FOR THE NINTH CIRCUIT
MALIBU TEXTILES, INC., a New York No. 14-56635
corporation,
D.C. No.
Plaintiff-Appellant, 2:14-cv-04054-R-MAN
v.
MEMORANDUM*
LABEL LANE INTERNATIONAL, INC.,
a California corporation, and ENTRY,
INC., dba ALT B., a California
corporation,
Defendants-Appellees.
Appeal from the United States District Court
for the Central District of California
Manuel L. Real, District Judge, Presiding
Argued and Submitted September 1, 2016
Pasadena, California
Before: SILVERMAN, IKUTA, and WATFORD, Circuit Judges.
The district court erred by granting the defendants’ motion to dismiss with
prejudice. Although Malibu did not plead sufficient facts to state a claim for
*
This disposition is not appropriate for publication and is not precedent
except as provided by Ninth Circuit Rule 36-3.
Page 2 of 4
copyright infringement, the district court abused its discretion by denying Malibu
the opportunity to amend its complaint. Dismissal with prejudice is appropriate
only if the complaint “could not be saved by any amendment.” Leadsinger, Inc. v.
BMG Music Publ’g, 512 F.3d 522, 532 (9th Cir. 2008). Here, that is not the case.
To state a claim for copyright infringement, Malibu had to allege facts
plausibly showing that the defendants copied the protected elements in Malibu’s
work. Three Boys Music Corp. v. Bolton, 212 F.3d 477, 481 (9th Cir. 2000). A
plaintiff may satisfy this element by showing either that the two works in question
are strikingly similar, or by showing that they are substantially similar and that the
defendant had access to the plaintiff’s work. Id. at 481, 485. In the absence of
direct evidence of access, a plaintiff can show that a chain of events linked the
protected work to the defendant, or that the work had been widely disseminated.
Id. at 482. Malibu’s complaint did not adequately allege copying of a protected
work under any of these theories.
However, Malibu potentially could have amended its complaint to cure this
deficiency in several ways. To allege striking or substantial similarity, Malibu
could have described the pattern’s protectible elements—such as the selection,
coordination, and arrangement of flowers, leaves, and branches—and identified
those same elements in the defendants’ patterns, perhaps with reference to photos
Page 3 of 4
showing a side-by-side comparison of the works. See L.A. Printex Indus., Inc. v.
Aeropostale, Inc., 676 F.3d 841, 850 (9th Cir. 2012). Although Malibu’s first
amended complaint described the arrangement of elements that was allegedly
incorporated into defendants’ product, and alleged that the layout and arrangement
of the two products were substantially similar or virtually identical, the complaint
did not provide photos that clearly showed these similarities and did not describe
the arrangement of the elements with sufficient specificity. And to allege access,
Malibu could have pleaded facts showing a chain of events that linked the
protected pattern with the allegedly infringing patterns, or provided sales figures
accompanied by dates and geographic distribution information plausibly showing
access via widespread dissemination. Because these allegations could cure the
complaint’s deficiencies, the district court’s conclusion that amendment would be
futile was incorrect.
The district court also relied incorrectly on Satava v. Lowry, 323 F.3d 805,
813 (9th Cir. 2003), in holding that Malibu failed to allege that any protectible
elements were substantially similar in both works. Stylized fabric designs
featuring floral elements are entitled to broad copyright protection under L.A.
Printex, 676 F.3d at 850 n.4, 851. Even if some of the elements in Malibu’s
pattern were not protectible on their own, copyright protection extends to the
Page 4 of 4
“[o]riginal selection, coordination, and arrangement of unprotectible elements.”
Id. at 849. The district court should have considered these aspects of the pattern in
its analysis of protected elements.
REVERSED and REMANDED.
|
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Education About Lower Back Pain – Learning While Improving
No matter your age, gender, or size, we can all be exposed contracting a type of back problem. You have likely groaned and complained just as much about back aches, and injuries. I’m here to reassure you are not alone.
Back Pain has a combination of a MAXIMUM, and Minimum. The range can vary in:
Low, called “Acute”
Mild, “sub-acute”
High, “Chronic”
All of these pains have one goal in common. They make you readjust your lifestyle.
I will be walking you into the ways you develop lower back pain, as well as what’s the best solutions that result in the #1 outcome for you.
We’re aiming for no more missed days at the office, no more reasons to call it a day, and absolutely no more time away from your necessities.
A dysfunctional, and immobile back translates to an overall lack of movement. But where there is an “end” there is always a “beginning”.
You’ll want to know questions like why you’re back muscles, tissues, and ligaments are not supporting you. Why is the pain persisting? and Why can’t I find the relief I need?
In the next part I will be breaking down these questions into 3 layers.
The first are the symptoms.
Second will be a diagnosis.
Third, about your root of the cause, and the best ways to improve it.
Importance Of Mobility Means Moving Freely
Back pain, from upper to lower has been evolving for many years. Not gradually but sporadically!
The pain has been with us humans since the “Bronze Age“. The Physicians during this era assumed the cause came from inflammation. Hit the fast forward button to our present time, there’s no need to assume. We have ” the TECHNOLOGY” God.
Now you can actually tell its associated with symptoms such as:
nerve weakness
psychological disorders
Lower back pain in particular is the number one cause among 300 OTHER diagnosis. It is the number 1 reason why you have been missing work! That’s INSANE if you were to ask me. These reasons back up the fact, there is no greater time in our western, and global apparatus to learn and educate ourselves about the back.
Studies show, but I first hand know, people will have back pain at least ONCE in their lives.
Lower back pain can secretly manifest itself and heckle you for the extent that you let it. Here’s an image below about more back pain statistics from TheGoodBody.com…
Not many people have a “proper” understanding of the anatomy of the lower back, let alone the whole top to bottom!
Let’s think mechanically for a minute…
All the muscles, ligaments, joints(facet joints, Sacroiliac Joints) contribute to mechanical movement, and allow you to the everyday things you need and want to do. Without them, it would be hard to move freely without risk.
One key thing to know is that your back is divided into three many components.
A straight and aligned body posture is the defining factor to let you move freely as you please.
Not all cases are understood under your own evaluation. Your pain can occur from a specific cause that a doctor can evaluate with image study.
There are 4 things we must take into consideration when fixing this issue.
Understand the symptoms. Why is your pain persisting?
A diagnosis. What do you have?
Root of the cause. How did it originate?
Ways to improve. Your secure future
It is important to follow the steps above ONE by ONE, because it will give you a better piece of mind, and it will help you and your doctor, chiropractor, or physical therapist.
Learn The Symptoms, Feel And Report
Symptoms and “signs” often get mixed and misinterpreted . It’s a good thing there is a way tell if you are experiencing one vs the other.
A symptom is what YOU can feel and report to anyone. A sign is what a medical professional such as doctor can detect.
Want an example?
An example of this would be:
Pain as opposed to a bug bite.
An ache or pain anywhere on your back, and at times down to your buttocks’ is the trigger of lower back pain.
I will specify, not only the symptoms but if you should be more aware.
These are the main symptoms that lead to pain in your lower back:
weight loss
a blow or trauma to the back
pain down the legs
body temperature increases
persistent back pain
Difficulty urinating
loss of bowel control
numbness around genitals’
numbness around buttocks’
numbness around anus
peeing unintentionally
inflammation on your back
There are certain characteristics that determine whether you should seek medical advice. Could you be one or more of these?
Age group <20 , and >55 years of age
drug abusers
cancer patients, or had it
depressed immune system
steroid users
NOTE:, I encourage you to not only become adequately familiar with these symptoms, but educating yourself enough to know what you’ve been doing wrong, so you can correct it. I was in the age group 20, when I had my more severe encounter with lower back pain. I found out I had been going through my own depressive issues.
As you can see, if you start at one of these, the rest can follow. One symptom can lead into the next.
Treatment might take days, weeks, and even months to begin, but you shouldn’t have to wait till the last minute.
Don’t wait to get checked. Would you like to know why the majority of individuals wait?
They were miss-informed. Despite that, with my abilities, I’m here to help you now, and not later. Next, we’ll look at a diagnosis.
Diagnosis, “Be Examination Ready”
The sooner you can understand your certain back pain, the faster you can get yourself a diagnosis the first thing you NEED to do is to touch bases with a general practitioner, or your primary care physician.
In very little cases will you need to have an image scan, because these medical professionals can asses a physical examination by interviewing you.
Here are the diagnosis and test ran within lower back pain:
Discography. Used to guide the injection of material into the center of spinal discs and helps identify the source of back pain. Not only that but it helps guide treatment of abnormal in-vertebral discs.
Imaging test for lower back pain. This diagnosis is done with X-rays, MRI, CT scans. It is proven that this process will likely lead to surgery.
Lower back pain symptom checker. A link that will get a diagnosis by asking you question and choosing a symptom.
Radiography assessment. This here uses X-rays to determine the cause of pain.
Chiropractor. Diagnosis by touching and visual inspection
Now let’s look at a range of lower back pains you are dealing with right now.
People worldwide are becoming a victim of lower back pain because they simply do not take care of their bodies how they should. Take a second, and imagine your body being like a car.
Visualize about it, now see your engine selection. Are you there? good….
You likely go about these things in this order:
You head to work
Sit in a cubicle for hours without a break
And even when you have a break you find yourself back in your seat for not a remainder, but a whole lot longer.
Right In the middle is the “teeny” “tiny” problem. You’ve been sitting in IDLE. You’re degrading the wear of your back. Your “engine” is loosing transmission.
Slouching on your desk chair is just one of many mistakes. Here are a few more to inject into the list:
1. Hereditary
What it looks like:
arthritis
stiffness
swelling
inflammation
2. Natural causes
What it looks like:
car accidents.
falls
strains
injuries to ligaments
tendons
muscles.
occurs by lifting
3. Lifestyle choices
What it looks like:
Overweight. Balancing a healthy diet is REALLY an important thing. It’s no fluke. I stressed it years back, and I’ll continue doing so now. The habits you chose dictate your day to day routine.
None or “limited” exercise. Physical activity needs to become your routine. By putting weight on the upper and importantly your lower back, it will significantly reduce your chance of having pain in the future. STRETCHING will allow you to loosen up your muscles, gain better traction with flexibility, and NOT allow your back to stiffen up(how pain begins).
Smoking. Constant smoking can cause disc disorders.
Wearing high heels. You get an arch in your back, pushing your body forward.
Improve By Treatment And Become Pain Free!
Believe this or not. The BEST way to removing your pain is the place closest to your heart. It keeps a roof over your head. That’s right, your HOME.
Medically you can support yourself
Physically you can
Mentally
The UPSIDE is yet to be said. The best habits you develop are those at home. Jump right into your home, and follow your treatment. Once you can, your habits will follow.
If you suffer from Lower Back Pain or Sciatica, and you’re in a rush and can’t check and start our complete Remove Back Pain System right now, you can still give your back a rest by checking out our “7 Day Back Pain Cure” book; its the antidote to the surgery-obsessed approach to back pain, and in here you’ll uncover treatments you’ve likely never heard of, and will most likely NEVER need back surgery if you follow these treatments and cures faithfully. See here for more.
You can take these actions:
Painkillers. Over-The-Counter(OTC) painkillers. and there are two different kinds. See below.
Acetaminophen. “Mask” and tells your brain to not feel any pain. An example of this is:
Tylenol
Non-steroidal anti-inflammatory drugs(NSAIDs). They bring down inflammation. Examples of these are:
Use Cognitive behavioral strategies. Working with lower back pain can get tricky. A minor pain can turn into a more problematic one, and that’s where Chronic and even sciatica pain enters in. There’s a reason why chronic pain turn hurts so much more than what it might be….
It’s not always mechanical or an inflammation that spikes up your pain to another level. Another huge contributor is your emotional state. Learning to improve the way you think about your pain will change your thinking patterns, and that creates a formula for controlling and eliminating your pain.
There is no question
The Education Of Your Back. “Execute” The Plan Of Attack.
[frontend-checklist name=”Endpoint checklist”]
These lessons should help you become more prepared and informed about how to counteract the pain you have. You will be become better educated, and will not lack the knowledge when you encounter such a problem.
Your age, gender, or size all play similar roles, they all can lead you to have a lower back pain once in your life.
The symptoms of your lower back pain don’t have to be your greatest fault. You’ll bounce back and take the knowledge and turn the tide.
A proper diagnosis will allow you to see where your pain is coming from, and what’s happening to your spine.
As far as I am concerned, anyone that experiences back pain can outgrow the worries when they are well informed on how to take the next step of action. The more that you know about your issue, the faster you can eliminate the pain.
Are you ready to change the course of your life for the better with my step-by-step system, which will help the everyone in their own pain, from the following categories:
☑ For acute lower back pain patients☑ For sub-acute lower back pain patients☑ For chronic lower back pain patients☑ For Sciatica☑ All diagnosis, causes, and symptoms☑ A comprehensive look
You can always leave me a comment, concerns, opinions, right below. I’ll get back to you right away!
The Remove Back Pain System
This is the begging of your better health and a better way to treat your mild to more severe back pain. A couple points to mention before we start. Each condition will have a direction, because obviously, the treatment process for acute, chronic and sciatica are all different journeys. But you will notice that they overlap.
They are all closely related, and there will be times when you find that you don’t need the rest of the information as an acute lower back pain patient, but I HIGHLY encourage to look thru if that means it will help you understand what chronic pain can look like. And for chronic lower back pain, please do try to read from start to finish, or continue from where you are and make it to the end.
Without further ado I open the gates of all my experience to you:
When you have acute lower back pain its important to follow a step by step process. Begin with the Remove Back Pain system here:
If you have chronic lower back pain or sciatica, you should learn about how to get rid of it first, this would be the right place to begin:
Michael
Hi My name is Michael Granados, I am of the age of 26 years, and I’m a back pain specialist, enthusiast, and expert. All of us have had or will have lower back pain at least once in our lives, and whether it’s acute or a more chronic condition, you can depend on us here at Remove Back Pain to take great care of you. I ensure you’ll take the right and most appropriate steps for you to heal the safest and most productive way. Get ready for a better lifestyle!
I also do experience back pain whenever I sit on my bed for a very long time when watching movies or doing some other things on my laptop.
Didn’t know the cause at first, but as time goes by I found out it was due to that lifestyle.
And, I must say ever since I started exercising and sitting the right way on my study table, I have stopped experiencing it.
It is also one of the reasons I try as much as possible to stay away from high-heeled shoes.
Yeah, sitting can easily aggregate your back, especially when it’s not conditioned to put up with the external stresses of a not so well cushioned area. It’s always important to have the right ergonomics, to ensure you can stand sitting well, keep your space clean and chair forward, or recliner. Also make sure you’re not hunching over when sitting, as this can cause your spinal alignment to move out of place. I had to get a whole new mattress after awhile of having mattress toppers, and that makes the best difference. But exercising is the best thing you can actually do. I’m glad you’ve taken those actions. Thank you! |
/*---------------------------------------------------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Copyright (C) 2011-2020 OpenFOAM Foundation
\\/ M anipulation |
-------------------------------------------------------------------------------
License
This file is part of OpenFOAM.
OpenFOAM is free software: you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
\*---------------------------------------------------------------------------*/
#include "Gulders.H"
#include "addToRunTimeSelectionTable.H"
// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
namespace Foam
{
namespace laminarFlameSpeedModels
{
defineTypeNameAndDebug(Gulders, 0);
addToRunTimeSelectionTable
(
laminarFlameSpeed,
Gulders,
dictionary
);
}
}
// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
Foam::laminarFlameSpeedModels::Gulders::Gulders
(
const dictionary& dict,
const psiuReactionThermo& ct
)
:
laminarFlameSpeed(dict, ct),
coeffsDict_(dict.optionalSubDict(typeName + "Coeffs").subDict(fuel_)),
W_(coeffsDict_.lookup<scalar>("W")),
eta_(coeffsDict_.lookup<scalar>("eta")),
xi_(coeffsDict_.lookup<scalar>("xi")),
f_(coeffsDict_.lookup<scalar>("f")),
alpha_(coeffsDict_.lookup<scalar>("alpha")),
beta_(coeffsDict_.lookup<scalar>("beta"))
{}
// * * * * * * * * * * * * * * * * Destructor * * * * * * * * * * * * * * * //
Foam::laminarFlameSpeedModels::Gulders::~Gulders()
{}
// * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * * //
inline Foam::scalar Foam::laminarFlameSpeedModels::Gulders::SuRef
(
scalar phi
) const
{
if (phi > small)
{
return W_*pow(phi, eta_)*exp(-xi_*sqr(phi - 1.075));
}
else
{
return 0.0;
}
}
inline Foam::scalar Foam::laminarFlameSpeedModels::Gulders::Su0pTphi
(
scalar p,
scalar Tu,
scalar phi,
scalar Yres
) const
{
static const scalar Tref = 300.0;
static const scalar pRef = 1.013e5;
return SuRef(phi)*pow((Tu/Tref), alpha_)*pow((p/pRef), beta_)*(1 - f_*Yres);
}
Foam::tmp<Foam::volScalarField> Foam::laminarFlameSpeedModels::Gulders::Su0pTphi
(
const volScalarField& p,
const volScalarField& Tu,
scalar phi
) const
{
tmp<volScalarField> tSu0
(
volScalarField::New
(
"Su0",
p.mesh(),
dimensionedScalar(dimVelocity, 0)
)
);
volScalarField& Su0 = tSu0.ref();
forAll(Su0, celli)
{
Su0[celli] = Su0pTphi(p[celli], Tu[celli], phi, 0.0);
}
volScalarField::Boundary& Su0Bf = Su0.boundaryFieldRef();
forAll(Su0Bf, patchi)
{
forAll(Su0Bf[patchi], facei)
{
Su0Bf[patchi][facei] =
Su0pTphi
(
p.boundaryField()[patchi][facei],
Tu.boundaryField()[patchi][facei],
phi,
0.0
);
}
}
return tSu0;
}
Foam::tmp<Foam::volScalarField> Foam::laminarFlameSpeedModels::Gulders::Su0pTphi
(
const volScalarField& p,
const volScalarField& Tu,
const volScalarField& phi
) const
{
tmp<volScalarField> tSu0
(
volScalarField::New
(
"Su0",
p.mesh(),
dimensionedScalar(dimVelocity, 0)
)
);
volScalarField& Su0 = tSu0.ref();
forAll(Su0, celli)
{
Su0[celli] = Su0pTphi(p[celli], Tu[celli], phi[celli], 0.0);
}
volScalarField::Boundary& Su0Bf = Su0.boundaryFieldRef();
forAll(Su0Bf, patchi)
{
forAll(Su0Bf[patchi], facei)
{
Su0Bf[patchi][facei] =
Su0pTphi
(
p.boundaryField()[patchi][facei],
Tu.boundaryField()[patchi][facei],
phi.boundaryField()[patchi][facei],
0.0
);
}
}
return tSu0;
}
Foam::tmp<Foam::volScalarField>
Foam::laminarFlameSpeedModels::Gulders::operator()() const
{
if (psiuReactionThermo_.composition().contains("ft"))
{
const volScalarField& ft = psiuReactionThermo_.composition().Y("ft");
return Su0pTphi
(
psiuReactionThermo_.p(),
psiuReactionThermo_.Tu(),
dimensionedScalar
(
"stoichiometricAirFuelMassRatio",
dimless,
psiuReactionThermo_.properties()
)*ft/max(1 - ft, small)
);
}
else
{
return Su0pTphi
(
psiuReactionThermo_.p(),
psiuReactionThermo_.Tu(),
equivalenceRatio_
);
}
}
// ************************************************************************* //
|
Comparing House and Senate Budget Proposals
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Senate Democrats began marking up a budget resolution Wednesday for the first time since 2009. The Democratic plan, released by Senate Budget Committee Chair Patty Murray of Washington, draws clear distinctions with the Republican proposal put forward last week by the House Budget Committee, led by Rep. Paul Ryan of Wisconsin.
Ryan’s budget resolution for the coming fiscal year largely follows the outlines of budgets he released in 2011 and 2012 that became guideposts for GOP priorities, outlining fundamental changes to entitlement programs in order to stabilize debt and deficits. Unlike Ryan's past proposals, however, his 2014 blueprint would balance the budget in 10 years, relying on trillions in spending cuts to get to a $7 billion surplus in 2013. The House Budget panel approved the Ryan plan on Wednesday on a party-line vote of 22-17.
The Murray budget is less ambitious in terms of deficit reduction, and unlike the Republican approach, would add new revenue by closing tax loopholes that benefit corporations and the wealthy. It also includes $100 billion in new stimulus funds for infrastructure investments.
The graphs above compare the outlay, revenue and deficit effects of each chamber's 2014 budget resolution compared to current law projections in the Congressional Budget Office's February baseline. |
Wagon panels painted gold, red and yellow with 3 horse shoes screwed on, these are left blank in the middle so I can personalise with a photo or picture of your choice to place in the middle. Small brass plated hinges secure the panels.
The ladders are hinged on and drop up and down so toddler can climb in also wooden crate, bucket, pegs, 2 planters. Height from top canopy to floor is 41 inches, length of middle base is 35inches. |
BALB/c mice injected with irradiated myeloma cells of a myeloma tumor (MOPC-167) of BALB/c origin form 1) antibodies that are specific for a surface antigen on cells of other BALB/c myeloma tumors, and 2) cytotoxic T lymphocytes (CTLs) that are a) specific for MOPC-167 and b) crossreact with many lymphomas of another mouse strain (DBA/2). Attempts will be made to identify the antigens recognized by the antibodies and CTLs. The specific CTLs to vesicular stomatitis virus-infected cells will also be studied as models to aid in developing general procedures for identifying the antigens recognized by CTLs. In a second line of investigation, the rare lambda 2 light chains of mouse immunoglobulins will continue to be studies as probes to the mechanism by which immunologic diversity originates. Several BALB/c myeloma tumors that produce lambda 2 chains have been identified and amino acids sequences of these chains will be compared with lambda 2 315, the prototype lambda 2 chain. |
Sedum Roof Dance Extension SW19
Rear Extension with Sedum Roof
Completion date: 2016
Size: c. 50 square metres
Contract value: c.£200,000 + VAT
About this project
The client made contact with aspirations for a large dance floor, initially thinking it could be undergound. With further exploration and consideration of options, discussing cost the client instructed our adding a six metre rear extension combining this with the rear of the house. Proposals evolved which also attempted to take the neighbours with them, which was eventually done when we incorporating a sedum roof on the 6m ground floor extension. The extension would look a rear garden when viewd from first floor windows. Sedum was also the clients preferred roof finish. It was the client's desire to have a uniform smooth floor where the design evolved into a seamless Terrazzo finish with under floor heating. The client preferred a shallow spiral wine cellar initially which increased in depth toward the latter stages.
The client carefully chose the finish of the kitchen with all appliances. The design also incorporated re-arranging the the ground floor to incorporate the preferred sanitary accommodation and reduced utility room.
The client had realistic expectations concerning cost and when a quote was received £2k less than their expected cost they appoint this builder, after I had taken them to two previous projects. The client chose to administer the contract with the builder. Photos courtesy of PRS Builders Ltd. |
Immunoaffinity chromatography.
This unit describes the isolation of soluble or membrane-bound protein antigens from cells or homogenized tissue by immunoaffinity chromatography. The technique involves the elution of a single protein from an immunoaffinity column after prior elution of nonspecifically adsorbed proteins. To elute the bound antigen from the immunoaffinity matrix, the antibody-antigen interaction is destabilized by brief exposure to high-pH or low-pH buffer. The use of batch purification of antigens is an alternate procedure and results in shorter column loading times. The detergent octyl beta-D-glucoside can be used instead of Triton X-100 for elution. Because octyl beta-D-glucoside has a high critical micelle concentration (CMC), it can be readily removed by dialysis, as described. |
Q:
datetime in bigint field
I am trying to add a date time to a bigint field and then display it in a gridview using SQL query...
First im not sure how to add the date time in big int field
so im using
long s= DateTime.Now.Ticks;
which is storing a sample value like 633896886277130000
then i want get only the date from it using the SQl Select statement and display on gridview..
SELECT MachineGroups.MachineGroupID, MachineGroups.MachineGroupName,
MachineGroups.MachineGroupDesc, **MachineGroups.TimeAdded**,
MachineGroups.CanBeDeleted, COUNT(Machines.MachineName) AS 'No. of PCs'
FROM MachineGroups
FULL OUTER JOIN Machines ON Machines.MachineGroupID = MachineGroups.MachineGroupID
GROUP BY MachineGroups.MachineGroupID, MachineGroups.MachineGroupName,
MachineGroups.MachineGroupDesc, MachineGroups.TimeAdded, MachineGroups.CanBeDeleted"
can i use this
SELECT CONVERT(BIGINT, DATEDIFF(SECOND, '1970-01-01T00:00:00',
'2008-05-20T06:00:00'));
long TimeAdded = (DateTime.Now.ToFileTime() - 116444736000000000) / 10000000;
i get this value
1254157826
A:
If you are saving .NET Ticks in your MachineGroups.TimeAdded field, then it can be converted to SQL DateTime like below. (Subtract Ticks of 1900-01-01 and divide by ticks per day)
Select convert(datetime, (MachineGroups.TimeAdded - 599266080000000000)/864000000000)
FROM MachineGroups
If you want just date use FLOOR:
Select convert(datetime, FLOOR((MachineGroups.TimeAdded - 599266080000000000)/864000000000))
FROM MachineGroups
EDIT You will get error if ticks is invalid you can use this for error checking:
Select CASE WHEN MachineGroups.TimeAdded < 599266080000000000 THEN null ELSE convert(datetime, (MachineGroups.TimeAdded - 599266080000000000)/864000000000) END
FROM MachineGroups
|
William McMahon (athlete)
William Francis "Billy" McMahon (January 3, 1910 – February 26, 1991) was an American long-distance runner. He won the national marathon championship in 1936 and qualified for the Olympic marathon in Berlin, where he failed to finish.
References
Category:1910 births
Category:1991 deaths
Category:American male marathon runners
Category:Sportspeople from Worcester, Massachusetts
Category:Athletes (track and field) at the 1936 Summer Olympics
Category:Olympic track and field athletes of the United States
Category:Track and field athletes from Massachusetts |
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<div class="header">
<div class="summary">
<a href="#pub-methods">Public Member Functions</a> |
<a href="#pub-static-methods">Static Public Member Functions</a> |
<a href="classb2_typed_intrusive_list_node-members.html">List of all members</a> </div>
<div class="headertitle">
<div class="title">b2TypedIntrusiveListNode< T > Class Template Reference</div> </div>
</div><!--header-->
<div class="contents">
<p><code>#include <<a class="el" href="b2_intrusive_list_8h_source.html">b2IntrusiveList.h</a>></code></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a6894d739328baee8a9fdf2ec9988faeb"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a6894d739328baee8a9fdf2ec9988faeb"></a>
void </td><td class="memItemRight" valign="bottom"><a class="el" href="classb2_typed_intrusive_list_node.html#a6894d739328baee8a9fdf2ec9988faeb">InsertAfter</a> (T *const obj)</td></tr>
<tr class="memdesc:a6894d739328baee8a9fdf2ec9988faeb"><td class="mdescLeft"> </td><td class="mdescRight">Insert this object after the specified object. <br/></td></tr>
<tr class="separator:a6894d739328baee8a9fdf2ec9988faeb"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a9f0d0fcf2f8c5b26938364a5ff2d97ed"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a9f0d0fcf2f8c5b26938364a5ff2d97ed"></a>
void </td><td class="memItemRight" valign="bottom"><a class="el" href="classb2_typed_intrusive_list_node.html#a9f0d0fcf2f8c5b26938364a5ff2d97ed">InsertBefore</a> (T *const obj)</td></tr>
<tr class="memdesc:a9f0d0fcf2f8c5b26938364a5ff2d97ed"><td class="mdescLeft"> </td><td class="mdescRight">Insert this object before the specified object. <br/></td></tr>
<tr class="separator:a9f0d0fcf2f8c5b26938364a5ff2d97ed"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aae40a37f35d5a8e3133aac16dc16fb3c"><td class="memItemLeft" align="right" valign="top">T * </td><td class="memItemRight" valign="bottom"><a class="el" href="classb2_typed_intrusive_list_node.html#aae40a37f35d5a8e3133aac16dc16fb3c">GetNext</a> () const </td></tr>
<tr class="separator:aae40a37f35d5a8e3133aac16dc16fb3c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:abaf87f46201673c6920f2e5d761de9a4"><td class="memItemLeft" align="right" valign="top">T * </td><td class="memItemRight" valign="bottom"><a class="el" href="classb2_typed_intrusive_list_node.html#abaf87f46201673c6920f2e5d761de9a4">GetPrevious</a> () const </td></tr>
<tr class="separator:abaf87f46201673c6920f2e5d761de9a4"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae526e3967c69e9c928e645b368481a4a"><td class="memItemLeft" align="right" valign="top">T * </td><td class="memItemRight" valign="bottom"><a class="el" href="classb2_typed_intrusive_list_node.html#ae526e3967c69e9c928e645b368481a4a">GetTerminator</a> () const </td></tr>
<tr class="separator:ae526e3967c69e9c928e645b368481a4a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:adc1d7a9e50bfe8e92f3d01fafd66aa67"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="adc1d7a9e50bfe8e92f3d01fafd66aa67"></a>
T * </td><td class="memItemRight" valign="bottom"><a class="el" href="classb2_typed_intrusive_list_node.html#adc1d7a9e50bfe8e92f3d01fafd66aa67">Remove</a> ()</td></tr>
<tr class="memdesc:adc1d7a9e50bfe8e92f3d01fafd66aa67"><td class="mdescLeft"> </td><td class="mdescRight">Remove this object from the list it's currently in. <br/></td></tr>
<tr class="separator:adc1d7a9e50bfe8e92f3d01fafd66aa67"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a3b1aabcab79d482b99a5a967442dc342"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a3b1aabcab79d482b99a5a967442dc342"></a>
bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classb2_typed_intrusive_list_node.html#a3b1aabcab79d482b99a5a967442dc342">InList</a> () const </td></tr>
<tr class="memdesc:a3b1aabcab79d482b99a5a967442dc342"><td class="mdescLeft"> </td><td class="mdescRight">Determine whether this object is in a list. <br/></td></tr>
<tr class="separator:a3b1aabcab79d482b99a5a967442dc342"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aaa8108273e8ebfeb7ea9435ea573b8ff"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aaa8108273e8ebfeb7ea9435ea573b8ff"></a>
bool </td><td class="memItemRight" valign="bottom"><b>IsEmpty</b> () const </td></tr>
<tr class="separator:aaa8108273e8ebfeb7ea9435ea573b8ff"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8e73f61571429c7381b7462b1b6153fa"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a8e73f61571429c7381b7462b1b6153fa"></a>
uint32 </td><td class="memItemRight" valign="bottom"><a class="el" href="classb2_typed_intrusive_list_node.html#a8e73f61571429c7381b7462b1b6153fa">GetLength</a> () const </td></tr>
<tr class="memdesc:a8e73f61571429c7381b7462b1b6153fa"><td class="mdescLeft"> </td><td class="mdescRight">Calculate the length of the list. <br/></td></tr>
<tr class="separator:a8e73f61571429c7381b7462b1b6153fa"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a6704dd771203c2049d78c4c6484b81e4"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a6704dd771203c2049d78c4c6484b81e4"></a>
 </td><td class="memItemRight" valign="bottom"><b>B2_INTRUSIVE_LIST_GET_NODE</b> (m_node)</td></tr>
<tr class="separator:a6704dd771203c2049d78c4c6484b81e4"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-methods"></a>
Static Public Member Functions</h2></td></tr>
<tr class="memitem:ad8f01da7dc1d8d7743d5051b262c277b"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ad8f01da7dc1d8d7743d5051b262c277b"></a>
static T * </td><td class="memItemRight" valign="bottom"><a class="el" href="classb2_typed_intrusive_list_node.html#ad8f01da7dc1d8d7743d5051b262c277b">GetInstanceFromListNode</a> (<a class="el" href="classb2_intrusive_list_node.html">b2IntrusiveListNode</a> *const node)</td></tr>
<tr class="memdesc:ad8f01da7dc1d8d7743d5051b262c277b"><td class="mdescLeft"> </td><td class="mdescRight">Get a pointer to the instance of T that contains "node". <br/></td></tr>
<tr class="separator:ad8f01da7dc1d8d7743d5051b262c277b"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<typename T><br/>
class b2TypedIntrusiveListNode< T ></h3>
<p><a class="el" href="classb2_typed_intrusive_list_node.html">b2TypedIntrusiveListNode</a> which supports inserting an object into a single doubly linked list. For objects that need to be inserted in multiple doubly linked lists, use <a class="el" href="classb2_intrusive_list_node.html">b2IntrusiveListNode</a>.</p>
<p>For example:</p>
<p>class IntegerItem : public b2TypedIntrusiveListNode<IntegerItem> { public: IntegerItem(int32 value) : m_value(value) { } ~IntegerItem() { } int32 GetValue() const { return m_value; } private: int32 m_value; };</p>
<p>int main(int argc, const char <em>arvg[]) { b2TypedIntrusiveListNode<IntegerItem> list; IntegerItem a(1); IntegerItem b(2); IntegerItem c(3); list.InsertBefore(&a); list.InsertBefore(&b); list.InsertBefore(&c); for (IntegerItem item = list.GetNext(); item != list.GetTerminator(); item = item-><a class="el" href="classb2_typed_intrusive_list_node.html#aae40a37f35d5a8e3133aac16dc16fb3c">GetNext()</a>) { printf("%d\n", item->GetValue()); } } </p>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a class="anchor" id="aae40a37f35d5a8e3133aac16dc16fb3c"></a>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename T> </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">T* <a class="el" href="classb2_typed_intrusive_list_node.html">b2TypedIntrusiveListNode</a>< T >::GetNext </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Get the next object in the list. Check against <a class="el" href="classb2_typed_intrusive_list_node.html#ae526e3967c69e9c928e645b368481a4a">GetTerminator()</a> before deferencing the object. </p>
</div>
</div>
<a class="anchor" id="abaf87f46201673c6920f2e5d761de9a4"></a>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename T> </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">T* <a class="el" href="classb2_typed_intrusive_list_node.html">b2TypedIntrusiveListNode</a>< T >::GetPrevious </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Get the previous object in the list. Check against <a class="el" href="classb2_typed_intrusive_list_node.html#ae526e3967c69e9c928e645b368481a4a">GetTerminator()</a> before deferencing the object. </p>
</div>
</div>
<a class="anchor" id="ae526e3967c69e9c928e645b368481a4a"></a>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename T> </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">T* <a class="el" href="classb2_typed_intrusive_list_node.html">b2TypedIntrusiveListNode</a>< T >::GetTerminator </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Get the terminator of the list. This should not be dereferenced as it is a pointer to b2TypedIntrusiveListNode<T> <em>not</em> T. </p>
</div>
</div>
<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="b2_intrusive_list_8h_source.html">b2IntrusiveList.h</a></li>
</ul>
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With the Bulls slated to play on TNT/NBA TV in the next couple of games, Blog A Bull was able to talk to a very special guest in Sekou Smith. He is a senior writer at NBA.com and also hosts the Hang Time Podcast along with being an NBA TV analyst. You can follow him on Twitter right here.
Speaking of some of the Bulls future games on TNT, here are the broadcast crews slated for each game.
Bulls vs. Heat: Vince Cellini, David Aldridge, Sam Mitchell in studio
For the Bulls against the Bucks next Thursday: Brian Anderson, Reggie Miller, and Dennis Scott.
Let’s get down to the interview:
Q: What is your overall take on the Bulls so far this season? Are you surprised by how well they are doing?
A: I’m pleasantly surprised with the way the Bulls have played. I wasn’t sure about how the “3 Alphas” of Rondo, Butler, and Wade would have worked and how Fred Hoiberg would have meshed them together. But I think Hoiberg has done a really nice job of it. The trio have done a great job of adjusting to each other and not stepping on each others toes. It was a nice win over the Spurs on Thursday where Jimmy didn’t play his best but he got some great support from Dwyane Wade and the rest of the cast. You are going to need that down the stretch of the season for a team that is going to be battling for a playoff spot.
Q: Do you think Jimmy Butler is the second best player in the East and if not, who is and why?
A: I think he would be in that conversation along with Carmelo Anthony and Kyrie Irving. Maybe Isaiah Thomas, who is going to be an All-Star again this year if he stays healthy. DeMar DeRozan, Paul George and John Wall are in that bunch as well. If you are talking about just the best two way players in the NBA, Jimmy Butler is on that five man list and that’s to me as valuable or more valuable than just being a great scorer or considered a great talent. Being a guy who is good on both ends is as good as you can get. That’s LeBron, Kawhi Leonard, Paul George and Jimmy Butler are the first names you think about when you talk about guys who are as good on the offensive end as they are on the defensive end.
Q: Do you think Cristiano Felicio deserves more playing time? Do you see him being a part of Chicago’s future moving forward?
A: Given the position that he plays and the fact that they basically get him for a bargain price, you have to try and use an asset like that and see if you can develop him into a part of your core. The thing about him that cracks me up is that I remember the first time I saw him on the bench and I wasn’t joking when I looked over at a buddy of mine and said “man looks like Orlando Pace in a basketball uniform”. He is unbelievably huge at a listed 6’9 and 266 pounds which I want to see him get on a scale and see that thing read 266. When you are that size in a league where rim protection is still valued the way it is and having a physical force where you can use in spot situations, he'd have to be a part of my future going forward. The fact that he is an immovable object with his size and he can get up and down the floor. He’s a very inexpensive piece that can come in handy come playoff time.
Q: What do you think the Bulls should do with Nikola Mirotic moving forward considering he’s a free agent this summer?
A: I think people want more from him statistically based on what they know he is capable of and what they have seen him do in international play but he is a relatively young player in terms of him being in the league. He’s a guy with his skill set and size, depending on how you play, he can do so many things for your team inside and out. You have a roster that you didn’t flip over to go into full rebuild mode. Expectations for Mirotic have increased or expanded based on the fact that you have Rondo and Wade added to the mix and you think “All right we are going to be a playoff team and we got a chance to build a core group that has to play at a certain level”. But he (Mirotic) is still young enough in his development in the NBA that you don’t allow him to go elsewhere and you keep him as a part of your core group.
Q: In terms of their matchup with Miami, who is the one player Chicago needs to pay attention to the most defensively?
A: They don’t have to worry too much about stopping but they have to have a physical answer for Hassan Whiteside. He has been playing decent and putting up good numbers. There aren’t enough quality back to the basket big men like him running around so you try to see guys like that as often as you can. He can get you out of your sets and your principles on defense if you are not careful. The Bulls have to find a way to have a body on him at all times and don’t allow him to get going offensively and keep him from deterring Chicago’s chances at the rim because he is such a great rim protector. You want to go at him and challenge and attack him and maybe get him into some foul trouble and not let him sit there and get comfortable and control the action around the rim on the defensive end.
Q: Do you think the Heat should try and move Goran Dragic this season and try and build the franchise around Hassan Whiteside?
A: No. I don’t think the Heat have the superstar player on their roster that they can build around for the future yet. I don’t think they are in a rush to find him either. A lot of the times, that guy won’t come via free agency or trade. That’s the guy who are going to draft. So the Heat are going to have to see how their season is going to shake out. If they are not in the playoffs this year, it is a fantastic draft to have a lottery pick. It is expected to be a deep and talented. I would be very hesitant to ship anybody out of Miami before draft time knowing that there is going to be quite a big of high level talent available.
Q: Who do you think will win the battle on the glass?
A: It’s a group effort for the Bulls on the glass. Chicago can come at Whiteside with numbers and they should be able to hold their own and win that battle. It’s going to be one on three or four and you usually favor the numbers. That’s one of the things I like about Chicago’s team is that they don’t have a stat hogger or guys who are piling up those big numbers. Taj Gibson is a guy who has always played bigger than his listed size. Robin Lopez is certainly big enough to make life hard for Whiteside. You use those two guys in particular and try and keep Whiteside off the glass.
Q: X-Factors/Prediction for this game
A: To me, X-Factors always tend to be the guys who you know are going to play at a significant role most nights. Everybody is going to be watching Dwyane Wade of course given he is playing against his former team. The X-Factor for the Bulls will be Isaiah Canaan believe it or not. Reason being is that this is a game where you are matching up backcourts and he’s been a wild card for the Bulls in that backcourt. He could end up playing a significant role in this game. As far as predictions, I’m not terribly huge on game predictions in December, certainly not before Christmas. But if you are looking at who needs it the most and who benefits the most from a win, it would be Chicago. The Bulls would like to have this game for several reasons and you don’t want to drop home games to teams that are inferior to you at this time of the year. You want to put those teams away and take care of business. |
Update from the streets of London
We've been checking in all morning with the gathering protestors in London the day before the G-20 summit. London is braced for a day of demonstrations ahead of tomorrow's summit of G-20 leaders. This morning anti-capitalist and climate change protestors converged on the financial heart of the city, while this afternoon an anti-war demonstration is expected outside the American Embassy. The organizers insist their protests will be peaceful, but windows at a Royal Bank of Scotland building and other shops have been smashed. We return once again to BBC reporter Jack Izzard who is on the scene. |
Special counsel Robert Mueller is not yet done investigating whether the Trump campaign colluded with Russia during the 2016 election after indicting 13 Russian nationals and three Russian entities for seeking to interfere in the 2016 election, according to a report Friday.
The indictments cover just a portion of the investigation, which is expected to continue on for months, a person familiar with the probe told Bloomberg. The probe is also seeking to determine if Trump obstructed justice, the person said. Mueller has not publicly confirmed that his team has ever looked into possible efforts obstruct justice.
Mueller’s office on Friday revealed that the 13 Russian nationals were indicted on charges of conspiracy to defraud the U.S. Additionally, three defendants were charged with conspiracy to commit wire fraud, and five were charged with aggravated identity theft.
Deputy Attorney General Rod Rosenstein, who is overseeing Mueller’s probe, announced Friday afternoon that the meddling started in May 2014 and that the Russian groups created posts, ads, and organized events on social media platforms by using names of Americans and other entities.
The ads primarily were primarily opposed to Democratic nominee Hillary Clinton, but at times were against President Trump. The indictment also said that the indictment does not suggest members of Trump's campaign were wittingly involved with the scheme.
Mueller is investigating if collusion between the Trump campaign and the Kremlin occurred during the 2016 election.
Trump has historically called Mueller’s probe a “witch hunt” and, in light of the Russian indictments, has continued to reiterate that “no collusion” ever happened.
"Russia started their anti-US campaign in 2014, long before I announced that I would run for President," Trump tweeted on Friday. "The results of the election were not impacted. The Trump campaign did nothing wrong — no collusion!" |
Det Chief Insp Jordan added: "The key to immobilising any mobile phone is to make a note of the unique IMEI number. This can be obtained by dialling *#06#.
"The number is built into the phone and cannot be altered.
"If the phone is lost or stolen, the IMEI number can be given to the network company which will immobilise it so it can no longer be used."
Det Chief Insp Jordan said phone companies should be congratulated for their efforts to combat theft.
"It goes without saying that if the mobile has no value it is no longer attractive to criminals," he said.
West Yorkshire police launched a force-wide campaign in May, texting more than 4,000 mobile phone users across the county with a message reminding them if their mobile is stolen they should contact their network and have it barred, ensuring it never works again.
"Young people are particularly vulnerable to this type of crime," said Det Chief Insp Jordan.
"It is important to keep mobile phones out of sight when they are not being used.
"Don't send text messages or make calls in crowded areas like shopping centres and high streets where they can be snatched out of your hand."
He said the message was also being given directly to criminals in police custody.
"Posters will be displayed in our cell areas and a leaflet will be given to everyone who is arrested to make them realise that stealing mobile phones is no longer profitable and a waste of time," he said.
Since April this year, almost one in five street robberies involved the theft of a mobile phone and 133 phones have been taken during house burglaries. |
Q:
prove matrix norm equivalence
Given $A \in R^{m\times n}$, I need to prove:
$$||A||_2 \le \sqrt {m}||A||_\infty$$
I have tried a number of things and I just cant seem to get it to work.
Also, I need to prove:
$$||A||_2 \le \sqrt {n} ||A||_1$$
For this one, I have done:
$e_i = [...,0,1,0,...] \in R^n$ where i is the position of the 1 in e.
$$||A||_1 = \max {\sum {|a_{ij}|}}=\max {||Ae_i||_1}$$
$$B => b_i = ||Ae_i||_1 \in R^n$$
$$||A||_1 = ||B||_\infty \le ||B||_2$$
$$||B||_2 = \sqrt {\sum {||Ae_i||_1^2}} \le \sqrt {\sum {||A||_1^2||e_i||_1^2}} = \sqrt {n}||A||_1$$
I dont know if this is correct or not because I have no idea how to get this to be greater than or equal to $||A||_2$. I feel like this is very close to what I need, just not quite there. Any help would be great.
A:
For $y \in \mathbb{R}^m$ you have $\|y\|_2 = \sqrt{\sum_k y_k^2} \leq \sqrt{\sum_k \|y\|_\infty^2}= \sqrt{m} \|y\|_\infty$.
Hence $\|Ax\|_2 \leq \sqrt{m} \|Ax\|_\infty$, for all $x$. Now suppose $\|x\|_\infty\leq 1$, then we have $\|Ax\|_2 \leq \sup_{\|x\|_\infty\leq 1} \sqrt{m} \|Ax\|_\infty = \sqrt{m} \|A\|_\infty$. Now suppose $\|x\|_2\leq 1$. Then we have $\|x\|_\infty \leq 1$ and so $\|A\|_2 = \sup_{\|x\|_2\leq 1} \|Ax\|_2 \leq \sqrt{m} \|A\|_\infty$.
Now note that for any norm and any $\sigma>0$ we have $\sup_{\|x\|\leq \sigma} \|Ax\| = \sigma \|A\|$. It is straightforward to show that if $y \in \mathbb{R}^m$ you have $\|y\|_2 \leq \|y\|_1$. It is also straightforward to show that if $x \in \mathbb{R}^n$ and $\|x\|_2\leq 1$, then $\|x\|_1 \leq \sqrt{n}$ (ie, $B_2(0,1) \subset B_1(0,\sqrt{n})$).
Hence we have $\|Ax\|_2 \leq \|Ax\|_1$. Now suppose $\|x\|_1 \leq \sqrt{n}$, then we have $\|Ax\|_2 \leq \sup_{\|x\|_1 \leq \sqrt{n}}\|Ax\|_1 = \sqrt{n} \|A\|_1$, and since $B_2(0,1) \subset B_1(0,\sqrt{n})$, we have $\|A\|_2 = \sup_{\|x\|_2\leq 1} \|Ax\|_2 \leq \sqrt{n} \|A\|_1$.
|
Tottenham Hotspur attacker Son Heung-min has broken the single-season goal record for a South Korean in European football after grabbing a brace against Leicester City.
Son scored twice in Tottenham's 6-1 over Leicester City in their English Premier League match at the King Power Stadium in Leicester, Britain, on Thursday (local time). Son now has 21 goals in all competitions this season, surpassing the previous record for a South Korean player in Europe held by Cha Bum-kun. Cha scored 19 goals during the 1985-86 season for the German side Bayer Leverkusen.
Son, 24, has bagged 14 goals in the EPL, in addition to six goals in the English Football Association Cup and one goal in the UEFA Champions League.
Tottenham Hotspur's Son Heung-min (L) and Leicester City's Wilfred Ndidi battle for the ball during their English Premier League match at the King Power Stadium in Leicester, England, on May 18, 2017. (AP-Yonhap)
"Now I can say I'm really proud," Son said to Spurs TV on the club's website. "But without my teammates, my coaching staff and Tottenham, this would have never happened. I really want to thank everyone and it's a really really happy night."
Son is now also the highest-scoring South Korean in England, moving past former Manchester United and Queens Park Rangers midfielder Park Ji-sung. Son, who joined Tottenham from Leverkusen in 2015, has amassed 29 goals in 86 matches over two seasons, while Park, who hung up his boots in 2014, had 27 goals in 230 matches over eight seasons in the EPL.
Against EPL defending champions Leicester, Son started as a winger. He first delivered an assist to striker Harry Kane in the 25th minute for Tottenham's 1-0 lead. It was Son's fifth assist in the EPL this season and his first since the match against Watford on April 8.
Son broke the tie with Cha in the 36th after his right-footed shot off Dele Alli's pass in the box found the net for the London club's 2-0 lead. It also ended his goalless streak that started April 15.
Son netted his second goal of the night in the 71st when his right-footed strike from distance beat Leicester goalkeeper Kasper Schmeichel. The South Korean was replaced by Vincent Jassen in the 78th minute.
Son, currently the only man to win the EPL Player of the Month award twice in the 2016-17 season, has one more chance to extend his goal scoring record on Sunday when Tottenham visit KCOM Stadium to face Hull City for their final EPL match of the season. He will try to become the first Asian to finish the season inside the top 10 in scoring. Son is currently ranked 12th, one goal outside of the top 10.
Tottenham have confirmed a second-place finish in the EPL behind Chelsea following their 2-1 win over Manchester United last Sunday.
Son will return to his homeland next Tuesday with his teammates Kyle Walker, Kevin Wimmer and Ben Davies for promotional events organized by Tottenham's main sponsor AIA. (Yonhap) |
Q:
Result with 2 digits after . eg:23.65
I want to do some calculations on my app the result will mostly have from 5 to 15 digits after the . for example 24.61835496354822 I want to display the result in a TextView and only show 2 digits after . for example 24.61 please help me
A:
double d = 24.61835496354822;
DecimalFormat f = new DecimalFormat("##.00");
System.out.println(f.format(d));
|
/*******************************************************************************
* Copyright (c) 2012, 2016, 2017 PDT Extension Group and others.
*
* This program and the accompanying materials are made
* available under the terms of the Eclipse Public License 2.0
* which is available at https://www.eclipse.org/legal/epl-2.0/
*
* SPDX-License-Identifier: EPL-2.0
*
* Contributors:
* PDT Extension Group - initial API and implementation
* Kaloyan Raev - [501269] externalize strings
*******************************************************************************/
package org.eclipse.php.composer.core.model;
import java.util.HashMap;
import java.util.Map;
import org.eclipse.core.resources.IProject;
import org.eclipse.core.resources.IResource;
import org.eclipse.core.resources.ResourcesPlugin;
import org.eclipse.core.runtime.preferences.ConfigurationScope;
import org.eclipse.core.runtime.preferences.IEclipsePreferences;
import org.eclipse.dltk.core.IScriptProject;
import org.eclipse.php.composer.api.collection.Psr;
import org.eclipse.php.composer.api.json.ParseException;
import org.eclipse.php.composer.core.ComposerPlugin;
import org.eclipse.php.composer.core.log.Logger;
import org.osgi.service.prefs.BackingStoreException;
/**
*
* Main ModelAccess to the workspaces composer model.
*
* @author Robert Gruendler <r.gruendler@gmail.com>
*
*/
public class ModelAccess {
private PackageManager packageManager = null;
private static ModelAccess instance = null;
private Map<String, Psr> psr0Map = new HashMap<>();
private ModelAccess() {
try {
initNamespaceMap();
} catch (Exception e) {
ComposerPlugin.logException(e);
}
}
protected void initNamespaceMap() throws ParseException {
IEclipsePreferences instancePreferences = ConfigurationScope.INSTANCE.getNode(ComposerPlugin.ID);
for (IProject project : ResourcesPlugin.getWorkspace().getRoot().getProjects()) {
String prefKey = "namespacemap#" + project.getName(); //$NON-NLS-1$
String json = instancePreferences.get(prefKey, "{}"); //$NON-NLS-1$
psr0Map.put(project.getName(), new Psr(json));
Logger.debug("loading namespacemap from preferences for project " + project.getName() + " " + json); //$NON-NLS-1$ //$NON-NLS-2$
}
}
public static ModelAccess getInstance() {
if (instance == null) {
instance = new ModelAccess();
}
return instance;
}
public PackageManager getPackageManager() {
if (getInstance().packageManager == null) {
PackageManager manager = new PackageManager();
synchronized (instance) {
if (instance.packageManager == null) { // ensure another
// package manager
// was not set while
// creating the
// instance above
instance.packageManager = manager;
}
}
}
return instance.packageManager;
}
public void updatePsr0(Psr psr0, IScriptProject scriptProject) {
// escape namespace separators to avoid deserialization problems
String json = psr0.toJson().replace("\\", "\\\\"); //$NON-NLS-1$ //$NON-NLS-2$
IEclipsePreferences instancePreferences = ConfigurationScope.INSTANCE.getNode(ComposerPlugin.ID);
psr0Map.put(scriptProject.getProject().getName(), psr0);
instancePreferences.put("namespacemap#" + scriptProject.getProject().getName(), json); //$NON-NLS-1$
Logger.debug("updating namespacemap for project " + scriptProject.getProject().getName()); //$NON-NLS-1$
try {
instancePreferences.flush();
} catch (BackingStoreException e) {
Logger.logException(e);
}
}
public Psr getNamespaceMappings(IProject project) {
if (psr0Map.containsKey(project.getName())) {
return psr0Map.get(project.getName());
}
return null;
}
public IResource getComposer(InstalledPackage installed, IScriptProject project) {
/*
* if (!namespaceMap.containsKey(project.getProject().getName())) {
* return null; }
*
* for (Namespace mapping :
* namespaceMap.get(project.getProject().getName())) {
*
* if (mapping.getPath().contains(installed.name)) { IPath path = new
* Path(mapping.getPath().substring(0,
* mapping.getPath().lastIndexOf(installed.name)+installed.name.length()
* )); if (installed.targetDir != null && installed.targetDir.length() >
* 0) { path = path.append(installed.targetDir); } return
* project.getProject().findMember(path.append(ComposerConstants.
* COMPOSER_JSON)); } }
*/
return null;
}
}
|
Nolin Lake State Park
Nolin Lake State Park is a park located in Edmonson County, Kentucky, United States. The park encompasses while Nolin Lake, the park's main feature, covers . The park is located on the northern perimeter of Mammoth Cave National Park.
The park contains a small beach, a country store, boat ramp, 32 developed campsites, 27 primitive campsites, and a playground.
On May 25, 1983, Nolin Lake set a record high of 549.9 mean sea level.
References
External links
Nolin Lake State Park Kentucky Department of Parks
Category:State parks of Kentucky
Category:Protected areas of Edmonson County, Kentucky
Category:Protected areas established in 2001 |
/* (c) 2014 Open Source Geospatial Foundation - all rights reserved
* (c) 2001 - 2013 OpenPlans
* This code is licensed under the GPL 2.0 license, available at the root
* application directory.
*/
package org.geoserver.wfs.xml.v1_1_0;
import javax.xml.namespace.QName;
import net.opengis.wfs.NativeType;
import net.opengis.wfs.WfsFactory;
import org.geotools.xsd.AbstractComplexBinding;
import org.geotools.xsd.ElementInstance;
import org.geotools.xsd.Node;
/**
* Binding object for the type http://www.opengis.net/wfs:NativeType.
*
* <p>
*
* <pre>
* <code>
* <xsd:complexType name="NativeType">
* <xsd:seq uence>
* <xsd:any processContents="lax" namespace="##other" minOccurs="0"/>
* </xsd:sequence>
* <xsd:attribute name="vendorId" type="xsd:string" use="required">
* <xsd:annotation>
* <xsd:documentation>
* The vendorId attribute is used to specify the name of
* vendor who's vendor specific command the client
* application wishes to execute.
* </xsd:documentation>
* </xsd:annotation>
* </xsd:attribute>
* <xsd:attribute name="safeToIgnore" type="xsd:boolean" use="required">
* <xsd:annotation>
* <xsd:documentation>
* In the event that a Web Feature Service does not recognize
* the vendorId or does not recognize the vendor specific command,
* the safeToIgnore attribute is used to indicate whether the
* exception can be safely ignored. A value of TRUE means that
* the Web Feature Service may ignore the command. A value of
* FALSE means that a Web Feature Service cannot ignore the
* command and an exception should be raised if a problem is
* encountered.
* </xsd:documentation>
* </xsd:annotation>
* </xsd:attribute>
* </xsd:complexType>
*
* </code>
* </pre>
*
* @generated
*/
public class NativeTypeBinding extends AbstractComplexBinding {
WfsFactory wfsfactory;
public NativeTypeBinding(WfsFactory wfsfactory) {
this.wfsfactory = wfsfactory;
}
/** @generated */
public QName getTarget() {
return WFS.NATIVETYPE;
}
/**
*
* <!-- begin-user-doc -->
* <!-- end-user-doc -->
*
* @generated modifiable
*/
public Class getType() {
return NativeType.class;
}
/**
*
* <!-- begin-user-doc -->
* <!-- end-user-doc -->
*
* @generated modifiable
*/
public Object parse(ElementInstance instance, Node node, Object value) throws Exception {
NativeType nativ = wfsfactory.createNativeType();
// <xsd:attribute name="vendorId" type="xsd:string" use="required">
nativ.setVendorId((String) node.getAttributeValue("vendorId"));
// <xsd:attribute name="safeToIgnore" type="xsd:boolean" use="required">
nativ.setSafeToIgnore(((Boolean) node.getAttributeValue("safeToIgnore")).booleanValue());
// <xsd:any processContents="lax" namespace="##other" minOccurs="0"/>
if (instance.getText() != null && instance.getText().length() != 0) {
nativ.setValue(instance.getText());
}
return nativ;
}
}
|
Does anyone here know a shop in Lebanon (or an online one that ships to Lebanon) that sells Retro Football Jerseys with printed names on 'em? the likes of Juve's Nedved, United's Cantona, etc.. so anyone..? |
Effect of CP-690,550, an orally active janus kinase inhibitor, on renal function in healthy adult volunteers.
CP-690,550 is a Janus kinase inhibitor being developed to prevent allograft rejection and treat several autoimmune diseases. This study examines the effect of multiple doses of CP-690,550 on renal function in healthy volunteers. Thirty-four volunteers are randomized in a 2:1 ratio in a double-blinded manner to receive CP-690,550 15 mg twice daily or placebo twice daily for 14 days. Volunteers are confined in-house to receive a controlled regimen of water intake and sodium intake of 4 to 5 g/d. The effect of CP-690,550 on glomerular filtration rate (GFR) is measured by iohexol serum clearance, effective renal plasma flow (ERPF) by para-aminohippuric acid (PAH) urinary clearance, and creatinine clearance by 24-hour urine collection on day 1 (predose) and day 15. Steady-state pharmacokinetics and tolerability are assessed. Comparing the day 15 and day 1 (predose) values shows that geometric mean ratios for iohexol serum clearance, PAH urinary clearance, and creatinine clearance are 0.995, 0.925, and 0.948, respectively. When adjusted for the corresponding placebo day ratios, the geometric mean ratios are 1.09, 0.978, and 1.05, respectively. CP-690,550 is well tolerated. These findings indicate that CP-690,550 does not affect GFR, ERPF, or creatinine clearance in healthy volunteers. |
Partisan media and fake newsonomics
This week The Listening Post 's Tariq Nafi takes a look at a kind of journalism that is a close cousin of "fake news" - the sort of reporting that tells people what they want to hear, as opposed to what they need to know; reporting that reinforces partisan opinions rather than challenging them.
As a recent Buzzfeed investigation revealed, it's the kind of output that a Miami-based company called American News LLC specialises in.
It does so not for ideological reasons, but for commercial ones. So it often covers the same story two different ways, sending a liberal, lefty version of it into one side of the blogosphere, while conservatives get a different take, dotted with right-wing arguments and buzzwords that push their buttons.
In the absence of vetted and contextualised and solid news information, people are just going to go for fake news, if it looks plausible enough, because that is human nature.
Brooke Binkowski, managing editor of Snopes
Sometimes it isn't just ideologically filtered, it's also flat-out fake.
Companies like American News LLC get plenty of clicks because, according to one study, it takes just a few believers to set off a news item on the social web.
Consumers are often much less concerned about the outlet doing the actual reporting and where the story originated than they are about who shares it - whose Facebook feed you find it on, whose tweet takes you to the article, or which friend sends it your way.
But how easy is it for American News LLC to exploit our biases?
"They use the same exact stories and the same exact formulas for the right and the left. It's very low effort and high output; so they don't really need to tweak that much of anything, except putting in the names of people that they know will get them to click," says Brooke Binkowski, managing editor and freelance journalist at Snopes.
LP contacted American News LLC to ask them about their editorial and business model, but received no response to our emails.
The growth of the partisan news landscape has been decades in the making, driven by the commercialisation of journalism, the deepening of political divides, and the polarisation of large segments of the population.
In the United States, before the internet and the social web turbocharged the spread of partisan outlets online, there was talk radio, dominated by strident conservative hosts and Fox News, which emerged as the televised voice of the Republican Party, later followed by MSNBC on the left.
Over the last quarter century, as the internet has offered platforms to anyone with a point of view, there has been an explosion of partisan media.
"I did a study for Axios in which I observed 89 news websites that have launched over the past 25 years, and what I found is there have been very few non-partisan websites that have launched," says Sara Fischer, a media reporter with Axios.
News consumers are partly to blame.
"In the absence of vetted and contextualised and solid news information, people are just going to go for fake news if it looks plausible enough, because that is human nature," offers Binkowski.
Multiple studies have concluded we have an appetite for content that feeds our biases and an aversion to material that doesn't.
"There's a natural tendency for people to like stories that already agree with their point of view," says Matthew Levendusky, associate professor of political science at the University of Pennsylvania. |
using System;
using System.Threading;
namespace FOCA.Analysis
{
public class DiarioFileAnalysis
{
public string FilePath { get; private set; }
public int Retries { get; set; }
public Action<DiarioFileAnalysis> Callback { get; set; }
public DiarioSDKNet.Diario.Prediction Prediction { get; set; }
public bool Completed { get; set; }
public string Error { get; set; }
public string Sha256Hash { get; set; }
public CancellationToken CancelToken { get; private set; }
public DiarioFileAnalysis(string file, Action<DiarioFileAnalysis> callback, CancellationToken token = default(CancellationToken))
{
if (String.IsNullOrWhiteSpace(file))
throw new ArgumentNullException(nameof(file));
if (callback == null)
throw new ArgumentNullException(nameof(callback));
this.FilePath = file;
this.Callback = callback;
this.Retries = 0;
this.CancelToken = token;
this.Completed = false;
}
}
}
|
Q:
table name in loop oracle pl/sql
declare
v_cnt NUMBER;
C SYS_REFCURSOR;
TMP_TBL_NM VARCHAR2(100);
stmt VARCHAR2(1000);
the_name varchar2 (50);
cursor c_table is
(SELECT a.table_name
--, a.column_name, a.constraint_name, c.owner,
--c.r_owner , c_pk.table_name r_table_name, c_pk.constraint_name r_pk
FROM all_cons_columns a
JOIN all_constraints c ON a.owner = c.owner AND a.constraint_name = c.constraint_name
JOIN all_constraints c_pk ON c.r_owner = c_pk.owner AND c.r_constraint_name = c_pk.constraint_name
WHERE c.owner like '%LTR' and c_pk.table_name like '%EnumerationValue%');
begin
stmt := 'SELECT table_name FROM ' || TMP_TBL_NM || ' ORDER BY 1';
OPEN C FOR stmt;
for t in C
loop
FETCH C INTO the_name;
EXIT WHEN C%NOTFOUND;
--my query for each table goes here
end loop;
end;
i want to use table names in loop as to check the records as per my query.
it is giving me error only by getting table name in the loop.
how can i get table name in a loop so that i can fetch rows as per my requirement from each table in a loop.
thanks in advance.
A:
I'm not entirely sure what you want to achieve here, but if it's just the table names you're interested in, you can make your code a lot less complicated doing it this way:
declare
cursor c_table is
SELECT a.table_name
--, a.column_name, a.constraint_name, c.owner,
--c.r_owner , c_pk.table_name r_table_name, c_pk.constraint_name r_pk
FROM all_cons_columns a
JOIN all_constraints c ON a.owner = c.owner AND a.constraint_name = c.constraint_name
JOIN all_constraints c_pk ON c.r_owner = c_pk.owner AND c.r_constraint_name = c_pk.constraint_name
begin
for t in c_table loop
--do something with the table name
dbms_output.put_line(t.table_name);
end loop;
end;
This kind of for loop also handles the opening and closing of the cursor and is the recommended way to do these kind of operations.
|
Released oil tanker photographed off Syria
Image caption
The Adrian Darya-1, formerly the Grace 1, was released after Iran said it would not head to Syria
The Iranian oil tanker at the centre of an international incident has been sailing just off the Syrian coast, satellite images appear to show.
The Adrian Darya-1 was seized by Gibraltar in July with the aid of British forces over fears it was bound for Syria, violating EU sanctions.
It was eventually released after assurances were given that it would not head for the war-ravaged country.
But images released on Saturday seemed to show it two nautical miles offshore.
The images, from US company Maxar Technologies, appeared to place the tanker very close to the Syrian port of Tartus on 6 September.
US National Security Advisor John Bolton tweeted that anyone who believed the ship was no longer headed for Syria was “in denial”.
“Tehran thinks it’s more important to fund the murderous Assad regime than provide for its own people,” he said, alongside another satellite picture. “We can talk, but #Iran’s not getting any sanctions relief until it stops lying and spreading terror!”
There is however no confirmation that the ship is unloading its cargo of 2.1 million barrels of Iranian crude oil.
Neither Iran nor Syria have commented.
In a statement, the UK’s Foreign Office called the reports “deeply troubling”.
A spokesperson said that if Iran had broken its assurances, it would be “a violation of international norms and a morally bankrupt course of action”.
The ship, originally known as Grace 1 when it was detained off the British territory in July, has caused a major diplomatic spat between Washington and Tehran.
British marines had helped Gibraltar authorities detain the vessel, partly drawing the UK into the row.
The United States made an official request to seize the ship in August, but the courts in Gibraltar denied it.
The EU has sought to salvage the accord but the Iranian tanker was seized because it was suspected of heading to Syria, which would breach EU sanctions on that country.
The Gibraltar authorities freed the vessel on 15 August after receiving assurances from Iran that it would not discharge its cargo in Syria.
The US has been seeking to seize the tanker since it was released by Gibraltar. It issued a warrant and blacklisted the vessel, threatening sanctions on any country which offered it aid. The ship has since been sailing east across the Mediterranean. |
Q:
How to get green bug (debug) icon on a stored procedure?
I have Oracle 10.5 installed on my system.
I created a stored procedure using Toad. It is running successfully.
I observed that there are different icons for stored procedures in Toad:
Red cross (error in procedure)
White rectangle (new procedure)
Green bug (debugged procedure)
My procedure has the white rectangle icon. I want to change it to the green bug icon.
I found online that I have to run the stored procedure in debug mode. I ran it but it didn't change the icon.
How I can get the green bug icon for my stored procedure?
A:
The green bug indicates that the stored procedure (or package) was compiled with debug information and can be debugged. In order to create the necessary debug information, you need to (re-)compile your stored procedure with
alter procedure PROCNAME compile debug;
Replace PROCNAME with the actual name of your stored procedure.
|
Nail Designs
How to make this Nail Design:
After applying a base coat. Paint two half triangle on the tip one with
black and the other with white.Now make dots on the border.Finally seal
with a top coat for shine.
How
to do this Nail Art:
First apply a base coat.Then apply light silvery glittery polish.On top
of it put dark pink glittery polish. For roses, witha black nailpain
draw spirals.Place tiny shining stones at the bottom.For shne finish
with a top coat.
How to make this Nail
Design:
First aplly tha base coat then put the light pink as base colour.Now in
a makeup sponge smudge the white and silver colour and the dab it over
your nails.Now with a black stripper dra the black stems. Then taking a
pink dotting tool create 3 dots over the alternate stems.Using a white
dotting tool, create smaller dots over the pink dots.Finsih with a top
base coat for shine.
How to make this Nail
Design:
First paint all your nails black.Then just in the middle draw a broad
stripe with purple colour.Now use a stripper to paint over the purple
strip. Then over it just put the pink powder and remove the remaining
powder from the sides.
How
to make this Nail Design:
Fisrt colour your nails in two different colours of your choice.
Then the cavier beads of the same colour.Now paint a second coat of the
paint and while the paint is still wet sprinkle the beads.Finish with a
top coat to seal in the beads.
How
to make this Nail Design:
Paint all nails grey colour.Then put black polka dots on the grey
nails.Now in one nail with a dotting tool, create a bow.Seal with a top
coat for shine.
How
to make this Nail Design:
First paint the nails with base coat.Then put light pink colour on it.
Now with white stripper paint the flowers and petals.Finish with a top
coat for shine. |
Teemu Selanne has been so great for so long, it’s hard to believe his career’s coming to an end. Heck, many don’t believe it’ll happen, even though he’s been very direct about his intentions.
So it’s appropriate the international phase of his career had a storybook ending, as Selanne scored two goals in his final Olympic contest — Saturday’s 5-0 win over the U.S. in the bronze medal game — making him the oldest medal winner in men’s Olympic hockey history.
“What a great ending,” Selanne said, per the Toronto Star. “Twenty-six years ago I played my first national team game. I’ve been carrying this jersey with a lot of pride and love.”
Since the NHL started sending its players to the Olympics in 1998, Finland has led the pack with four medals and Selanne is a big part of the reason why. Just as he has excelled on the NHL stage, Selanne has consistently found a way to elevate his game.
He has 24 goals and 43 points in 37 Olympic contests. He tied the Olympic lead in scoring twice (1998 and 2006) and goals twice (1992 and 2006) and, as noted by Sportsnet’s John Shannon, has been a pretty consistent scoring threat (save a slump in Vancouver):
Despite being 43 and having his role with the Anaheim Ducks being significantly diminished, Selanne played a critical role in Finland’s success from start to finish on Sochi. He had six points in six games and, for the first time, agreed to lead the Finns while serving as captain.
“Usually I’m [alternate] captain and a lot of times if they have asked if I want to be captain, I don’t really need a letter to be a leader,” Selanne explained to NHL.com before the tournament started. “A lot of times it’s better if somebody else going to be [captain]. But now it’s my last one, this time I felt it’s time to be captain and I’m very honored.”
Selanne wanted to make the most of his last trip to the Olympics as a player. As has been the case so many times before, he succeeded.
Reilly Smith scored his 20th goal of the season for Vegas on Wednesday night and gives Vegas five 20-goal scorers. Not many expansion teams have done that. Of course, not many expansion teams have been capable of doing a lot of the things Vegas has accomplished this season.
With the trade deadline inching closer the Los Angeles Kings made their second trade in as many weeks on Wednesday evening.
Let us take a look at the deal!
The trade: The Kings acquire Tobias Rieder and Scott Wedgewood from the Arizona Coyotes for Darcy Kuemper. Arizona is also retaining 15 percent of Rieder’s salary. He will be a restricted free agent after this season.
Why the Kings are making this trade: Let’s check in with Kings general manager Rob Blake for his take on the deal.
“We continue to look for opportunities to improve our team speed and Tobias will bring that dynamic to our club.”
Okay, that’s actually pretty important. A few days ago I wrote about how the Kings needed to hit the reset button on how they play because the league seems to have passed them by. They are not overly skilled. They do not have a ton of speed. They could use more in both areas.
Rieder, though having a really down year, could help improve that. He certainly improves the speed dynamic for the team and he seems to have the potential for a bounce back in Los Angeles because he is capable of more production than he has shown so far this season.
Kuemper has been great in a backup role this season so it’s a little surprising to see the Kings make that swap, but Rieder is at least an interesting addition.
Why the Coyotes are making this trade: That’s actually … a little bit of a mystery?
One potential angle on it is that Antti Raanta is an unrestricted free agent after this season while Kuemper is signed for two more years at a pretty cheap salary cap hit. The Coyotes make it sound like they still plan on keeping Raanta, but if nothing else this provides them with a little bit of insurance in case they can’t.
Here is Coyotes general manager John Chayka.
“Darcy is a big, talented goaltender who is having an excellent year. You need great goaltending in this league in order to be successful and with Antti and Darcy, we are confident that we have an excellent tandem for the future.”
Who won the trade? I like what it does for the Kings because they need someone like Rieder to step into their lineup. Someone fast, someone that still has the chance to score a bit more than they have shown this season. With Jonathan Quick locked in place for the foreseeable future Kuemper was never going to be anything more than a backup there so they did not really have to give up a significant piece.
GANGNEUNG, South Korea (AP) — To three-time Olympian Hilary Knight, the thought of finally hoisting the gold medal means giving women’s hockey a big boost in the United States.
How big?
Huge.
”The U.S. wants to be No. 1 in everything, and I think we’ve all been raised as awesome competitors so at the end of the day we want a victory,” Knight said. ”We want to win, and that would be winning a gold medal.”
That’s the only shade of medal that has eluded the Americans since 1998, the last time they won it all in Nagano when women’s hockey made its Olympic debut. They took home a disappointing bronze from Turin in 2006 and silver from the past two finals – no loss more crushing than in 2014 in Sochi when Canada rallied from an 0-2 deficit to win 3-2 in overtime.
Now the Americans have their latest chance at Olympic gold (Wednesday, 11:10 p.m. ET, NBCSN) against their archrival in a showdown Thursday that will include Marie-Philip Poulin, whose two goals snatched gold from U.S. hands in Sochi. She is back again as Canada’s captain.
”For me, it’s been a fairy tale for the last Olympics,” Poulin said. ”But it’s in the past now. It’s a new Olympics, and we have to bring our best game and go from there.”
This game once again features the only two nations ever to win Olympic gold.
Nothing less than a fifth straight gold medal is expected in the country that created the sport, and the Canadians have won the past four Olympic gold-medal games. Only the United States in basketball has dominated a women’s team sport more thoroughly with its streak of six straight golds.
The Canadians haven’t lost even a single Olympic game since the 1998 Nagano final won by the United States. Their streak stands at 24 consecutive games, including a 2-1 win over the United States to cap pool play a week ago. They’ve also won five straight over the Americans, including four exhibition victories in December prepping for the Olympics.
”Maybe I’m biased, but one of the best rivalries in sports and especially in our game,” said Canadian forward Emily Clark, who played college hockey at Wisconsin. ”So we obviously have a lot on the line, mostly pride. All of us are going to bring our best game.”
Yet the Americans have owned the world championships, winning the last four and eight of the last 10. That has only made the U.S. drought at the Olympics all the more noticeable and makes this game even more special.
”It’s been something I’ve been dreaming about since I was little,” said U.S. forward Dani Cameranesi. ”So it means a lot, and to be here with this group of girls and to be with them all year has really been an honor.”
The 10 Americans who lost the final in Sochi have left that game in the past. No need to waste energy dwelling on such a heartbreaker when the chance at history is at hand. Cameranesi is among 13 Americans on the roster at their first Olympics, so Sochi is just a game they may have watched on TV.
”We’re in South Korea, and it’s 2018 and you want a different result,” U.S. coach Robb Stauber said . ”They’ve put a lot of energy and focus into transforming things that they needed to get better at, and that’s now. You drop the puck, see what happens.”
When the Americans and Canadians play, it’s essentially a heavyweight bout even if nobody drops the gloves.
”Every single time we play them, it’s a big game,” Canada coach Laura Schuler said. ”You know the crowds there, people. There’s always pressure every single time when you represent your country and you play best on best competition. I think it’s something that we’re used to.”
At least, that appears to be the plan for the Nashville Predators, as assistant GM Paul Fenton told Craig Custance of The Athletic (sub required) that they expect to bring in Tolvanen once his KHL “out clause” kicks in following his season with Jokerit.
“We’ll have a contract in place to be able to execute and have him come over here,” Fenton said. “That’s the plan. Funnier things have happened. I don’t want to say 100 percent. I never do that in our business. Yes, our plan is to have him.”
Now, depending upon whom you ask, the “funnier things” might involve a trade … although the odds seem pretty low on that, as Custance notes:
And yes, teams have been calling the Predators about Tolvanen. No, he's not going anywhere*: https://t.co/R9chLmeA5n
*usual trade deadline caveat that anything can happen and maybe there's a blockbuster that turns the world on its axis.
OK, so let’s assume that Tolvanen isn’t the one who’s traded. There’s the possibility, mind you, that Tolvanen’s emergence and Mike Fisher’s hopeful return might force a bit of a logjam, or at least a theoretical one. Maybe GM David Poile would use that anticipated influx of even more depth to make an upgrade?
OK, so all of that is important, but let’s take a moment to bask in the gloriousness of what might be another talented player added to a fun Predators roster already brimming with depth and skill. (Custance describes the Predators as “salivating” over clips from Tolvanen at the 2018 Winter Olympics.)
The beautiful thing about the Finnish 18-year-old, who was almost instantly heralded as a steal as the 30th pick of the 2017 NHL Draft, is that he’s checking just about all the boxes.
While his Finnish team fell to Canada and were eliminated in the quarterfinal today, he was absolutely sensational. Quick reference: when you’re getting mentioned in the same breath as vintage Eric Lindros, you’re probably doing something very, very right.
Canada eliminates Finland. Eeli Tolvanen (NSH) finishes with nine points in five games. Tied for second best total points by a U19 player ever at the Olympics. Two points behind Lindros who played in three more games in 1992.
Of course, five games is a small sample size, and the talent on hand during the 2018 Winter Olympics was a mixed bag.
The Predators must be heartened, then, to see Tolvanen produce in the KHL. He currently has 17 goals and 17 assists for 34 points in 47 games. That ranks Tolvanen second on his team in scoring, just one point behind former Canucks and Rangers forward Nicklas Jensen, who’s collected his 35 points in 52 games.
Ultimately, the Predators enjoy an embarrassment of riches, with the luxury of bickering over whether they should keep the promising prospect or move him in a Rick Nash trade. The stakes are high when you’re aiming for a Stanley Cup, yet it’s also remarkable just how loaded the Predators are from their roster to their farm system.
GM David Poile on @1045TheZone on his plans for Eeli Tolvanen with the #Preds this season: "After watching him last night, I'd sure like to have him on our team. *laughs* … we're very interested in bringing him onto our roster." |
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Archive for the Medical Devices Category
Tungsten and Medicine versus Gold
Tungsten, a gold competitor, has a long history of use in medical products, dating back to the manufacture of x-ray tubes in the 1800s. It’s particularly well suited to applications that require hardness and high heat resistance. Tungsten is also a highly conductive metal. But whereas electronic arcing can become an issue for other highly conductive materials, tungsten avoids this problem entirely.
Tungsten is 97% as dense as gold, with a similar resistance to bodily fluids and atmospheric contaminants. Tungsten’s density and electronic performance are also comparable to those of gold. These similarities allow tungsten to serve as a stand-in for gold in some instances. Manufacturers will often apply a gold coating to tungsten wire to cut costs.
Tungsten is frequently used to establish radio opacity in medical devices, often ones implanted inside the body. This is due to tungsten’s very high density, a property that allows it to transmit signals reliably. One such example is tungsten’s use in catheters. Catheters are threaded through veins to get where they need to go inside the body. To ensure accurate placement, doctors track the location of the catheters through the use of x-rays. Tungsten is also used in the manufacture of hand held devices utilized to conduct sonograms, once again due to the metal’s innate ability to transmit signals.
Tungsten is a durable, cost effective metal, and a resource to the medical device industry.
Comments Off on As Good as Gold – Establishing Radio Opacity in Medical Devices with Tungsten
Atlantic Equipment Engineers
Atlantic Equipment Engineers,
a Division of Micron Metals, Inc. was founded in 1963, as a materials
engineering company. Our primary activity was to support the growing R&D efforts of companies involved with the expanding NASA space
program. |
---
abstract: 'We suggest a workable approach for the description of multiscale magnetization reversal phenomena in nanoscale magnets and apply it to CoPt-type alloys. We show that their hysteretic properties are governed by two effects originating at different length scales: a peculiar splitting of domain walls and their strong pinning at antiphase boundaries. We emphasize that such multiscale nature of hysteretic phenomena is a generic feature of nanoscale magnetic materials.'
author:
- 'K. D. Belashchenko'
- 'V. P. Antropov'
title: 'Multiscale nature of hysteretic phenomena: Application to CoPt-type magnets'
---
The problem of magnetization reversal (MR) is a central and longstanding problem in the theory of magnetism. Main complications in its treatment stem from the fact that effects due to magnetostatic and elastic forces manifest themselves in the whole nanoscale range while local interactions must still be treated on the atomistic scale. As the length scale increases, new physical effects arise, but coarse-graining over the lower-scale degrees of freedom is not easily accomplished. Specifically, MR is realized by motion of domain walls (DW), the two-dimensional surfaces where magnetization changes its direction. DW’s may easily move unless they are pinned by defects, which implies that MR properties are not intrinsic and depend strongly on the microstructure. Experimentally, this results in huge variations of the coercive force $H_{c}$ and other properties depending on material processing. It is crucial to address the DW structure and its interaction with microstructure on different length scales ranging from interatomic to submicron.
In modern micromagnetic methods [@MM] complex microstructures of hard magnets are defined by (usually piecewise constant) fields of macroscopic material properties such as the exchange constant $A({\bf r})$ and the magnetocrystalline anisotropy (MCA) constant $K({\bf r})$. Such calculations were mainly focussed on the role of grain boundaries; since they are extremely hard to describe microscopically, their properties are postulated in an *ad hoc* manner making reliable predictions problematic. From the other hand, typical microstructures of hard magnets with L1$_{0}$ crystal structure including CoPt, FePt and FePd are dominated by other defects [@Kandaurova-JMMM; @Leroux91; @Soffa2000; @Khach; @BPSV; @Shur-CoPt], antiphase boundaries (APB) and twin boundaries (TB), which are crystallographically coherent and easier to treat than grain boundaries. Although these materials were used and studied for many decades and the formation of their microstructure is well understood, the mechanism of MR is still a mystery. The goal of the present letter is to lay the foundation of a consistent multiscale theory of MR in CoPt type magnets.
Microstructural evolution during L1$_0$ ordering is strongly affected by tetragonal lattice distortions [@Khach; @BPSV]. After a relatively short ‘tweed’ stage of annealing after quench, when the ordered domains achieve some characteristic size $l_0\sim$ 10 nm, they develop so-called polytwinning, i.e. the formation of regular arrays (‘stacks’) of ordered bands (‘$c$-domains’) separated by [TB’s ]{} [@Kandaurova-JMMM; @Leroux91; @Soffa2000; @Khach; @BPSV]. The tetragonal axes $c$ of the $c$-domains (pointing along one of the three cubic axes of the parent fcc phase) alternate regularly making 90$^{{\rm o}}$ angles between the adjacent domains (below we use the obvious terms ‘X-domain’, ‘XY-stack’, etc.). In addition to polytwinning, the observed and simulated microstructures always contain a high density of APB’s in the $c$-domains [@Leroux91; @Soffa2000; @Khach; @BPSV; @Shur-CoPt].
Polytwinned magnets were extensively studied with analytical micromagnetic methods [@Kandaurova-JMMM]. Due to high MCA the DW width $\delta=\pi\sqrt{A/K}$ is quite small (5–10 nm), while the anisotropy field $H_a=2K/M$ ($M$ is the saturation magnetization) significantly exceeds the typical magnetostatic field $H_{m}=4\pi M$ (parameter $\eta=H_m/H_a$ is close to 0.1 in CoPt and FePt and 0.38 in FePd [@Kandaurova-JMMM]). Therefore, at $d\agt\delta$ ($d$ is the $c$-domain thickness) each $c$-domain may be regarded as an individual magnetic domain with intrinsic 90$^{{\rm o}}$ DW’s at the [TB’s ]{} [@Kandaurova-JMMM]. It is assumed that MR is associated with ‘macrodomain walls’ (MDW) crossing many $c$-domains. Such MDW’s were observed experimentally [@Kandaurova-JMMM; @Soffa2000], but their internal structure and mechanisms of coercivity are unknown [@Kandaurova-JMMM].
#### Microscopic mean-field method.
Consider a binary alloy AB with the classical Hamiltonian $$\begin{aligned}
H=H_{{\rm conf}}\{n_i\}+\sum_{i<j}n_{i}n_{j}\left[ -J_{ij}{\vec{\mu}}_{i}{\vec{\mu}}_{j}+{\vec{\mu}}_{i}\widehat{D}_{ij}{\vec{\mu}}_{j}\right]\nonumber\\
+\sum_{i}n_{i}[\epsilon_i({\vec{\mu}}_{i})-{\bf H}_{0}{\vec{\mu}}_{i}]
\label{H-Heisenberg}\end{aligned}$$ where $H_{{\rm conf}}$ is the configurational part of the Hamiltonian; $i$ and $j$ run over lattice sites; $n_{i}=1$ if site $i$ is occupied by a magnetic atom A and $n_{i}=0$ otherwise (let B be non-magnetic for simplicity); ${\vec{\mu}}_{i}$ is the rigid classical magnetic moment of the atom at site $i$; $J_{ij}$, the Heisenberg exchange parameters; ${\bf H}_{0}$, the external magnetic field; $\epsilon_i({\vec{\mu}}_{i})$, the MCA energy equal to $-b_{i}({{\roarrow\mu}}_{i}\mathbf{e}_i)^{2}$ for easy-axis anisotropy; and $\widehat{D}_{ij}$, the magnetic dipole-dipole interaction tensor.
The free energy in the mean-field approximation (MFA) may be related to the ‘mean fields’ ${\bf H}_{i}={\bf H}_{0}+\sum_{j}(J_{ij}-\widehat{D}_{ij})c_{j}{\bf m}_{j}$ where ${\bf m}_{i}=\langle {\vec{\mu}}_{i}\rangle$ and $c_{i}=\langle n_{i}\rangle$ are local magnetizations and concentrations, respectively: $$F=-E_{J,DD}-T\sum_{i}c_{i}\ln \int d\widehat{\mu }_{i}\exp \left[\beta({\bf H}_{i}{\vec{\mu}}_{i}-\epsilon_i)\right].
\label{F}$$Here $E_{J,DD}=\sum c_{i}c_{j}{\bf m}_{i}(-J_{ij}+\widehat{D}_{ij}){\bf m}_{j}$ is the total exchange and dipole-dipole energy. Equilibrium states may be found using self-consistency relation ${\bf m}_{i}=-\partial F/\partial {\bf H}_{i}$.
If magnetization ${\bf M}({\bf r})$ slowly varies in space and is constant in magnitude, Eq. (\[F\]) reduces to the micromagnetic free energy [@Aharoni]. In this case all choices of $J_{ij}$ and $b_i$ in the defect-free regions are equivalent if they produce the same macroscopic properties $A$ and $K$. However, variation of $J_{ij}$ and $b_i$ near defects like APB’s must be studied using first-principles techniques. Microscopic MFA calculations with these parameters may be used to describe DW interaction with a defect at the length scale of $\delta$. At larger, microstructural length scales micromagnetic methods [@MM] may be used with singularities of $A$ and $K$ at the defects. However, in hard magnets the microscopic approach also turns out to be convenient for the studies of regions containing up to $\sim10^6$ atoms; in such calculations some model $J_{ij}$ and $b_i$ reproducing the actual defect properties may be used.
Below, we first address the equilibrium structure of MDW’s in a defect-free system and find a peculiar MDW splitting phenomenon. Then we explore the behavior of MDW’s in external field, briefly report our results for pinning at APB’s, and finally deduce the combined effect of MDW splitting and pinning on coercivity.
#### Equilibrium macrodomain walls.
It is convenient to use the body-centered tetragonal (bct) representation of the fcc lattice (with $c/a=\sqrt{2}$ and $c$ equal to the fcc lattice parameter). Two opposite edges of a rectangular simulation box are aligned with the (110) [TB’s ]{}in the XY-stack; MDW’s are normal to them. The boundary conditions are periodic, and the dipole-dipole fields are computed using the Fourier transforms. Equilibrium MDW’s of two characteristic (1$\overline1$0) and (001) orientations are shown in Fig. \[DWnoAPB\] for the CoPt model. Infinite stack of $c$-domains is assumed with ideal [TB’s ]{}in the (110) planes. Fully ordered $c$-domains have the same thickness $d=64a\simeq17$ nm, which corresponds to an early stage of annealing shortly after the polytwinned stacks are formed [@Soffa2000; @BPSV]. The anisotropy is uniaxial with $\mathbf{e}_i$ pointing along the local direction of the tetragonal axis and $b_i=b$. Room temperature $T=0.4T_c$ is assumed averywhere (for CoPt $T_c\simeq720$ K). For simplicity, only $3d$-metal atoms are assumed to have magnetic moment $\mu$. Parameters $b$ and $\mu$ were chosen so that MFA gives experimental room-temperature values of $K=4.9\times10^7$ erg/cm$^3$ and $\eta=0.082$ for CoPt [@Kandaurova-JMMM]. The parameters $J_{ij}$ for nearest and next-nearest neighbors were chosen as $J_2/J_1=2/3$, $J_3/J_1=1/6$; $A$ is isotropic with this choice.
MDW’s of both orientations shown in Fig. \[DWnoAPB\] have a peculiar feature which turns out to be the key to the understanding of MR in polytwinned magnets: the DW segments (DWS) located in adjacent $c$-domains are displaced in respect to each other. Such configuration with regularly alternating displacements is beneficial for the exchange energy because magnetization within each DWS is parallel to that in the adjacent $c$-domains (note that the color of horizontal DWS’s in Fig. \[DWnoAPB\]a,c matches that of adjacent $c$-domains). The magnetostatic energy for this MDW configuration is higher compared to the rectilinear one due to the presence of short magnetically charged (in micromagnetic terms [@Aharoni]) segments of 90$^{{\rm o}}$ DW’s at the [TB’s ]{}(note the red and blue ‘blobs’ in Fig. \[DWnoAPB\]d). Actual MDW configuration emerges as a result of competition between these interactions. However, due to small $\eta$ the dipole-dipole interaction is, in fact, unimportant at the length scale of $\delta$.
As it is clear from Fig. \[DWnoAPB\], the magnetic charges both at the DWS’s of a (1$\overline1$0) MDW and at the [TB’s ]{}alternate in sign, so that each MDW is magnetically uncharged as a whole, and its magnetic field quickly falls off at $r\agt d$. DWS’s of (001) MDW’s do not carry magnetic charge.
The orientation of DWS’s within $c$-domains in (1$\overline1$0) MDW is determined by the anisotropy of the exchange constant $\alpha_A=A_\perp/A_\parallel$ ($A_\perp$ and $A_\parallel$ are values of $A$ normal and parallel to $c$), and by the parameter $\xi=\eta d/\delta$. At $\xi\ll1$ the DW orientation is determined solely by $\alpha_A$. At $\xi\gg1$ the DW aligns parallel to the tetragonal axis, and $\alpha_A$ is irrelevant. The (1$\overline1$0) MDW shown in Fig. \[DWnoAPB\]a,b is in the crossover region with $\xi\sim0.2$ and $\alpha_A=1$.
#### Partial macrodomain walls.
MDW’s behave remarkably in external magnetic field ${\bf H}_0$ because DWS’s are held together only by magnetostatic forces. If these forces were absent ($\eta\to0$ limit), each DWS would be able to move freely until it meets another DWS in an adjacent $c$-domain. Some of this freedom remains at small $\eta$. Consider an XY-stack with (110) [TB’s ]{}, as above. Component $H_z$ does not exert any force on DWS’s, and the effect of ${\bf H}_0$ on MDW’s depends only on the orientation of its projection ${\bf H}_{\perp}$ on the $xOy$ plane. If ${\bf H}_{\perp}$ is normal to the [TB’s ]{}($H_x=H_y$), then the forces acting on all DWS’s are in the same direction, and both MDW’s shown in Fig. \[DWnoAPB\] move as a whole like usual DW’s in a homogeneous crystal. However, if ${\bf H}_{\perp}$ is parallel to the [TB’s ]{}($H_x=-H_y$), the forces acting on X- and Y-DWS’s differ in sign, and the total force acting on the MDW is zero.
Let us call a set of DWS’s of a MDW in all even or odd $c$-domains as a *partial macrodomain wall* (PMDW), e.g. X-PMDW. There are two MDW realizations differing in the sign of the relative displacement $L$ of the two PMDW’s. For one of them ${\bf H}_{\perp}$ increases $|L|$ (‘splitting’), and for the other, reduces it (‘swapping’). If ${\bf H}_\perp$ is inverted, splitting turns to swapping and vice-versa. Accordingly, two threshold fields may be introduced. Let us fix, for instance, Y-PMDW and examine the effect of $H_x$ on X-PMDW. The *threshold splitting field* $H_{\text{sp}}$ is the minimal value of $H_x$ required to move the X-PMDW far from the Y-PMDW. The *threshold swapping field* $H_{\text{sw}}$ is required to ‘drag’ the X-PMDW through Y-PMDW in the opposite direction, overcoming the exchange barriers at the [TB’s ]{}. $H_{\text{sw}}$ is of lesser importance than $H_{\text{sp}}$ because even if $H_{\text{sp}}<H_{\text{sw}}$, the existence of some MDW’s in the ‘splitting relation’ with ${\bf H}_x$ is sufficient to complete the MR. Note also that $H_{\text{sw}}\propto d^{-1}$ and quickly falls off with increasing $d$. Both $H_{\text{sp}}$ and $H_{\text{sw}}$ are *‘intrinsic’* properties for a given $d$, i.e. they exist even if there are no defects (APB’s) in the $c$-domains.
$H_{\text{sp}}$ may be easily estimated micromagnetically for a (001) MDW. When its two PMDW’s are displaced at distance $L$, the alternating magnetic charges appearing at the [TB’s ]{} form a regular stack of ‘capacitors’ (see Fig. \[splitting\]). For $L\agt d$, the magnetic field is concentrated inside these capacitors, and the total magnetostatic energy is proportional to $L$; the coefficient in this proportionality determines $H_{\text{sp}}$. Such calculation gives $H_{\text{sp}}=\pi M$ (or, alternatively, $H_{\text{sp}}=H_a\eta/4$). The splitting threshold for (1$\overline1$0) MDW is larger because of the magnetic charges on its segments. In the above estimate we neglected the deviation of ${\bf M}$ from the easy axis at distances $\sim\delta$ from the [TB’s ]{}, which reduces $H_{\text{sp}}$ for small $d$.
Thus, at $\eta\ll1$ we have $H_{\text{sp}}\ll H_{a}$. In particular, using the room-temperature values of $M$ [@Kandaurova-JMMM], we obtain $H_{\text{sp}}$ of 2.5 kOe for CoPt and 3.5 kOe for FePt and FePd. These values are close to the typical fields at which hysteresis is observed in these magnets. Quite naturally, they are much less than the coercive fields corresponding to uniform rotation of magnetization in the $c$-domains [@Kandaurova-JMMM]. A peculiar feature of a PMDW in the polytwinned crystal is that it separates qualitatively different magnetic domains with different free energies, and hence there is an intrinsic force acting on an isolated PMDW (its density per unit cross-section of the $c$-domain is $f_{s}=2MH_{\text{sp}}$).
#### Domain wall segments, pinning and coercivity.
Real polytwinned alloys, as we noted above, usually contain a high density of APB’s in the $c$-domains. It is known that DW’s may be pinned by APB’s [@pinning], and it was argued that this mechanism may explain high coercivity of CoPt type alloys [@Shur-CoPt; @Zhang94]. Here we show that this pinning is indeed quite strong, but the MDW ‘dissociation’ into segments also has a profound effect on MR.
The APB pattern within $c$-domains determines the statistical properties of the random value $U(x)$ where $x$ is the coordinate of a DWS, and $U$ is its APB-induced excess free energy. For the following basic consideration we assume that $U(x)$ describes a distribution of similar pinning centers with the typical distance $l_d$ between them. The maximal slope of $U(x)$ determines the *unpinning threshold* $H_u$, i.e. the value of the field ${\bf H}_0\parallel c$ required to unpin a single $c$-DWS. Thus, in the absence of magnetostatic forces at $H_0<H_u$ each $c$-DWS is pinned, and at $H_0>H_u$ it can move freely to the surface of the polytwinned stack. These assumptions are obvious for patterns with isolated APB’s as in Fig. 5 of Ref. [@Leroux91] where $l_d\sim5$–$10d$; however, main features of more complex patterns [@Soffa2000; @Khach; @BPSV; @Zhang94] may also be described by some characteristic values of $H_u$ and $l_d\alt d$.
The maximum possible $H_{u}$ is achieved when DWS’s are parallel to isolated plain APB’s. To evaluate this maximum in the studied alloys, we explored the modification of exchange and anisotropy at an isolated (101)-oriented APB in CoPt, FePt and FePd using the tight-binding linear muffin-tin orbital method. We found that MCA is strongly suppressed at the APB leading to a DW *attraction* to the APB with $H_{u}$ of about 11, 7 and 1.5 kOe for CoPt, FePt and FePd, respectively. These values significantly exceed the observed coercivities [@Zhang94]. Since high MCA is associated with L1$_{0}$ ordering, it is natural that local disorder at an APB suppresses MCA.
Let us now explore the role of intrinsic magnetostatic forces in MR. We restrict ourselves to the case of ${\bf H}_0\parallel Ox$ in a single crystal with different types of polytwinned stacks (‘single crystal’ refers to the parent fcc lattice). Such field does not affect YZ-stacks, except for a reversible transverse magnetization. In other stacks ${\bf H}_0$ exerts a force density $f=2MH_0$ on X-DWS’s [*only*]{}.
From our definition of $H_{\text{sp}}$ it follows that if $c$-PMDW in X$c$-stack ($c=$Y or Z) is held in place (e.g., by pinning), then the free (unpinned) X-PMDW moves to infinity at $H_x\geq H_{\text{sp}}$ (neglecting the demagnetizing effects). At $H_x<H_{\text{sp}}$ the X-PMDW moves to a finite distance $L(H_x)$ from the $c$-PMDW. By definition, $L(H_{\text{sp}})=\infty$. Except for a close vicinity of $H_{\text{sp}}$, $L\alt d$.
The path of MR differs qualitatively in two cases: (a) $H_{\text{sp}}>H_u$, and (b) $H_{\text{sp}}<H_u$. In case (a) the MDW can only move as a whole (intrinsic forces $f_s$ are strong enough to unpin a PMDW), but DWS’s may to some extent ‘adapt’ to the local pinning potential. Let us define the characteristic displacement $l_m$ ‘allowed’ by magnetostatic forces as $l_m=L(H_u)$. Obviously, $l_m$ increases with $H_u$, and $l_m\to\infty$ at $H_u\to H_{\text{sp}}$. If $l_m>l_d$, the effective unpinning field of the MDW is $H_U\sim2H_u$ (${\bf H}_0$ affects one half of the DWS’s, while all DWS’s can be effectively pinned). However, as $l_m$ becomes smaller than $l_d$, $H_U$ is quickly reduced, because only a fraction of DWS’s can be pinned simultaneously (MDW is effectively ‘rigid’ and can not make ‘kinks’ comparable with $l_d$).
Now, in case (b) the MDW may split in two PMDW’s at sufficiently large ${\bf H}_0$. The MDW is ‘soft’, and each DWS can be effectively pinned. During the whole cycle of remagnetization pinned Y- and Z-PMDW’s do not move at all, and hence the intrinsic (magnetostatic) force acting on a moving X-PMDW will change its sign every time that it crosses, e.g., an Y-PMDW (in XY-stack). Thus, for an X-PMDW we have $H_U=H_u+H_{\text{sp}}$. Different MR properties may, in principle, be observed if the sample was previously magnetized to saturation by ${\bf H}_0$ along, e.g., (111). In this case there are no Y- and Z-PMDW’s, and in some stacks the switching threshold is $H_U=H_u-H_{\text{sp}}$. The hysteresis loop in this case may have a peculiar double-step feature with magnetization jumps at $H_0=H_u\pm H_{\text{sp}}$. Such ‘hysteresis memory’ effects provide a test of the $H_{\text{sp}}<H_u$ relation and may be used to design ‘programmable’ magnets.
Thus, for an initially demagnetized sample with the given $H_u$ the coercive force $H_c$ first rises with $H_{\text{sp}}$, reaches its maximum $\sim2H_u$ at $H_{\text{sp}}\approx H_u$, stays roughly constant in the range $\infty>l_m>l_d$, and finally falls off at $l_m<l_d$. High coercivity of CoPt is probably due to the fact that this magnet with suitable processing is close to the optimal $H_{\text{sp}}\sim H_u$ condition. By contrast, in FePd $H_{\text{sp}}$ is too large ($H_{\text{sp}}/H_u\approx2.3$ even for maximal possible $H_u$), so that $l_m\ll d$; this conclusion agrees with the relatively small observed $H_c/H_a$ ratio.
In our analysis we neglected the demagnetizing fields. Close to saturation they are comparable to $H_{\text{sp}}$, but they have little effect on $H_c$, because they are small when the total magnetization is close to zero.
In conclusion, we developed a workable technique for the description of multiscale MR phenomena in hard magnets and applied it to CoPt-type alloys. We have shown that coercivity of these materials has at least two sources originating at different length scales: strong pinning of MDW’s by APB’s and their splitting at [TB’s ]{}. This DW splitting seems to be a generic effect that may also affect MR in other groups of materials, including some nanostripes [@nanostripes] and multilayers; it may also occur at grain boundaries of certain misorientations.
The authors are grateful to V.G. Vaks for useful discussions. This work was carried out at Ames Laboratory, which is operated for the U.S. Department of Energy by Iowa State University under Contract No. W-7405-82. This work was supported by the Director for Energy Research, Office of Basic Energy Sciences of the U.S. Department of Energy.
[99]{}
R. Fischer and H. Kronmüller, Phys. Rev. B [**54**]{}, 7284 (1996); J. Fidler, T. Schrefl, J. Phys. D [**33**]{}, R135 (2000).
N.I. Vlasova, G.S. Kandaurova and N.N. Shchegoleva, J. Magn. Magn. Mater. [**222**]{}, 138 (2000).
C. Leroux, A. Loiseau, D. Broddin and G. van Tendeloo, Phil. Mag. B [**64**]{}, 58 (1991).
C. Yanar, J.M.K. Wiezorek and W.A. Soffa, in [*Phase Transformations and Evolution in Materials*]{}, ed. P. Turchi and A. Gonis (TMS, Warrendale, 2000), p. 39.
L.-Q. Chen, Y. Wang and A.G. Khachaturyan, Phil. Mag. Lett. [**65**]{}, 15 (1992).
K.D. Belashchenko, I.R. Pankratov, G.D. Samolyuk and V.G. Vaks, J. Phys.: Condens. Matter [**14**]{}, 565 (2002).
Ya.S. Shur [*et al.*]{}, Phys. Met. Metallogr. [**26**]{}, 241 (1968).
B. Zhang and W.A. Soffa, Phys. Stat. Sol. (a) [**131**]{}, 707 (1992); Scr. Met. Mater. [**30**]{}, 683 (1994).
A. Aharoni, [*Introduction to the theory of ferromagnetism*]{} (Clarendon, Oxford, 1996).
H. Kronmüller, J. Magn. Magn. Mater [**7**]{}, 341 (1978).
M. Pratzer [*et al.*]{}, Phys. Rev. Lett. [**87**]{}, 127201 (2001).
|
Q:
Make flex items have equal width in a row
If you look at the example below, I want the headers (h4.child-title) to have the same length within the parent container.
But I'm not successful in achieving this.
Any help is appreciated.
.top-level {
display: flex;
flex-flow: row wrap;
}
.section {
display: flex;
flex-flow: row nowrap;
border: 1px solid;
margin-right: 12px;
margin-top: 12px;
}
.section-child {
display: flex;
flex-flow: column nowrap;
align-items: center;
flex: 1 1 0;
}
.child-title {
white-space: nowrap;
}
.vertical-separator {
width: 1px;
background-color: rgba(0, 0, 0, 0.3);
margin: 8px;
}
<div class="top-level">
<section class="section">
<div claas="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
<section class="section">
<div claas="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
<section class="section">
<div claas="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
</div>
A:
Flexbox method
In order to make the text items (.section-child) equal width, you need to use flex: 1 1 0, which you have done. This is the same as saying flex: 1.
However, this by itself doesn't achieve the goal for two reasons:
The parent of .section-child, a flex container, but also a flex item in a larger container, is limited to the width of its content, by default. So it won't expand and the text can overflow the container. You need to apply flex: 1 to .section, as well.
A flex item cannot be smaller than the size of its content, by default. The initial setting is min-width: auto. So flex: 1 cannot work to equally distribute container space, because a flex item cannot shrink past the longest item. You need to override this behavior with min-width: 0.
.top-level {
display: flex;
flex-flow: row wrap;
}
.section {
display: flex;
flex-flow: row nowrap;
border: 1px solid;
margin-right: 12px;
margin-top: 12px;
flex: 1;
min-width: 0;
}
.section-child {
display: flex;
flex-flow: column nowrap;
align-items: center;
flex: 1;
min-width: 0;
}
.child-title {
white-space: nowrap;
}
.vertical-separator {
width: 1px;
background-color: rgba(0, 0, 0, 0.3);
margin: 8px;
}
<div class="top-level">
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
</div>
Now all flex items are equal width. However, because you have the text set to nowrap, it can overflow its boundaries. If you remove nowrap, everything fits nicely.
.top-level {
display: flex;
flex-flow: row wrap;
}
.section {
display: flex;
flex-flow: row nowrap;
border: 1px solid;
margin-right: 12px;
margin-top: 12px;
flex: 1;
min-width: 0;
}
.section-child {
display: flex;
flex-flow: column nowrap;
align-items: center;
flex: 1;
min-width: 0;
}
.child-title {
/* white-space: nowrap; */
}
.vertical-separator {
width: 1px;
background-color: rgba(0, 0, 0, 0.3);
margin: 8px;
}
<div class="top-level">
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
</div>
More information:
Make flex-grow expand items based on their original size
Why doesn't flex item shrink past content size?
CSS Grid method
If your actual goal is to make all flex items in the row equal to the width of the longest item, that's something flexbox cannot do.
Flex can do equal width and equal height flex items, because it provides flex: 1 on the main axis.
Flex can also do equal width and equal height columns / rows, because it provides align-items: stretch on the cross axis.
But there is nothing in the flexbox spec about equal size flex items based on the size of a particular sibling. However, flexbox's sister technology, CSS Grid, can do it.
By using Grid's fr unit, the width of columns in a grid can be set to the width of the longest column.
.top-level {
display: flex;
flex-flow: row wrap;
}
.section {
display: grid;
grid-template-columns: 1fr 1px 1fr 1px 1fr;
margin-right: 12px;
margin-top: 12px;
}
.section-child {
display: flex;
justify-content: center;
align-items: center;
min-width: 0;
background-color: green;
}
.child-title {
/* white-space: nowrap; */
}
.vertical-separator {
background-color: rgba(0, 0, 0, 0.3);
margin: 8px;
}
<div class="top-level">
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title text text text text text text text text text text</h4>
<!--A lot more content here-->
</div>
</section>
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title text text text text text text</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="vertical-separator"></div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
</div>
Here's how it works:
Equal height rows in CSS Grid Layout
A:
Flexbox is not the perfect choice for table like layout, but you can get close though:
add flex: 1 1 100% to sectionchild, and it will shrink (or grow) equally, based on being set to be 100%
add overflow: hidden, or min-width, to tell the section-child they are allowed to be smaller than their content
add flex-basis: 100%, or flex-grow: 1, to section and it will take full with of its parent, the top-level
As vertical-separator, I instead used a pseudo ::after on every section-child but the first, and since it use absolute position, position: relative is needed on the section-child.
.top-level {
display: flex;
flex-flow: row wrap;
}
.section {
flex-basis: 100%; /* added */
display: flex;
flex-flow: row nowrap;
border: 1px solid;
margin-right: 12px;
margin-top: 12px;
}
.section-child {
position: relative; /* added */
display: flex;
flex-flow: column nowrap;
align-items: center;
flex: 1 1 100%; /* added */
overflow: hidden; /* added */
}
.child-title {
white-space: nowrap;
}
.section-child + .section-child::after {
content: '';
position: absolute;
left: 0;
top: 10%;
height: 80%;
border-left: 1px solid rgba(0,0,0,0.3);
}
<div class="top-level">
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
<section class="section">
<div class="section-child">
<h4 class="child-title">Title</h4>
<!--A lot more content here-->
</div>
<div class="section-child">
<h4 class="child-title">Longer title</h4>
<!--A lot more content here-->
</div>
<div class="section-child">
<h4 class="child-title">Much much longer title</h4>
<!--A lot more content here-->
</div>
</section>
</div>
|
Archive for civil rights
WASHINGTON — The Trump administration is preparing to redirect resources of the Justice Department’s civil rights division toward investigating and suing universities over affirmative action admissions policies deemed to discriminate against white applicants, according to a document obtained by The New York Times. Click here to read more
Please, Don’t Call Me “African-American!” Join our “American Identity Project” By Ward Connerly I was born in Leesville, LA in 1939. At birth, I was “colored.” From that moment until now, the color of my skin (race) has been the factor that my society has tried to use to define…
AN AGENDA FOR AMERICA’S RENEWAL By Ward Connerly Traditionally, political campaigns are waged between the 40-yard lines of the political football field. As a candidate for president in 2016, Donald J. Trump dramatically changed this tradition and expanded the field of play from the 40 yard lines to goal post…
Ward Connerly comment on the Fisher v University of Texas decision: The SCOTUS has, once again, betrayed the United States Constitution and a central tenet of American society and law that the color of a person’s skin should not be a factor in the public domain. As President John F….
In a 4-3 decision, the Supreme Court ruled that the University of Texas’s use of race in its admissions process does not violate the Constitution. Justice Kennedy wrote the Court’s opinion. The decision is what you’d expect from an opinion upholding the university’s race-based admissions plan — deferential and uncritical….
Heritage legal fellows Elizabeth Slattery and Hans von Spakovsky say this decision “is a loss for advocates of a truly colorblind society, a betrayal of our core beliefs as Americans” not only is it a betrayal of our beliefs but they also argue that this decision is “fundamentally unfair to… |
Rudgwick
Rudgwick is a village and civil parish in the Horsham District of West Sussex, England. The village is west from Horsham on the north side of the A281 road. The parish's northern boundary forms part of the county boundary between Surrey and West Sussex.
The parish covers . The 2001 Census recorded 2,791 people living in 1,013 households, of whom 1,425 were economically active.. The 2011 Census recorded a population, including Tisman's Common of 2,722.
History
Historically Ridgewick was an alternative form of the toponym. Riccherwyk may be another, seen in 1377.
The Church of England parish church of the Holy Trinity has a 12th-century Norman font of Sussex Marble. The belltower is early 13th century. The church was largely rebuilt in the 14th century, when the north aisle was added and probably the present chancel was built.
The parish has two 17th century farmhouses. Garlands, south of the village, is early 17th century and Redhouse Farm north of the village is late 17th century. Naldrett House, south of the village, is an 18th-century Georgian farmhouse of three bays and two storeys, built of brick with stone quoins.
Rudgwick had a Dissenters' chapel by 1848.
Rudgwick railway station on the Cranleigh Line was opened in 1865 and closed in 1965, as part of the Beeching cuts.
Education
Pennthorpe School is on in Church Street.
Rudgwick Primary School is located in the community.
The Rikkyo School in England, a Japanese boarding school, is also located in Rudgwick.
Notable people
Bertram Prance (1889-1958), artist and illustrator, lived in the village.
References
Sources
External links
Category:Horsham District
Category:Villages in West Sussex |
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New Candle Line
Introducing our new candle line...Circle 21 Candles!!
Scent is said to be the strongest of all five senses with the power to invoke past memories. Our newest line of candles made by Circle 21 Candles bring these memories to life with names like Tuscan Sun, Garden Party, Moroccan Tile, and Plantation Cotton.
Made of pure soy wax with all cotton wicks, Circle 21 Candles, produces the cleanest, longest lasting candles possible. Hand poured into re-purposed wine bottles with stamped cork tops, these candles are clean and uncomplicated. Leaving us just the pure, fresh scent to enjoy!
Come check out our new line of Circle 21 Candles available at all three stores now! |
Redstone Block PC: Blood + Sweat + Tears
Redstone is a key component for making virtual computers in Minecraft. It’s also Spencer Kern’s key inspiration for his meticulously crafted mini ITX PC.
Spencer built the 8.5″x 8.5″x 8.5″ case almost entirely out of acrylic. The outer shell with the design is separate from the frame.
The shell and lights alone would be cool enough, but Spencer went all out. He customized the power switch and had the fan cables and PSU cables custom made to fit the red and gray color scheme. He also applied matching decals and graphics to his Xbox One controller, chatpad and mouse. Finally, he designed and ordered custom printed keycaps for his mechanical keyboard. |
Illinois State Library
Electronic Documents of Illinois
Electronic Documents of Illinois
Document Identification
Users should pay particular attention to version identification or dates of publication of documents retrieved. Earlier, possibly superseded, versions of documents are also stored here.
Title
Section 8 Woods Nature Preserve Boardwalk Repair Project Dedicated
Description
Officials from the Illinois Department of Natural Resources (IDNR), the Cache River Wetlands Joint Venture Partnership, and volunteers from the Friends of the Cache River Watershed today joined Illinois Lt. Gov. Sheila Simon and students from Creal Springs Schools Wetland Warriors program in celebrating the reopening of the Section 8 Woods Nature Preserve Boardwalk at the Cache River State Natural Area in southern Illinois. |
Sports
Tying for third at the USA Ultimate Division III Championship last weekend in Appleton, WI, Eclipse solidified their place among the top women’s D-III teams in the country. As Robyn Fennig writes in her review of day one of the tournament, “Eclipse might be the most fundamentally sound team from top to bottom from what I saw today” (skydmagazine.com).
Carleton College swimmer Erik Klontz ‘13 was voted to the Capital One Academic All-District At-Large Team as selected by the College Sports Information Directors of America (CoSIDA). The award honors the nation’s top student-athletes for their combined performance in competition and in the classroom.
CUT, Carleton’s top Ultimate Frisbee team, will be travelling to Boulder, Colorado this weekend to compete in the Division I USA Ultimate National Championships. The third seed overall, CUT looks to defend its 2011 Championship title.
Kathryn Schmidt ’12 ended her career as a Carleton Knight with a fourth consecutive trip to the NCAA Individual Championships. A three-time All-American, Schmidt was one of just 32 players in the nation selected to participate in the tournament. |
Characterization of a human ovarian carcinoma cell line with estrogen and progesterone receptors.
The potential significant therapeutic and prognostic roles for the sex steroid receptors in ovarian cancer are recognized. The authors present in detail the biochemical, morphologic, cytogenetic, and growth characteristics of an ovarian carcinoma cell line, BG-1, which has functional estrogen and progesterone receptors (23 and 300 fmol/mg protein, respectively) in clinically significant levels. In particular, BG-1 has a DNA index of 1.14, a stable karyotype with specific translocations, and produces and secretes CA 125 into the media. |
Whale watchers aboard Captain Dave’s Dolphin and Whale Watching Safari had an unexpected and heartbreaking encounter with a pod of bottlenose dolphins yesterday. A deceased dolphin calf was being carried by an adult bottlenose dolphin on its back.
This video sends a powerful message and it is a window into a dolphins heart. This animal is laboring under the strain of carrying the deceased calf on its back and is probably keeping it near the surface so the departed dolphin can breathe. Dolphins do not normally swim with their dorsal fins sticking out of the water continuously like this bottlenose did. This poor grieving mother dolphin takes us, without words, to a place where as one of our passengers said in the video “humans and dolphins are not so different.”
The pair were surrounded by other dolphins, almost as if they were being protected, during this profoundly sad time. The dolphin was seen an hour later by another boat still carrying the calf. |
SMRT compounds abrogate cellular phenotypes of ataxia telangiectasia in neural derivatives of patient-specific hiPSCs.
Ataxia telangiectasia is a devastating neurodegenerative disease caused primarily by loss of function mutations in ATM, a hierarchical DNA repair gene and tumour suppressor. So far, murine models of ataxia telangiectasia have failed to accurately recapitulate many aspects of the disease, most notably, the progressive cerebellar ataxia. Here we present a model of human ataxia telangiectasia using induced pluripotent stem cells, and show that small molecule read-through compounds, designed to induce read-through of mRNA around premature termination codons, restore ATM activity and improve the response to DNA damage. This platform allows for efficient screening of novel compounds, identification of target and off-target effects, and preclinical testing on relevant cell types for the pathogenic dissection and treatment of ataxia telangiectasia. |
#pragma once
#include "Inline/BasicTypes.h"
#include "Inline/DenseStaticIntSet.h"
#include <string>
namespace NFA
{
// A set of characters.
typedef DenseStaticIntSet<U8,256> CharSet;
// An index of a DFA state. A negative index indicates an "accepting" or terminal state.
typedef I16 StateIndex;
enum
{
edgeDoesntConsumeInputFlag = (StateIndex)0x4000, // A flag that's set on terminal DFA state transitions that don't consume any input
unmatchedCharacterTerminal = (StateIndex)0x8000, // An implicit terminal state that indicates the DFA didn't recognize the input
maximumTerminalStateIndex = (StateIndex)0xbfff, // Should be the largest negative number that doesn't have edgeDoesntConsumeInputFlag set.
};
// Creates an abstract object that holds the state of an under-construction BFA.
struct Builder;
Builder* createBuilder();
// Functions to add states and edges to the under-construction DFA.
StateIndex addState(Builder* builder);
void addEdge(Builder* builder,StateIndex initialState,const CharSet& predicate,StateIndex nextState);
void addEpsilonEdge(Builder* builder,StateIndex initialState,StateIndex nextState);
StateIndex getNonTerminalEdge(Builder* builder,StateIndex initialState,char c);
// Dumps the NFA's states and edges to the GraphViz .dot format.
std::string dumpNFAGraphViz(const Builder* builder);
// Encapsulates a NFA that has been translated into a DFA that can be efficiently executed.
struct Machine
{
Machine(): stateAndOffsetToNextStateMap(nullptr), numClasses(0), numStates(0) {}
~Machine();
Machine(Machine&& inMachine) { moveFrom(std::move(inMachine)); }
void operator=(Machine&& inMachine) { moveFrom(std::move(inMachine)); }
// Constructs a DFA from the abstract builder object (which is destroyed).
Machine(Builder* inBuilder);
// Feeds characters into the DFA until it reaches a terminal state.
// Upon reaching a terminal state, the state is returned, and the nextChar pointer
// is updated to point to the first character not consumed by the DFA.
inline StateIndex feed(const char*& nextChar) const
{
Iptr state = 0;
do
{
state = stateAndOffsetToNextStateMap[state + charToOffsetMap[(U8)nextChar[0]]];
if(state < 0) { nextChar += 1; break; }
state = stateAndOffsetToNextStateMap[state + charToOffsetMap[(U8)nextChar[1]]];
if(state < 0) { nextChar += 2; break; }
state = stateAndOffsetToNextStateMap[state + charToOffsetMap[(U8)nextChar[2]]];
if(state < 0) { nextChar += 3; break; }
state = stateAndOffsetToNextStateMap[state + charToOffsetMap[(U8)nextChar[3]]];
nextChar += 4;
}
while(state >= 0);
if(state & edgeDoesntConsumeInputFlag)
{
--nextChar;
state &= ~edgeDoesntConsumeInputFlag;
}
return (StateIndex)state;
}
// Dumps the DFA's states and edges to the GraphViz .dot format.
std::string dumpDFAGraphViz() const;
private:
typedef I16 InternalStateIndex;
enum { internalMaxStates = INT16_MAX };
U32 charToOffsetMap[256];
InternalStateIndex* stateAndOffsetToNextStateMap;
Uptr numClasses;
Uptr numStates;
void moveFrom(Machine&& inMachine);
};
} |
OTTAWA – Measuring the effects of money on wellbeing, a report released Friday comparing employee life-quality to that of the world’s top executives says that the average CEO is now 270 times happier than the average worker.
According to the Blithe Institute, a think-tank that tracks economic trends, the so-called “happiness gap” has increased by 930% since 1978, adding a solid foundation to the many anecdotal accounts that the world’s wealthiest people are also by far the world’s happiest.
“Now we know exactly how much happier the notoriously jovial world’s business elites,” said lead author of the report Samantha Gregory of the world’s CEOs, who spend much of their lives in opulent country clubs, going on long vacations with their gorgeous spouses to exciting and exotic locations, or merrily lounge about in their world-class mansions. “The average worker who is barely able to make ends meet is typically not very happy, whereas the luxurious existence the average executive can afford to purchase puts them several orders of magnitude happier than the vast majority of their own employees.”
“This proves our hypothesis that there is a direct correlation between money and happiness.”
The report surveyed a representative sample size of middle class workers, who tended to value small luxuries, or merely more time with their families, or the ability to relax after a hard day of work. The authors then compared their relative happiness to their executive sample, who tended to generate immense pleasure from valuing yachts, fine wine vintages, private jets, rare art and large structures with their names on them, all of which they could easily afford, therefore making them extraordinarily happy at all times, without exception.
The same study concluded that the bulk of the happiness gains seen over the last 20 years have gone to a handful of ecstatic billionaires, who currently experience the same amount of happiness than the combined bottom 3.5 billion people.
Image via Deposit Photos |
Hybrid Fiber Coax (HFC) cable networks were originally built to deliver broadcast-quality TV signals to homes. The wide availability of such systems and the extremely wide bandwidth of these systems led to the extension of their functionality to include delivery of high-speed broadband data signals to end-users. Data over Cable System Interface Specifications (DOCSIS), a protocol elaborated under the leadership of Cable Television Laboratories, Inc., has been established as the major industry standard for two-way communications over HFC cable plants.
The basic elements of a DOCSIS-compliant cable network are the cable modem (CM), located on the subscriber's site, and the cable modem termination system (CMTS) and head end located in facilities operated by the cable service provider. The medium between the CMTS and the different CMs is a two-way shared medium, in which the downstream channels carry signals from the head-end to users and upstream channels carry signals from users to head-end. A CM is normally tuned to one upstream channel and the associated downstream channel. The upstream channel is an inherently shared medium in which slots are reserved using a contention system while the downstream is a broadcast dedicated link from the CMTS to the CM.
In recent years, packet-switched networks, such as the Internet, wireless communication, ADSL and CATV, have become more widespread. Packet-switched networks, such as networks based on the TCP/IP protocol suite, can distribute a rich array of digital content to a variety of client applications. It is often advantageous when distributing digital content across a packet-switched network to provide a distributed system that includes a plurality of servers dispersed throughout the distribution network, wherein the content is mirrored on the distributed servers. A more recent alternative to mirroring is content distribution networks (CDNs) that dynamically redirect content requests to an edge server situated closer to the client issuing the request.
As IP or packet-based solutions for providing content increases, the infrastructure for distributing content and services will be changing. For example, the infrastructure may need to evolve to support additional devices or different types of devices. Even for supporting set-top boxes, a different infrastructure may be used than that currently implemented.
Today, most content is maintained at a centralized backoffice server, i.e., at the corporate level rather than in the network. For example, in the cable industry there are many different systems and/or service areas that are supported. The centralized location provides broad access for all subscribers. Thus, the central server services several content delivery networks (CDNs).
The CDN serve as relay servers located in respective regions, wherein the edge servers store a content that includes favorites of users. Thereby, by accessing the edge servers without directly accessing the archive server, the users may be able to download favorite content in a relatively short time. Although the edge servers store relatively popular content, the edge servers may not match actual users' preferences, in which case the users may have to directly access the archive server. Repeated occurrence of such a situation would increase the load on the archive server, make it difficult to maintain a given service quality, and lose opportunities to provide services for customers. |
Jakkrit Panichpatikum
Jakkrit Panichpatikum (; ; January 31, 1973 – October 19, 2013) was a Thai sport shooter who competed in the men's 10 metre air pistol, men's 50m pistol, and men's 25m rapid fire pistol.
At the 2012 Summer Olympics, he finished 37th in the qualifying round for the 10 metre air pistol event. He finished in 14th in the qualifying round for the 50 metre pistol competition and 15th in the qualifying round for the men's 25 metre rapid fire pistol.
Assassination
He was shot to death on October 19, 2013, at age of 40 after being attacked as he sat in his car, police said. On television the following month, his mother-in-law confessed responsibility for his assassination, which she said she had arranged in order to free her daughter, Dr. Nitiwadee Pucharoenyos, from spousal abuse which he had allegedly been inflicting for several years.
Royal decoration
2005 - Commander (Third Class) of The Most Admirable Order of the Direkgunabhorn
References
Category:1973 births
Category:2013 deaths
Category:Thai male sport shooters
Category:Olympic shooters of Thailand
Category:Shooters at the 1996 Summer Olympics
Category:Shooters at the 2004 Summer Olympics
Category:Shooters at the 2008 Summer Olympics
Category:Shooters at the 2012 Summer Olympics
Category:Asian Games medalists in shooting
Category:Deaths by firearm in Thailand
Category:Assassinated Thai people
Category:Thai male actors
Category:Shooters at the 1994 Asian Games
Category:Shooters at the 1998 Asian Games
Category:Shooters at the 2002 Asian Games
Category:Shooters at the 2006 Asian Games
Category:Murdered sportspeople
Category:Asian Games bronze medalists for Thailand
Category:Medalists at the 1994 Asian Games
Category:Medalists at the 2006 Asian Games
Category:Southeast Asian Games gold medalists for Thailand
Category:Southeast Asian Games silver medalists for Thailand
Category:Southeast Asian Games bronze medalists for Thailand
Category:Southeast Asian Games medalists in shooting
Category:Competitors at the 2007 Southeast Asian Games |
Education in Johannesburg
School system in Johannesburg
South Africa has 12.3-million learners, some 386 600 teachers and 26 292 schools, including 1 098 registered independent or private schools. Of all schools, roughly 6 000 are high schools (grade 7 to grade 12) and the rest primary (grade 0 to grade 6). In government-funded public schools, the average ratio of scholars (known as "learners" in terms of the country's outcomes-based education system) to teachers ("educators") is 32.6 to one, while private schools generally have one teacher for every 17.5 scholars. The national Department of Education is responsible for education across the country as a whole, while each of the nine provinces has its own education department. The central government provides a national framework for school policy, but administrative responsibility lies with the provinces.
The national Department of Education is also responsible for higher education. Private schools and higher education institutions have a fair amount of autonomy, but are expected to fall in line with certain government non-negotiables - no child may be excluded from a school on grounds of his or her race or religion, for example.
South Africa's National Qualifications Framework (NQF) recognises three broad bands of education:
General Education and Training,
Further Education and Training,
and Higher Education and Training.
School life spans 13 years or grades, from grade 0, otherwise known as grade R or "reception year", through to grade 12 or "matric" - the year of matriculation.
General Education and Training runs from grade 0 to grade 9. Under the South African Schools Act of 1996, education is compulsory for all South Africans from age 7 (grade 1) to age 15, or the completion of grade 9. General Education and Training also includes Adult Basic Education and Training. Further Education and Training takes place from grades 10 to 12, and also includes career-oriented education and training offered in other Further Education and Training institutions - technical colleges, community colleges and private colleges. Diplomas and certificates are qualifications recognised at this level.
The South African Qualifications Framework (SAQF) was established in 1995 with the enactment of the South African Qualifications Authority (SAQA) Act. The framework attempts to rectify the past fragmented and segregated education and training system by adopting a single and integrated qualification system. The general concept of building a coherent and integrated system with more equitable access and improved levels of outcomes is seen as part of the process of reconciliation and rebuilding after the apartheid era.
Compared with most other countries, education in South Africa gets a really big slice of the pie - usually around 20% of total government expenditure. In the 2006 Budget education received R92.1-billion, amounting to 17.8% of total spending. However, there is still much ground to be made up in repairing the damage of 40 years of apartheid education. Under that system, White South African children received high quality schooling virtually for free, while their Black counterparts had only "Bantu education".
Although private colleges and universities are a more recent phenomenon, South Africa has had private primary and secondary schools for centuries. There are around 1 098 registered private schools, catering for some 340 000 students - 2.8% of the total schooling population. Many private schools chart a path of excellence, adopting cutting-edge trends, or offering solid, religious-based education since their origins as mission schools. There are many also outstanding state-aided schools, on a par with some of the top private institutions. Top-quality schools and universities are to be found in both the state and the private education sector.
Although subsidised by the state, the universities are autonomous, reporting to their own councils rather than government. Higher Education and Training, or tertiary education, includes education for undergraduate and postgraduate degrees, certificates and diplomas, up to the level of the doctoral degree. A matric endorsement is required for the study of university degrees, with a minimum of three subjects passed at the higher, rather than standard, grade, although some universities set additional academic requirements. A standard school-leaving South African senior certificate is sufficient for technical qualifications and diplomas. If you obtained a degree outside South Africa you can request recognition of the degree from the South African Qualifications Authority .
South Africa has a vibrant higher education sector, with more than a million students enrolled in the country's 24 state-funded tertiary institutions: 11 universities, five universities of technology, and six comprehensive institutions. Johannesburg has a well-developed higher education system of both private and public universities. Johannesburg is served by the public universities University of the Witwatersrand and the University of Johannesburg. University of Johannesburg was formed on 1 January 2005 when three separate universities and campuses — Rand Afrikaans University, Technikon Witwatersrand, and the Johannesburg campuses of Vista University — were merged. The new university offers education primarily in English and Afrikaans, although courses may be taken in any of South Africa's official languages. The University of the Witwatersrand is one of the leading universities in South Africa, and is famous as a centre of resistance to apartheid, earning it the nickname "Moscow on the Hill." Private universities include Monash University, which has one of its eight worldwide campuses in Johannesburg (six of the other campuses are in Australia, while the eighth is in Malaysia). Monash University was named after the prominent Australian general Sir John Monash and took its first students in 1961. Many of the buildings in Monash University are also named after prominent Australians in various fields. Midrand Graduate Institute is located in Midrand.
Below is a listing of universities in and around Johannesburg:
Stellenbosch University Situated in the wine-growing region of Stellenbosch, 60km from Cape Town, Stellenbosch University is one of South Africa's leading research institutions. The university's Centre for Invasion Biology, a Department of Science and Technology centre of excellence, studies the impact of invasive plant species on southern Africa's agriculture, biodiversity and ecotourism.
Tshwane University of Technology Incorporating the former Northern Gauteng, North West and Pretoria technikons, the university offers over 180 programmes, some of these unique to the institution, such as sport and exercise technology, equine studies, medical orthotics and prosthetics, and environmental management.
University of Johannesburg Incorporating the former Rand Afrikaans University, Technikon Witwatersrand and Vista University (Johannesburg campuses), the university offers both technical and academic programmes for around 45 000 students.
University of the Witwatersrand The University of the Witwatersrand, commonly known as Wits University, is one of the country's leading research institutions. A cosmopolitan campus close to the Johannesburg city centre, Wits University attracts a large number of students from across Africa. The university offers degrees in the faculties of engineering and the built environment, humanities, health sciences, science and commerce. Wits University also hosts the Department of Science and Technology's Centre of Excellence in Strong Materials, the Wits Institute for Social and Economic Research, and the Wits Business School.
Vaal University of Technology Vaal University has around 15 000 students spread across its main campus in Vanderbijlpark, 60km south-west of Johannesburg, and four satellite campuses, which include the Sebokengcampus of the former Vista University. |
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