text:
Maximilian von Spee
Page views of Maximilian von Spees by language »
Among MILITARY PERSONNELS »
In Denmark »
Among MILITARY PERSONNELS In Denmark »
Maximilian Johannes Maria Hubert Reichsgraf von Spee (22 June 1861 – 8 December 1914) was a naval officer of the German Kaiserliche Marine (Imperial Navy), who commanded the East Asia Squadron during World War I. Spee entered the navy in 1878 and served in a variety of roles and locations, including on a colonial gunboat in German West Africa in the 1880s, the East Africa Squadron in the late 1890s, and as commander of several warships in the main German fleet in the early 1900s. During his time in Germany in the late 1880s and early 1890s, he married his wife, Margareta, and had three children, his sons Heinrich and Otto and his daughter Huberta. Read more on Wikipedia
Since 2007, the English Wikipedia page of Maximilian von Spee has received more than 365,238 page views. His biography is available in 33 different languages on Wikipedia (up from 32 in 2019). Maximilian von Spee is the 376th most popular military personnel (down from 289th in 2019), the 106th most popular biography from Denmark (down from 77th in 2019) and the most popular Danish Military Personnel.
Maximilian von Spee was a German naval officer who commanded the German East Asia Squadron. He was most famous for his victory in the Battle of the Falkland Islands in 1914.
Page views of Maximilian von Spees by language
Among MILITARY PERSONNELS
Among military personnels, Maximilian von Spee ranks 376 out of 1,466. Before him are Ivan Paskevich, Horatius Cocles, Thrasybulus, Jean-Baptiste Jourdan, Jean-Baptiste Bessières, and Omar Pasha. After him are Yonatan Netanyahu, Erich Kempka, Osman Nuri Pasha, Alexander Samsonov, Hermann Balck, and Pierre-Charles Villeneuve.
Most Popular Military Personnels in Wikipedia
Ivan Paskevich
Horatius Cocles
600 BC - Present
Thrasybulus
440 BC - 389 BC
Jean-Baptiste Jourdan
Jean-Baptiste Bessières
Omar Pasha
Yonatan Netanyahu
Erich Kempka
Osman Nuri Pasha
Alexander Samsonov
Hermann Balck
Pierre-Charles Villeneuve
Among people born in 1861, Maximilian von Spee ranks 23. Before him are Aristide Maillol, H. H. Holmes, José Rizal, Prince Carl, Duke of Västergötland, Antoine Bourdelle, and Pehr Evind Svinhufvud. After him are Anton Arensky, Italo Svevo, William Bateson, Solomon R. Guggenheim, Edmund Allenby, 1st Viscount Allenby, and Armando Diaz. Among people deceased in 1914, Maximilian von Spee ranks 22. Before him are Georges Picquart, Ismail Gaspirali, Eduard Suess, Eugen Böhm von Bawerk, Alphonse Bertillon, and Joseph Swan. After him are Alexander Samsonov, Alfred Thayer Mahan, Charles Péguy, Alain-Fournier, Theodor Kittelsen, and Joseph Chamberlain.
Aristide Maillol
José Rizal
Prince Carl, Duke of Västergötland
Antoine Bourdelle
Pehr Evind Svinhufvud
Anton Arensky
William Bateson
Solomon R. Guggenheim
Edmund Allenby, 1st Viscount Allenby
Armando Diaz
Georges Picquart
Ismail Gaspirali
Eduard Suess
Eugen Böhm von Bawerk
Joseph Swan
Alain-Fournier
Theodor Kittelsen
Joseph Chamberlain
Among people born in Denmark, Maximilian von Spee ranks 106 out of 783. Before him are Niels Gade (1817), Prince Valdemar of Denmark (1858), Vilhelm Hammershøi (1864), Princess Ingeborg of Denmark (1878), Eric II of Denmark (1090), and Harald Bohr (1887). After him are Princess Thyra of Denmark (1853), Hastein (810), Frederik, Crown Prince of Denmark (1968), Erik Bruhn (1928), Ejnar Hertzsprung (1873), and Prince George of Denmark (1653).
Others born in Denmark
Niels Gade
Prince Valdemar of Denmark
Vilhelm Hammershøi
Princess Ingeborg of Denmark
Eric II of Denmark
Harald Bohr
Princess Thyra of Denmark
Frederik, Crown Prince of Denmark
Erik Bruhn
Ejnar Hertzsprung
Prince George of Denmark
Among MILITARY PERSONNELS In Denmark
Among military personnels born in Denmark, Maximilian von Spee ranks 1. After him are Adam Ludwig Lewenhaupt (1659) and Søren Kam (1921).
Danish born Military Personnels
Adam Ludwig Lewenhaupt


text:
Q: Add bootstrap-sass in fountainjs error using fountainjs to generate a new angular project, I have issue in adding bootstrap-sass library to my project.
here is the my generate-project flow: Fountain->angular1->bower->babel->sass
then, since I need to use bootstrap, I installed it using bower, and included it in my index.scss with @import "../bower_components/bootstrap-sass/assets/stylesheets/bootstrap";
It works fine when I run gulp serve but when I build it using gulp build, the following error occured:
Error in plugin 'gulp-cssnano' Message: "bower-components/bootstrap-sass/assets/stylesheets/_bootstrap.scss" is not int the SourceMap
So, what goes wrong here and how to fix that?

A: I'm not certain of the fix, but a workaround that might help you move along is to comment out or remove the sourcemaps usage in your gulp.conf.js.  This will allow your sass to compile, but it won't give you sourcemaps for your style code.
Below is the standard gulp.conf.js with the sourcemaps lines commented out.
const gulp = require('gulp');
const browserSync = require('browser-sync');
//const sourcemaps = require('gulp-sourcemaps');
const sass = require('gulp-sass');
const postcss = require('gulp-postcss');
const autoprefixer = require('autoprefixer');

const conf = require('../conf/gulp.conf');

gulp.task('styles', styles);

function styles() {
  return gulp.src(conf.path.src('index.scss'))
    //.pipe(sourcemaps.init())
    .pipe(sass({outputStyle: 'expanded'})).on('error', conf.errorHandler('Sass'))
    .pipe(postcss([autoprefixer()])).on('error', conf.errorHandler('Autoprefixer'))
    //.pipe(sourcemaps.write())
    .pipe(gulp.dest(conf.path.tmp()))
    .pipe(browserSync.stream());
}

A: On line 17 of /gulp_tasks/styles.js, replace this line:

.pipe(sourcemaps.write())

with:

.pipe(sourcemaps.write(undefined, { sourceRoot: null }))

The issue is caused by a bug in gulp-sourcemaps when including files from the node_modules or bower_components folder.

redpajama_set_name: RedPajamaStackExchange


text:
Human Person
The Catholic Problem of History
Many common historical claims leveled against the Church fall flat: they fail to recognize what the Church claims to be and what it claims to offer.
Perhaps you have found yourself in this sort of a situation: you are in a conversation that touches on Christianity, and at a certain point a historical Molotov cocktail is thrown into the middle of it, "Yes, but what about the Crusades (or the Inquisition, or the trial of Galileo, or the imperialistic colonial missionaries, or the Renaissance popes with their mistresses and poisons)?" There you stand, stuttering, partly because such questions often have no applicability to the current conversation, partly because you do not know very much about any of these things, and partly because you are sure that the person tossing the cocktail does not know much about them, either. There seems to be nothing that can be said or done: it is simply a conversation stopper, which might have been the point of flinging the cocktail in the first place.
Part of the difficulty with such situations is that many modern people have dim notions of these historical claims that have been passed on as part of the tradition of anti-Catholic propaganda that supposedly everyone knows. People have picked them up somewhere, and they think they are dealing in settled facts. When one takes the time to investigate these various failures of the Church, however, one finds that they are seldom what they have been reported to be. In many cases it turns out that they were not failures at all, or that they were failures in a way quite different from what has been reported, or that while failure was involved the degree of failure has been exaggerated greatly. The disparity between what "everyone knows" and what actually can be ascertained by historical study is often very striking – even astonishing – and steady historical research seems to have little influence on dispelling these errors in the popular mind.
There is something anomalous about this. No one, least of all Christians, should be surprised at finding sins, faults, and errors of judgment by Christians in the historical record; indeed, even the best members of the Church are sinful humans of limited talent and wisdom. There has never been a lack of nominal believers – and even outright hypocrites – within the Church to further compound the problem. Beyond that, there are always differing judgments about matters of history, occasional mistakes, or even purposeful misrepresentations in historical treatments of any kind. History is not an exact science, as the human past is a complex matter and historical data are often scarce or incomplete. In the case of the Catholic Church, however, the magnitude of the errors concerning its history, the vehemence with which the errors are held, and the great difficulty encountered by serious historians in correcting the historical record are without parallel, which all seems to demand some kind of explanation. It can be troubling for the believer to be confronted constantly with the supposed dark past of the Church. Christians who do not have the time to sort out the historical record can come unconsciously to accept the errors as simply true.
This brief article is an attempt to explain why this anomalous situation exists and to give some principles of historical analysis that can help the honest inquirer gain a more accurate picture of the Christian past.
The historical problem might be put simply this way: the Christian Church, despite the flaws of its members, is on any fair hearing among the most impressive institutions in the history of the world. It has been at the heart of innumerable civilizational achievements and has been instrumental in the development of just forms of government, notably democracy. In addition to being a consistent patron of the arts, it has preserved and creatively developed human education and has provided a fertile soil for the development of science. The Christian Church has been decisive in the repudiation of slavery and a great promoter of human rights, and it has been by far the largest charitable organization that the world has ever known. Yet, despite these and other remarkable achievements, it is often held to be the source of all manner of evils, and to be among the worst, or even the very worst, of human institutions that ever came to exist. Its contributions tend to be denied or minimized, and its sins and errors exaggerated or presented in an egregiously one-sided way. Why?
As it happens, there are reasons for this inaccurate and often unfair historical treatment, reasons that go to the heart of the drama of the human race and the place of the Church in that drama. These reasons do not excuse the historical errors, but they help to make those errors explicable and can point to ways of viewing the historical record with greater accuracy.
Reason #1: The Church is unique among human institutions in its essence.
We never want to stray far from Aristotle's fundamental maxim about the proper way to investigate any given aspect of reality: one studies a thing according to the nature of the thing being studied.
One of the roots of the historical problem we are addressing is to be found in a serious misunderstanding right at the start. The Church needs to be studied with a different lens than other human institutions insofar as it is unlike any other human institution, not just in its details, but in its essence. To say this is not to indulge in a kind of Christian jingoism or to insist that Christianity is somehow special because we happen to be part of it. The uniqueness of the Church comes from a fact of its nature. Because Christ is God himself come among the human race, and because the Church is the Body of Christ – the mysterious but real incarnation of Christ's Holy Spirit on earth – the Church has a quality that no other organization or institution possesses: it is by its nature both human and divine.
As to its humanity, the Church shares with other human institutions all the various aspects of institutional life. It has a government, a set of ideals, a way of gathering, a multitude of cultural expressions, and an economic and a social existence, the same as any other large assembly of humans organized for a particular purpose. It is likewise comprised of people who are of the same flawed and sinful stuff as those around them. In all these ways and in many others, the Church is similar to other human organizations and can be viewed and examined as one institution among many of a similar kind.
At the same time, and more essentially, the Church is a divine institution. Christians point to this when they recite creeds that call the Church "holy." The Church is holy not because of the impressive quality of its human members, but because it is the dwelling place and the visible clothing of the invisible Holy Spirit. God himself resides in the Church and reveals Himself through it in an entirely unique way. This presents certain difficulties in understanding its history.
It is instructive that a similar difficulty presents itself in studying the life of Jesus of Nazareth. Jesus was human, with all the characteristics of other humans. It is therefore possible to view him simply in his human qualities and relations. He lived and died in a particular place; he came from a specific family; he had the same outward possibilities and limitations as other members of the human species. Many who study his life put him alongside other influential people who seem to be in the same category: Moses and Mohammed; Lao Tzu and Confucius; Buddha and Zoroaster. Given the human nature of Jesus, this is understandable – but it is a serious error. Jesus was not only a human. He was also the divine Son of God. In this he is radically unlike all those others: he is in a category by himself. In coming to terms with his character and his history, his divinity will need to be taken into account.
The Church is holy not because of the impressive quality of its human members, but because it is the dwelling place and the visible clothing of the invisible Holy Spirit.
One sees the quagmire that engulfs those who view Jesus only from his human side. They cannot deny that Jesus has been hugely influential. They see that during the very brief time of his public activity he divided everyone who met him into two distinct camps: those who thought him so impressive that they worshipped him as God, and those who found him so evil that they thought he needed to be killed. This dramatic response demands an explanation. Why did Jesus so rivet all who heard him and provoke them to such opposite reactions? Why has he continued to be so potent a personality that he has become the most loved and the most resented human who has ever lived? There is no special difficulty in answering that question once it is understood that Jesus is both human and divine, God himself come among our race to confront us with our rebellion and to call us back to our true allegiance. Both the worship of him and the resistance he provokes have a clear explanation. When his divine nature is left out of the picture, however, it becomes necessary to look for other reasons for the intense and radically polarized responses to him. As a result, various false pictures of Jesus have been constructed to provide a plausible human explanation: we are given Jesus the political revolutionary, or Jesus the romantic breaker of rules, or Jesus the militant pacifist, or Jesus the crazed apocalyptic prophet. We are even given what is certainly the least convincing historical picture of Jesus among them all: Jesus the "nice guy," the sadly misunderstood moral teacher.
Something similar happens when those who deal with the Church's history fail to take into account its divine quality. Christians know that the intense response the Church has provoked through the ages has little to do with the impressive talent or the dark deeds of its human members, and everything to do with the presence of the Holy Spirit within it. When the Holy Spirit is taken out of the picture, however, merely human reasons need to be found for its powerful effect on human affairs. Through such a merely human lens, the Church's ability to gain ardent love and loyalty becomes a sign of its seductive and manipulative character. The Church's remarkable vitality and continuing influence is the result of secretive and highly organized conspiracies. The implacable resistance it has often inspired can only be due to the horrible crimes it has perpetrated. Otherwise, how can one explain the fact that the Church has been the most consistently beloved and hated institution in the history of the world?
Reason # 2: The Church cannot be studied "objectively."
Since the Church is the staging ground for God's appeal to every member of the exiled human race, and since it is the privileged instrument through which he calls to his "straying sheep" to return to the Shepherd and Guardian of their souls (1 Peter 2:25), it is impossible for fallen humans to deal with the Church impartially. Maybe Martians, if they existed, could manage it. They might view the Church as something entirely apart from themselves. They could hear the appeal at its heart as not being addressed to them, and so could attempt an objective account of its life and its doings. No earthling, on the other hand – and here again the connection to the life of Christ arises – can stand aloof from the action of the Creator as he deals decisively with each of his fallen creatures. There are no "objective" human bystanders in the story of Jesus, no one who can view his life and hear his words from a disinterested vantage point. Everyone has a highly personal and deeply momentous stake in the truth or falsity of the Church's claims, whether those claims are received joyfully, denied categorically, or ignored with a posture of indifference. Even human law notes the difficulty in being objective concerning matters that touch us closely. It is hard to give a fair hearing to those we love or those we hate. It is hard to maintain an impartial view when we have a serious personal stake in the matter. Hence the category of "conflict of interest" by which judges and jurors will be recused from a case, or evidence will be received with a grain of salt when such obvious personal interests are in play. When it comes to reporting on Christ and his Church, everyone has a conflict of interest. No one is simply impartial.
This is not to suggest that there can be no reasonably accurate picture of the Church's history, or that recognized standards of good historical work should not be insisted upon: it is only to say that no one can pretend to be a disinterested party with no skin in the game. The modern discipline of history was developed largely during the eighteenth and especially the nineteenth centuries in post-Protestant and often post-revolutionary countries, where the mythic picture of progress was displacing an earlier overall Christian narrative of history. Most of the history of the West has been written by historians out of sympathy with Christianity, and often actively hostile to it for personal reasons of their own. Edward Gibbon, the eighteenth-century anti-Christian author of The Decline and Fall of the Roman Empire, was the father of this school of historical writing, and advanced the highly dubious claim that the Roman Empire fell because of the rise of Christianity. It is therefore not surprising that, coming from such sources, widely differing accounts of the Church and its history have arisen and are still tenaciously held.
In this regard, it is suggestive to note that when the Church has been most profoundly opposed and most deeply detested, it has not been for its obvious sins and failures – though these have been common enough and have provided reasonable grounds for critique. The fiercest opposition to the Church has come from the Church's stubborn adherence to the message of Christ. The Church gets along best with the wider world when it is least faithful to its Founder and Master. It suffers its worst attacks when it is most loyal to Christ's teaching. Even much of the justifiable anger against the Church for the sins of its adherents has a particular intensity due to what the Church positively stands for. The uncomfortable call of Christ to repentance, humility, and moral discipline that issues forth from the Church can be more easily disregarded if the misdeeds of some of its members are kept in focus.
Reason #3: The Church is not utopian in its claims or in its effects.
One occasionally hears a comment that goes something like this: "Christianity's day is past. It was tried, and it didn't work." If the matter is pursued further, one is then given a list of failures that prove the point. For over a thousand years in European lands, the Church was the dominant social institution in setting the ultimate goals and articulating the moral ideals of the society. What was the result? Did wars cease? Did greed and lust for power disappear? Was injustice eradicated, individually and socially? Were the most vulnerable members of society always well cared for? Were the Christians of those past times paragons of good behavior? At this point in the conversation, one of those "well-known" historical sins of Christianity will usually be trotted out to clinch the argument. With this, the matter is presented as clear and settled: "Christianity directed the whole of a civilization for many generations and it fell seriously short. We obviously need to come up with a different model to secure human happiness and to arrange for the perfecting of human society."
The careful historian will want to correct this picture in many of its details by noting that Christianity did in fact make a serious difference in all these areas: in lessening the ravages of war, in making inroads against slavery, injustice, and practices of rapacity, and in encouraging concern for the weak and the oppressed. Nevertheless, even given these reasonable adjustments, the picture in its broad outlines remains true: the so-called "Christian centuries" did not produce anything like a perfect society.
There is a fundamental first principle behind this kind of negative assessment, one that many moderns assume without reflection as a self-evident truth, but that Christians know to be profoundly false. That first principle is the denial of the reality of the Fall. Christians know that this world will never be a place of perfect justice, peace, and brotherly love as long as it is peopled by a race whose inner moral being is profoundly wounded and who are under the influence of dark and powerful spiritual beings. Those who deny the existence of the devil and who repudiate the idea of an inner moral wound see no reason that we cannot structure the world in such a way as to eradicate most of its evil. Instead, they come up with all kinds of schemes to accomplish their purpose. Hemmed in by their utopian assumptions, they naturally view Christianity as another such scheme for human perfection, and since it has not produced the utopian world for which they hope, they pronounce it a dismal failure.
This is radically to misunderstand the point of Christ's coming and the nature of the Christian Church. God did not visit the human race in Christ to fashion a perfect human society – not yet. The perfection for which we all long will certainly come, but not in this age of the world. Instead, God came among us to set up a kind of colony of heaven in the midst of a darkened world, a society of humans still fallen but on the road to their recovery that could act as a light and a leaven for those who were seeking their true home. The Church is a kind of resistance movement, set up under the reigning spiritual powers, an organized society "in the world but not of the world" through which Christ makes his appeal to generation after generation, setting them internally free from their oppression with the promise of full freedom when all things are restored. No one would fault the French Resistance during World War II for not being able to topple Nazi rule and transform France into a free society. That was not their task. They knew that an invasion was coming and that the dark powers that ruled their country would then be confronted in open battle. They dedicated themselves to making things as difficult for those powers as they could, ardently calling their fellow citizens back to their rightful allegiance in view of the coming invasion.
You will undergo many hardships, and the hardest of all will be to remember your true identity in the midst of a people who know nothing of our kingdom.
"Remembering Who We Are"
A fair assessment of Christianity will start by asking what the Church has always claimed to be doing, and then judge its success or failure on the basis of that purpose. It is a fair critique if an institution that understands itself as the "pillar and ground of truth" is found to be dealing in obvious falsehoods, or if a society that claims brotherly love as its special mark is found seriously lacking in care for others. It is not a fair critique of Christianity to claim that Christians have not perfected humanity or brought about a fully just society. They have never claimed to be able to do those things and they are sure that no one else will be able to accomplish them either, whatever their utopian dreams might be.
Due partly to the reasons given above, it is a simple fact that Christianity and the Church tend not to get a fair shake from the propaganda of this world. This is not something Christians should be particularly worried about. It was predicted by our Divine Master that his followers would regularly encounter hostility. Christians should do what they can to set the record straight, such that fair-minded people will have access to a more accurate account of history and honest inquirers will not held back by a false notion of the Church. Nevertheless, there are good reasons why their attempts seem to have little power to set the record straight.
Christ spoke of himself as a physician, and the Church has been understood as a kind of hospital for the morally and spiritually sick. The prevalence of sin in the Church is a sign not that the Church is a bad hospital or that Christ is an incompetent doctor, but only that we, the patients, are so often unwilling to follow the doctor's orders. The proof of the Church's healing power is seen in the lives of those who have listened to their divine physician, taken the medicine he has prescribed, and followed the protocols he has laid out: the saints. For those who seek God's word in the Church's Scriptures and who desire to be united with God in the Church's sacramental life, Christ in the Church has never failed – not even once. While the human side of the Church is riddled with the weaknesses of humanity, the divine presence within the Church is a sure and unfailing road to the marvelous destiny intended for us beyond the confines of this age of the world.
More in The Search for Truth
Sacramental or Scientistic?
While scientism denies the existence of anything beyond the material world, the Christian sacramental vision affirms the existence and intermeshing of realities visible and invisible.
All in The Search for Truth
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redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Simple Javascript to change a header image based on Domain name I'm struggling here.
I need to change an image in our header based on the domain name that the user entered.
We have 2 domains that point to the same location.  We have a header image map that is called.

This is the image I need to change.
Just want the header image to be "header_image1.jpg" when user us at www.domain1.com and "header_image2.jpg" to be displayed when at www.domain2.com
It should be simple.  But I'm just lost, any help would be greatly appreciated.
Thank you.

A: This should fix the problem

var url = window.location.host;
if (url == "stackoverflow.com"){
  // Make this visible
  document.getElementById("one").style.display = "block";
  // Make this invisible
  document.getElementById("two").style.display = "none";
} else {
  // Make this invisible
  document.getElementById("one").style.display = "none";
  // Make this visible
  document.getElementById("two").style.display = "block";
}


text:
package com.samsung.sec.dexter.daemon.p2;

import java.net.URI;

import org.eclipse.core.runtime.IProgressMonitor;
import org.eclipse.core.runtime.IStatus;
import org.eclipse.core.runtime.NullProgressMonitor;
import org.eclipse.core.runtime.OperationCanceledException;
import org.eclipse.core.runtime.SubMonitor;
import org.eclipse.equinox.p2.core.IProvisioningAgent;
import org.eclipse.equinox.p2.operations.ProvisioningJob;
import org.eclipse.equinox.p2.operations.ProvisioningSession;
import org.eclipse.equinox.p2.operations.UpdateOperation;
import org.eclipse.equinox.p2.repository.artifact.IArtifactRepositoryManager;
import org.eclipse.equinox.p2.repository.metadata.IMetadataRepositoryManager;

import com.samsung.sec.dexter.daemon.DexterDaemonActivator;
import com.samsung.sec.dexter.eclipse.ui.util.EclipseUtil;

/**
 * Source code from
 *

 *
Equinox Wiki pages, Adding self update

 *

 *
 * @author mahieddine.ichir@free.fr
 */
public class P2Util {

	/**
	 * Check for application updates.
	 * @param agent
	 * @param monitor
	 * @return
	 * @throws OperationCanceledException
	 */
	public static IStatus checkForUpdates(IProvisioningAgent agent, IProgressMonitor monitor) throws OperationCanceledException {
		ProvisioningSession session = new ProvisioningSession(agent);
		UpdateOperation operation = new UpdateOperation(session);

		SubMonitor sub = SubMonitor.convert(monitor, "Checking for application updates...", 200);
		IStatus status =  operation.resolveModal(sub.newChild(100));
		DexterDaemonActivator.LOG.info("Check Result; " + status.toString());
		return status;
	}

	public static IStatus checkForUpdates2(IProvisioningAgent agent) throws OperationCanceledException {
		ProvisioningSession session = new ProvisioningSession(agent);
		UpdateOperation operation = new UpdateOperation(session);
		IStatus status =  operation.resolveModal(new NullProgressMonitor());
		DexterDaemonActivator.LOG.info("Check Result; " + status.toString());
		return status;
	}

	/**
	 * Download and install application updates.
	 * @param agent
	 * @param monitor
	 * @return
	 * @throws OperationCanceledException
	 */
	public static IStatus installUpdates(IProvisioningAgent agent, IProgressMonitor monitor) throws OperationCanceledException {
		DexterDaemonActivator.LOG.error("run installUpdates....");

		ProvisioningSession session = new ProvisioningSession(agent);
		UpdateOperation operation = new UpdateOperation(session);
		SubMonitor sub = SubMonitor.convert(monitor, "Installing updates ...", 200);
		operation.resolveModal(sub.newChild(100));
		ProvisioningJob job = operation.getProvisioningJob(monitor);

		IStatus status =  job.runModal(sub.newChild(100));

		DexterDaemonActivator.LOG.info(">>>>>>>>>>>>>>>>>>>>>>UPdate Result; " + status.toString());

		return status;
	}

	public static IStatus installUpdates2(IProvisioningAgent agent) throws OperationCanceledException {
		DexterDaemonActivator.LOG.error("run installUpdates....");

		ProvisioningSession session = new ProvisioningSession(agent);
		UpdateOperation operation = new UpdateOperation(session);
		operation.resolveModal(new NullProgressMonitor());

		ProvisioningJob job = operation.getProvisioningJob(new NullProgressMonitor());
		IStatus status =  job.runModal(new NullProgressMonitor());

		DexterDaemonActivator.LOG.info(">>>>>>>>>>>>>>>>>>>>>>UPdate Result; " + status.toString());

		return status;
	}

	/**
	 * Add a repository to declared updates repositories.
	 * @param repo
	 * @return
	 */
	public static boolean addRepository(IProvisioningAgent agent, String repo) {
		IMetadataRepositoryManager metadataManager = (IMetadataRepositoryManager) agent.getService(IMetadataRepositoryManager.SERVICE_NAME);
		IArtifactRepositoryManager artifactManager = (IArtifactRepositoryManager) agent.getService(IArtifactRepositoryManager.SERVICE_NAME);
		if (metadataManager == null) {
			DexterDaemonActivator.LOG.error("metadataManager is null!!!");
			return false;
		}
		if (artifactManager == null) {
			DexterDaemonActivator.LOG.error("artifactManager is null!!!");
			return false;
		}

		try {
			URI uri = new URI(repo);
			metadataManager.addRepository(uri);
			artifactManager.addRepository(uri);

			DexterDaemonActivator.LOG.error("repository is added : " + uri.toString());
			return true;
		} catch (Exception e) {
			EclipseUtil.errorMessageBox("failed when add repository", e.getMessage() + " - " + repo);
			DexterDaemonActivator.LOG.error(e.getMessage(), e);
			return false;
		}
	}
}

redpajama_set_name: RedPajamaGithub


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All people with developmental disabilities enjoy full citizenship and inclusion in communities where they are valued and accepted.


text:
Върколакът (вълколак) е митологично същество, считано за създание на злото, обикновено дух на умрял човек. Той живее сред хора или в много гъсти иглолистни гори. Когато те захапе върколак, той те заразява, превръщайки те в такъв като него.

Върколаците могат да бъдат убити със сребърни прибори, куршуми и оръжия. Ако човек разяри лесник, той може да го превърне във върколак. Върколаците живеят в изоставени воденици, ханове, плевници и край кръстопътища, далеч от села и градове. Когато някой мине покрай обиталищата им, те го нападат, удушават, изпиват му кръвта или направо го изяждат. Върколаците могат да примамят и прелъстят жени, да встъпят в полово сношение с тях, в резултат на което се раждат деца, които нямат хрущял на носа, виждат злите духове и имат свръхестествени способности (виж сдухач). Сред българите и сърбите се вярвало, че върколаците предизвикват слънчеви и лунни затъмнения, отхапвайки част от небесното светило.

За него свидетелства кремонският епископ Лиудпранд през 949 г. посланик на немския император Отон I в Цариград:
"Той (Симеон) имал два[ма] сина; единият се наричал Баян, а другият, който и до ден-днешен още живее и здраво управлява българите, Петър. Баян обаче чак дотам бил изучил магията, че от човек ставал веднага на вълк и на какъвто друг звяр поискаш. ...бе силен в магия, вълшебство и тайно очарование" Византийски хронисти също го споменават и пишат, че той приемал формата на различни животни – вълк и орел.

Суеверието за върколаците същестува още и сред гърците под името βρυκόλακας (вриколакас) и сред румънците, при които думата звучи като pricolic (приколик).

Има вярвания, че върколаците също могат да се отслабят или убият чрез вълче биле (синя самакитка) или имел.

Вижте също
 Вълчи зъб (корниз)
 Славянски митични същества
 Славянска религия
 Ликантропия

Източници

 Попов P. За върколака в българските народни вярвания (исторически корени и място в народната култура) // Известия на Националния исторически музей. – 1985. – № 5. – С. 213 – 227.

Българска митология
Славянска митология

redpajama_set_name: RedPajamaWikipedia


text:
Q: Run jQuery slideDown on each hover Im a newbie at jQuery, and Im trying to make a slide-down menu list. I have the following script:
<script>
$(document).ready(function() {
$('.menu>li').hover(function(){
$('.menu>li>ul').slideDown("slow");
});
});
</script>

It does slide down the drop-down list the first time after page load, but after that it just appears without sliding down until the page is refreshed. How would i get it to keep sliding down on each hover? I tried this, but it didn't work either:
<script>
$(document).ready(function() {
$('.menu>li').hover(function(){
$('.menu>li>ul').stop(true,true).slideDown("slow");
});
});
</script>

Here is the website I'm working on, and you can hover over "practice areas" to see. It's on an IP 72.41.8.193
Thanks.

A: You are telling jquery to slide the element down but never telling it to slide up again.
The hover function will take a mouse in and mouse out parameter, try.
$(document).ready(function() {
    $('.menu>li').hover(function(){
        $('.menu>li>ul').stop(true,true).slideDown("slow");
    }, // <-- this comma is important.
//the anonymous function after this will run on mouse out
    function(){
        $('.menu>li>ul').stop(true,true).slideUp("slow");
    });
});

A: You may need to refactor some of your code a bit:
$('.menu > li').hover(function(){
    $(this).find('ul').stop().slideDown('slow');
}, function()
    $(this).find('ul').stop().slideUp('slow');
});

You will want to use this to find out WHICH menu item you're hovering over as well.  the .find('ul') will get the next closest ul from .menu > li.  Always remember to stop the animation so it doesn't bubble, then remember to use your second function of your hover to do something when you hover off.


A student at the Architectural Association from 1956-8, Edward Reynolds (1926-59) produced work of startling originality, including faceted and curvilinear geometries, zoomorphic forms and complex circulation systems. This talk sets Reynolds within the context of architectural discourse in 1950s London, exploring his connections with other students and his tutors Bill Howell, John Killick, James Gowan and others.
Geraint Franklin is an architectural historian specialising in British architecture since 1945. His book Howell Killick Partridge & Amis will be published by Historic England in June 2017.


text:
\section{ \bf Introduction}
Let $R$ be a unital ring.
An involution $\ast$ in $R$ is an anti-isomorphism of degree 2 in $R$,
that is to say,
$(a^{\ast})^{\ast}=a, (a+b)^{\ast}=a^{\ast}+b^{\ast}$ and $(ab)^{\ast}=b^{\ast}a^{\ast}$ for all $a, b\in R$.
An element $a\in R$ is Hermitian if and only if $a^{\ast}=a$.
And $a\in R$ is called an idempotent if $a^{2}=a$.
A Hermitian idempotent is said to be a projection.

Let $e,f\in R$ be two invertible Hermitian elements.
We say that $a\in R$ has a weighted Moore-Penrose inverse with weights $e, f$ if there exists an $x$ satisfying the following four equations (see for example, \cite{KPS2, Wei, Mosic}):
\begin{equation*}
\begin{split}
    (1)~axa=a,~(2)~xax=x,~(3e)~(eax)^{\ast}=ax,~(4f)~(fxa)^{\ast}=xa.
\end{split}
\end{equation*}
If such an $x$ exists,
then it is called a weighted Moore-Penrose inverse of $a$,
it is unique and denoted by $a^{\dagger}_{e, f}$.
If $e=f=1$,
then $a^{\dagger}_{e, f}=a^{\dagger}$ is the ordinary Moore-Penrose inverse of $a$.
The sets of all Moore-Penrose invertible elements and weighted Moore-Penrose invertible elements with weights $e, f$ are denoted by the symbols $R^{\dagger}$ and $R^{\dagger}_{e, f}$,
respectively.

If $x$ satisfies the equations $(1)$ and $(3e)$,
then $x$ is called a $\{1,3e\}$-inverse of $a$ and denoted by $a^{(1,3e)}$,
and a $\{1,4f\}$-inverse of $a$ can be similarly defined.
The symbols $a\{1,3e\}$ and $a\{1,4f\}$ denote the sets of all $\{1,3e\}$-inverses and $\{1,4f\}$-inverses of $a$,
respectively.
An element $a\in R$ is group invertible if there is an $x\in R$ satifying
$$(1)~axa=a,~~~(2)~xax=x,~~~(5)~ax=xa.$$
Such an $x$ is the group inverse of $a$,
and it is unique if it exists and denoted by $a^{\#}$.
The sets of all group invertible,
invertible,
$\{1,3e\}$-invertible and $\{1,4f\}$-invertible elements in $R$ are denoted by the symbols $R^{\#}$,
$R^{-1}$,
$R^{(1,3e)}$ and $R^{(1,4f)}$,
respectively.

Mosi\'{c} et al. \cite{Mosic2} give introduced the definitions of the $e$-core inverse and the $f$-dual core inverse,
which extended the concepts of the core inverse and the dual core inverse (see \cite{OM, DSR, XSZ}).
The element $a\in R$ has a weighted core inverse with weight $e$ (or $e$-core inverse),
if there exists $x\in R$ such that
$$axa = a, ~~~xR = aR, ~~~Rx = Ra^{\ast}e.$$
If such an $x$ exists,
then it is called a $e$-core inverse of $a$,
it is unique and denoted by $a^{e, \co}$.
The element $a\in R$ has a weighted dual core inverse with weight $f$ (or $f$-dual core inverse),
if there exists $x\in R$ such that
$$axa = a, ~~~fxR = a^{\ast}R, ~~~Rx = Ra.$$
If such an $x$ exists,
then it is called a $f$-core inverse of $a$,
it is unique and denoted by $a_{f, \co}$.
If $e=1$ (resp., $f=1$),
then $a^{e, \co}=a^{\co}$ (resp., $a_{f, \co}=a_{\co}$) is the ordinary core inverse (resp., dual core inverse) of $a$.
The sets of all $e$-core invertible elements and $f$-dual core invertible elements in $R$ are denoted by the symbols $R^{e, \co}$ and $R_{f, \co}$,
respectively.
In addition,
they defined that an element $a\in R$ is weighted-$\mathrm{EP}$ with respect to $(e, f)$ if $a\in R^{\#}\cap R^{\dagger}_{e, f}$ and $a^{\#}=a^{\dagger}_{e, f}$.
When $e=f=1$,
it is the ordinary EP element.

In this paper,
we investigate the characterizations of $e$-core inverse,
$f$-dual core inverse,
right $e$-core inverse and weighted-$\mathrm{EP}$ with respect to $(e, f)$ in a ring with involution.
These results will generalize and improve conclusions in \cite{Li}.

We will also use the following notations:
$aR=\{ax ~|~ x\in R\}$, $Ra=\{xa ~|~ x\in R\}$, $^{\circ}\!a=\{x\in R ~|~ xa=0\}$, $a^{\circ}=\{x\in R ~|~ ax=0\}$.

Some auxiliary lemmas and results are presented for the further reference.

\begin{lemma} \cite[Proposition $7$]{H}\label{group-inverse}
Let $a\in R$.
$a\in R^{\#}$ if and only if $a=a^{2}x=ya^{2}$ for some $x, y\in R$.
In this case, $a^{\#}=yax=y^{2}a=ax^{2}$.
\end{lemma}

\begin{lemma} \cite{BAB, DSC}\label{J.L}
Let $a, b\in R$.
$1+ab$ is invertible if and only if $1+ba$ is invertible.
\end{lemma}

\begin{lemma} \cite[Proposition $2.1$ and $2.2$]{HHZ}\label{13e-14f-inverse}
Let $a\in R$ and let $e\in R$ be an invertible Hermitian element.
We have the following results:\\
$(i)$ $a$ is $\{1,3e\}$-invertible if and only if $a\in Ra^{\ast}ea$.
Moreover,
if $a=xa^{\ast}ea$ for some $x\in R$,
then $x^{\ast}e\in a\{1, 3e\}$;\\
$(ii)$ $a$ is $\{1,4f\}$-invertible if and only if $a\in af^{\-1}a^{\ast}R$.
Moreover,
if $a=af^{\-1}a^{\ast}y$ for some $y\in R$,
then $f^{-1}y^{\ast}\in a\{1, 4f\}$.
\end{lemma}

\begin{lemma} \cite[Theorem $2.1$ and $2.2$]{Mosic2}\label{e-core-inverse}
Let $a\in R$ and let $e, f\in R$ be two invertible Hermitian elements.
Then \\
$(I)$ The following statements are equivalent:\\
\indent $(i)$ $a\in R^{e, \co}$;\\
\indent $(ii)$ there exists $x\in R$ such that
$$(1)~axa=a,~(2)~xax=x,~(3e)~(eax)^{\ast}=eax,~(6)~xa^2=a,~(7)~ax^2=x;$$
\indent $(iii)$ there exists $x\in R$ such that
$$(3e)~(eax)^{\ast}=eax,~(6)~xa^2=a,~(7)~ax^2=x;$$
\indent $(iv)$ $a\in R^{\#}\cap R^{(1, 3e)}$.\\
\indent In this case,
$$a^{e, \co}=x=a^{\#}aa^{(1, 3e)}.$$
$(II)$ The following statements are equivalent:\\
\indent $(i)$ $a\in R_{f, \co}$;\\
\indent $(ii)$ there exists $x\in R$ such that
$$(1)~axa=a,~(2)~xax=x,~(4f)~(fxa)^{\ast}=fxa,~(8)~a^2x=a,~(9)~x^2a=x;$$
\indent $(iii)$ there exists $x\in R$ such that
$$(4f)~(fxa)^{\ast}=fxa,~(8)~a^2x=a,~(9)~x^2a=x;$$
\indent $(iv)$ $a\in R^{\#}\cap R^{(1, 4f)}$.\\
\indent In this case,
$$a_{f, \co}=x=a^{(1, 4f)}aa^{\#}.$$
\end{lemma}

\begin{lemma} \cite{WL2}\label{r-core}
Let $a\in R$ and let $e\in R$ be an invertible Hermitian element,
$n\geqslant 2$.
Then the following statements are equivalent:\\
$(i)$ $a\in Ra^{\ast}ea\cap a^nR$;\\
$(ii)$ $a\in R(a^{\ast})^nea$.
\end{lemma}

\section{Main results}\label{a}
In this section,
we present some new equivalent conditions for the existences of core inverses.

\begin{theorem}\label{thm1}
Let $a\in R$ and let $e\in R$ be an invertible Hermitian element,
$n\geqslant 2$.
We have the following results:\\
$(i)$ $a\in R^{e, \co}$ if and only if $a\in R(a^{\ast})^{n}ea\cap Ra^{n}$.
If $a=s(a^{\ast})^{n}ea$ for some $s\in R$,
then $a^{e, \co}=a^{n-1}s^{\ast}e$;\\
$(ii)$ $a\in R_{f, \co}$ if and only if $a\in af^{-1}(a^{\ast})^{n}R\cap a^{n}R$.
If $a=af^{-1}(a^{\ast})^{n}t$ for some $t\in R$,
then $a_{f, \co}=f^{-1}t^{\ast}a^{n-1}$.
\end{theorem}

\begin{proof}
$(i)$. According to Lemma~\ref{group-inverse},
it is easy to deduce that $a\in R^{\#}$ if and only if $a\in a^{n}R\cap Ra^{n}$ for $n\geqslant 2$.
From Lemma~\ref{r-core} we know that $a\in R(a^{\ast})^nea$ if and only if $a\in Ra^{\ast}ea\cap a^nR$,
thus

\begin{equation*}
\begin{split}
    a\in R^{e, \co}
    &~\xLongleftrightarrow{Lemma~\ref{e-core-inverse}} a\in R^{(1,3e)}\cap R^{\#}\\
    &~\xLongleftrightarrow{Lemma~\ref{13e-14f-inverse}} a\in Ra^{\ast}ea\cap R^{\#}\\
    &~\Longleftrightarrow a\in Ra^{\ast}ea\cap a^{n}R\cap Ra^{n}\\
    &~\Longleftrightarrow a\in R(a^{\ast})^{n}ea\cap Ra^{n}.
\end{split}
\end{equation*}

Next,
we give the representation of $a^{e, \co}$.
Since $a\in R(a^{\ast})^{n}ea\cap Ra^{n}$,
there exists $s\in R$ such that $a=s(a^{\ast})^{n}ea$.
By Lemma~\ref{13e-14f-inverse},
we have
\begin{equation*}
\begin{split}
    (s(a^{\ast})^{n-1})^{\ast}e=a^{n-1}s^{\ast}e\in a\{1,3e\}.
\end{split}
\end{equation*}
Using Lemma~\ref{e-core-inverse},
we obtain
\begin{equation*}
\begin{split}
    a^{e, \co}=a^{\#}aa^{(1,3e)}=a^{\#}a(a^{n-1}s^{\ast}e)=a^{n-1}s^{\ast}e.
\end{split}
\end{equation*}

$(ii)$. Similarly as $(i)$.
\end{proof}

From the above proof,
it is easy to see that Theorem~\ref{thm1} is also true in a semigroup.
Next we characterize the existence of $e$-core inverse by idempotents and units.

\begin{theorem} \label{thm2}
Let $a\in R$ and let $e\in R$ be an invertible Hermitian element,
$n\geqslant 1$ is a positive integer.
The following statements are equivalent: \\
$(i)$ $a\in R^{e, \co}$; \\
$(ii)$ there exists a unique idempotent $p$ such that $(ep)^{\ast}=ep$, $pa=0$, $u=a^{n}+p\in R^{-1}$;\\
$(iii)$ there exists an element $s$ such that $(es)^{\ast}=es$, $sa=0$, $v=a^{n}+s\in R^{-1}$;\\
$(iv)$ there exists a unique idempotent $q$ such that $(eq)^{\ast}=eq$, $qa=0$, $w=a^{n}(1-q)+q\in R^{-1}$;\\
$(v)$ there exists an element $t$ such that $(et)^{\ast}=et$, $ta=0$, $z=a^{n}(1-t)+t\in R^{-1}$.\\
In this case,
when $n=1$,
$$a^{e, \co}=u^{-1}(1-p)=v^{-1}av^{-1}=(1-q)w^{-1}=z^{-1}a(1-t)z^{-1},$$
when $n\geqslant 2$,
$$a^{e, \co}=a^{n-1}u^{-1}=a^{n-1}v^{-1}=a^{n-1}(1-q)w^{-1}=a^{n-1}(1-t)z^{-1}.$$
\end{theorem}

\begin{proof}
$(i)\Rightarrow (ii).$ Set $p=1-aa^{e, \co}$,
we observe first that $p$ is an idempotent satisfying $(ep)^{\ast}=ep$ and $pa=0$.
Next we show that $u=a^{n}+p=a^{n}+1-aa^{e, \co}\in R^{-1}$.

When $n=1$,
it is easy to verify
\begin{equation*}
\begin{split}
    (a+1-aa^{e, \co})(a^{e, \co}+1-a^{e, \co}a)=1=(a^{e, \co}+1-a^{e, \co}a)(a+1-aa^{e, \co}),
\end{split}
\end{equation*}
thus $u=a+1-aa^{e, \co}\in R^{-1}$.

When $n\geqslant 2$,
we prove the invertibility of $u$ by induction on $n$.
Since $1+aa^{e, \co}(a-1)=a+1-aa^{e, \co}\in R^{-1}$,
from Lemma~\ref{J.L} we obtain that $a^{2}a^{e, \co}+1-aa^{e, \co}=1+(a-1)aa^{e, \co}\in R^{-1}$.
Therefore,
$a^{2}+1-aa^{e, \co}=(a^{2}a^{e, \co}+1-aa^{e, \co})(a+1-aa^{e, \co})$ is invertible.
Assume that $n>2$ and $a^{n-1}+1-aa^{e, \co}\in R^{-1}$,
then $a^{n}+1-aa^{e, \co}=(a^{2}a^{e, \co}+1-aa^{e, \co})(a^{n-1}+1-aa^{e, \co})$ is invertible.

Finally,
we prove the uniqueness of the idempotent $p$.
It is necessary to show that $^{\circ}\!(a^{n})=$ $^{\circ}\!(1-p)$.
If $xa^{n}=0$,
then
\begin{equation*}
\begin{split}
    0=xa^{n}=x(1-p)a^{n}=x(1-p)(a^{n}+p).
\end{split}
\end{equation*}
Since $a^{n}+p\in R^{-1}$,
we have $x(1-p)=0$.
Conversely,
if $y(1-p)=0$,
then $ya^{n}=y(1-p)a^{n}=0$.
Thus $^{\circ}\!(a^{n})=$ $^{\circ}\!(1-p)$.
Assume that $p, p_1$ are both idempotents which satisfy the statement $(ii)$,
then $^{\circ}\!(1-p)=$ $^{\circ}\!(a^{n})=$ $^{\circ}\!(1-p_1)$.
By $p\in$ $^{\circ}\!(1-p)=$ $^{\circ}\!(1-p_1)$,
we obtain $p=pp_1$.
Similarly,
we can get $p_1=p_1p$ from $p_1\in$ $^{\circ}\!(1-p_1)=$ $^{\circ}\!(1-p)$.
Then
\begin{equation*}
\begin{split}
    ep=(ep)^{\ast}=(epp_1)^{\ast}=(epe^{-1}ep_1)^{\ast}=(ep_1)^{\ast}(e^{-1})^{\ast}(ep)^{\ast}=ep_1e^{-1}ep=ep_1p=ep_1,
\end{split}
\end{equation*}
thus $p=p_1$.

$(ii)\Rightarrow (i).$ Suppose that there exists a unique idempotent $p$ such that $(ep)^{\ast}=ep$, $pa=0$, $u=a^{n}+p\in R^{-1}$.

When $n=1$,
set $x=u^{-1}(1-p)$.
Now we prove that $x$ is the $e$-core inverse of $a$.
Since $(1-p)u=a$,
$ua^2=a$ and $pu=p$,
we obtain
\begin{equation}\label{2.1}
\begin{split}
    1-p=au^{-1},
\end{split}
\end{equation}
\begin{equation}\label{2.2}
\begin{split}
    a=u^{-1}a^2,
\end{split}
\end{equation}
\begin{equation}\label{2.3}
\begin{split}
    (1-p)u^{-1}=u^{-1}-p.
\end{split}
\end{equation}
Therefore,
\begin{equation*}
\begin{split}
    eax=eau^{-1}(1-p)\stackrel{(\ref{2.1})}{=}e(1-p)(1-p)=e-ep \text{~is Hermitian},
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
    xa^2=u^{-1}(1-p)a^2=u^{-1}a^2\stackrel{(\ref{2.2})}{=}a,
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
    ax^2
    &~=au^{-1}(1-p)u^{-1}(1-p)\stackrel{(\ref{2.1})}{=}(1-p)u^{-1}(1-p)\\
    &~\stackrel{(\ref{2.3})}{=}(u^{-1}-p)(1-p)=u^{-1}(1-p)=x.
\end{split}
\end{equation*}
As a consequence,
$a\in R^{e, \co}$ with $a^{e, \co}=u^{-1}(1-p)$ by Lemma~\ref{e-core-inverse}.

When $n\geqslant 2$,
from $u=a^{n}+p\in R^{-1}$ and $p^{\ast}=(e^{-1}ep)^{\ast}=epe^{-1}$,
we get $u^{\ast}=(a^{\ast})^{n}+epe^{-1}\in R^{-1}$.
Since $ua=a^{n+1}$ and $u^{\ast}ea=(a^{\ast})^{n}ea$,
\begin{equation*}
\begin{split}
    a=u^{-1}a^{n+1}\in Ra^{n}
\end{split}
\end{equation*}
and
\begin{equation*}
\begin{split}
    a=(u^{\ast}e)^{-1}(a^{\ast})^{n}ea\in R(a^{\ast})^{n}ea.
\end{split}
\end{equation*}
Thus $a\in R(a^{\ast})^{n}ea\cap Ra^{n}$,
and then $a\in R^{e, \co}$ and $a^{e, \co}=a^{n-1}(eu)^{-1}e=a^{n-1}u^{-1}$ by Theorem~\ref{thm1}.

$(ii)\Rightarrow (iii)$ is trivial.

$(iii)\Rightarrow (i).$ Assume that there exists an element $s$ such that $(es)^{\ast}=es$, $sa=0$, $v=a^{n}+s\in R^{-1}$.

When $n=1$.
Since $v=a^{n}+s\in R^{-1}$ and
\begin{equation}\label{2.4}
\begin{split}
    s^{\ast}=(e^{-1}es)^{\ast}=ese^{-1},
\end{split}
\end{equation}
we get $v^{\ast}=a^{\ast}+ese^{-1}\in R^{-1}$.
From $va=a^2$ and $v^{\ast}ea=a^{\ast}ea$ we obtain
\begin{equation}\label{2.5}
\begin{split}
    a=v^{-1}a^2\in Ra^2
\end{split}
\end{equation}
and
\begin{equation}\label{2.6}
\begin{split}
    a=(v^{\ast}e)^{-1}a^{\ast}ea\in Ra^{\ast}ea.
\end{split}
\end{equation}
It remains to show that $a\in a^2R$.
By Lemma~\ref{13e-14f-inverse},
the equation (\ref{2.6}) shows that $a\in R^{(1, 3e)}$ with $v^{-1}\in a\{1, 3e\}$.
Hence
\begin{equation}\label{2.7}
\begin{split}
    a=aa^{(1, 3e)}a=av^{-1}a.
\end{split}
\end{equation}
In addtion,
$sv=s^2$ leads to $s=s^2v^{-1}$,
thus
\begin{equation}\label{2.8}
\begin{split}
    es^2v^{-1}
    &~=es=(es)^{\ast}=(es^2v^{-1})^{\ast}=(v^{\ast})^{-1}s^{\ast}es\\
    &~\stackrel{(\ref{2.4})}{=}(v^{\ast})^{-1}ese^{-1}es=(v^{\ast})^{-1}es^2.
\end{split}
\end{equation}
Moreover,
\begin{equation}\label{2.9}
\begin{split}
    esv^{-2}
    &~\stackrel{(\ref{2.8})}{=}[(v^{\ast})^{-1}es^2]v^{-2} = (v^{\ast})^{-1}(es^2v^{-1})v^{-1}\\
    &~\stackrel{(\ref{2.8})}{=}(v^{\ast})^{-1}[(v^{\ast})^{-1}es^2]v^{-1}=(v^{\ast})^{-2}es^2v^{-1}\stackrel{(\ref{2.8})}{=}(v^{\ast})^{-2}es,
\end{split}
\end{equation}
thus
\begin{equation}\label{2.10}
\begin{split}
    ev^{-1}
    &~=evv^{-2}=e(a+s)v^{-2}=eav^{-2}+esv^{-2}\stackrel{(\ref{2.9})}{=}eav^{-2}+(v^{\ast})^{-2}es.
\end{split}
\end{equation}
Therefore,
\begin{equation}\label{2.11}
\begin{split}
    a
    &~\stackrel{(\ref{2.7})}{=}av^{-1}a=ae^{-1}(ev^{-1})a\stackrel{(\ref{2.10})}{=}ae^{-1}[eav^{-2}+(v^{\ast})^{-2}es]a=a^2v^{-2}a\in a^2R.
\end{split}
\end{equation}
According to Lemma~\ref{group-inverse},
equations (\ref{2.5}) and (\ref{2.11}) show that $a\in R^{\#}$ with $a^{\#}=v^{-2}a$.
And from (\ref{2.6}) and Lemma~\ref{e-core-inverse},
$a\in R^{e, \co}$ with
\begin{equation*}
\begin{split}
    a^{e, \co}=a^{\#}aa^{(1, 3e)}=v^{-2}aav^{-1}\stackrel{(\ref{2.5})}{=}v^{-1}av^{-1}.
\end{split}
\end{equation*}

When $n\geqslant 2$,
from $v=a^{n}+s\in R^{-1}$ and $s^{\ast}=ese^{-1}$,
we get $v^{\ast}=(a^{\ast})^{n}+ese^{-1}\in R^{-1}$.
Since $va=a^{n+1}$ and $v^{\ast}ea=(a^{\ast})^{n}ea$,
\begin{equation*}
\begin{split}
    a=v^{-1}a^{n+1}\in Ra^{n}
\end{split}
\end{equation*}
and
\begin{equation*}
\begin{split}
    a=(v^{\ast}e)^{-1}(a^{\ast})^{n}ea\in R(a^{\ast})^{n}ea.
\end{split}
\end{equation*}
Thus $a\in R(a^{\ast})^{n}ea\cap Ra^{n}$,
and then $a\in R^{e, \co}$ and $a^{e, \co}=a^{n-1}(ev)^{-1}e=a^{n-1}v^{-1}$ by Theorem~\ref{thm1}.

$(i)\Rightarrow (iv).$ Set $q=1-aa^{e, \co}$,
then $q$ is an idempotent satisfying $(eq)^{\ast}=eq$ and $qa=0$.
Now we prove that $w=a^{n}(1-q)+q=a^{n+1}a^{e, \co}+1-aa^{e, \co}\in R^{-1}$.

When $n=1$,
from the proof of $(i)\Rightarrow (ii)$ we know that $1+aa^{e, \co}(a-1)=a+1-aa^{e, \co}\in R^{-1}$,
thus $w=a^{2}a^{e, \co}+1-aa^{e, \co}=1+(a-1)aa^{e, \co}\in R^{-1}$ by the Lemma~\ref{J.L}.

When $n\geqslant 2$,
from the proof of $(i)\Rightarrow (ii)$ we know that $1+aa^{e, \co}(a^n-1)=a^n+1-aa^{e, \co}\in R^{-1}$,
thus $w=a^{n+1}a^{e, \co}+1-aa^{e, \co}=1+(a^n-1)aa^{e, \co}\in R^{-1}$ by the Lemma~\ref{J.L}.

In the end,
we prove the uniqueness of the idempotent $q$.
It is necessary to show that $^{\circ}\!(a^{n})=$ $^{\circ}\!(1-q)$.
If $xa^{n}=0$,
then
\begin{equation*}
\begin{split}
    0=xa^{n}(1-q)=x(1-q)[a^{n}(1-q)+q].
\end{split}
\end{equation*}
From $a^{n}(1-q)+q\in R^{-1}$ we have $x(1-q)=0$.
Conversely,
if $y(1-q)=0$,
then $ya^{n}=y(1-q)a^{n}=0$.
Hence $^{\circ}\!(a^{n})=$ $^{\circ}\!(1-q)$.
Suppose that $q, q_1$ are both idempotents which satisfy the statement $(iv)$,
then $^{\circ}\!(1-q)=$ $^{\circ}\!(a^{n})=$ $^{\circ}\!(1-q_1)$.
From $q\in$ $^{\circ}\!(1-q)=$ $^{\circ}\!(1-q_1)$ we obtain $q=qq_1$.
Similarly,
$q\in$ $^{\circ}\!(1-q_1)=$ $^{\circ}\!(1-q)$ leads to $q_1=q_1q$.
Then
\begin{equation*}
\begin{split}
    eq=(eq)^{\ast}=(eqq_1)^{\ast}=(eqe^{-1}eq_1)^{\ast}=(eq_1)^{\ast}(e^{-1})^{\ast}(eq)^{\ast}=eq_1e^{-1}eq=eq_1q=eq_1,
\end{split}
\end{equation*}
thus $q=q_1$.

$(iv)\Rightarrow (i).$ Assume that there exists a unique idempotent $q$ such that $(eq)^{\ast}=eq$, $qa=0$, $w=a^{n}(1-q)+q\in R^{-1}$.

When $n=1$,
let $x=(1-q)w^{-1}$.
Now we show that $x$ is the $e$-core inverse of $a$.
Since $(1-q)w=a(1-q)$ and $wa^2=a$,
we get
\begin{equation}\label{2.12}
\begin{split}
    1-q=a(1-q)w^{-1},
\end{split}
\end{equation}
\begin{equation}\label{2.13}
\begin{split}
    a=w^{-1}a^2.
\end{split}
\end{equation}
Therefore,
\begin{equation*}
\begin{split}
    eax=ea(1-q)w^{-1}\stackrel{(\ref{2.12})}{=}e(1-q)=e-eq \text{~is Hermitian},
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
    xa^2=(1-q)w^{-1}a^2\stackrel{(\ref{2.13})}{=}(1-q)a=a,
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
    ax^2
    &~=a(1-q)w^{-1}(1-q)w^{-1}\stackrel{(\ref{2.12})}{=}(1-q)w^{-1}=x.
\end{split}
\end{equation*}
As a consequence,
$a\in R^{e, \co}$ with $a^{e, \co}=(1-q)w^{-1}$ by Lemma~\ref{e-core-inverse}.

When $n\geqslant 2$,
from $w=a^{n}(1-q)+q\in R^{-1}$ and $q^{\ast}=(e^{-1}eq)^{\ast}=eqe^{-1}$,
we get $w^{\ast}=(1-p)^{\ast}(a^{\ast})^{n}+eqe^{-1}\in R^{-1}$.
Since $wa=a^{n+1}$ and $w^{\ast}ea=(1-q)^{\ast}(a^{\ast})^{n}ea$,
\begin{equation*}
\begin{split}
    a=w^{-1}a^{n+1}\in Ra^{n}
\end{split}
\end{equation*}
and
\begin{equation*}
\begin{split}
    a=(w^{\ast}e)^{-1}(1-q)^{\ast}(a^{\ast})^{n}ea\in R(a^{\ast})^{n}ea.
\end{split}
\end{equation*}
Therefore,
$a\in R(a^{\ast})^{n}ea\cap Ra^{n}$,
and then $a\in R^{e, \co}$ and $a^{e, \co}=a^{n-1}(1-q)(ew)^{-1}e=a^{n-1}(1-q)w^{-1}$ by Theorem~\ref{thm1}.

$(iv)\Rightarrow (v)$ is trivial.

$(v)\Rightarrow (i).$ Assume that there exists an element $t$ such that $(et)^{\ast}=et$, $ta=0$, $z=a^{n}(1-t)+t\in R^{-1}$.

When $n=1$.
Since $z=a^{n}(1-t)+t\in R^{-1}$ and
\begin{equation}\label{2.14}
\begin{split}
    t^{\ast}=(e^{-1}et)^{\ast}=ete^{-1},
\end{split}
\end{equation}
we get $z^{\ast}=(1-t)^{\ast}a^{\ast}+ese^{-1}\in R^{-1}$.
From $za=a^2$ and $z^{\ast}ea=(1-t)^{\ast}a^{\ast}ea$ we obtain
\begin{equation}\label{2.15}
\begin{split}
    a=z^{-1}a^2\in Ra^2
\end{split}
\end{equation}
and
\begin{equation}\label{2.16}
\begin{split}
    a=(z^{\ast}e)^{-1}(1-t)^{\ast}a^{\ast}ea\in Ra^{\ast}ea.
\end{split}
\end{equation}
It remains to show that $a\in a^2R$.
By Lemma~\ref{13e-14f-inverse},
the equation (\ref{2.16}) shows that $a\in R^{(1, 3e)}$ with $(1-t)z^{-1}\in a\{1, 3e\}$.
Hence
\begin{equation}\label{2.17}
\begin{split}
    a=aa^{(1, 3e)}a=a(1-t)z^{-1}a.
\end{split}
\end{equation}
In addtion,
$tz=t^2$ leads to $t=t^2z^{-1}$,
thus
\begin{equation}\label{2.18}
\begin{split}
    et^2z^{-1}
    &~=et=(et)^{\ast}=(et^2z^{-1})^{\ast}=(z^{\ast})^{-1}t^{\ast}et\\
    &~\stackrel{(\ref{2.14})}{=}(z^{\ast})^{-1}ete^{-1}et=(z^{\ast})^{-1}et^2.
\end{split}
\end{equation}
Moreover,
\begin{equation}\label{2.19}
\begin{split}
    etz^{-2}
    &~\stackrel{(\ref{2.18})}{=}[(z^{\ast})^{-1}et^2]z^{-2} = (z^{\ast})^{-1}(et^2z^{-1})z^{-1}\\
    &~\stackrel{(\ref{2.18})}{=}(z^{\ast})^{-1}[(z^{\ast})^{-1}et^2]z^{-1}=(z^{\ast})^{-2}et^2z^{-1}\stackrel{(\ref{2.18})}{=}(z^{\ast})^{-2}et,
\end{split}
\end{equation}
thus
\begin{equation}\label{2.20}
\begin{split}
    ez^{-1}
    &~=ezz^{-2}=e[a(1-t)+t]z^{-2}=ea(1-t)z^{-2}+etz^{-2}\\
    &~\stackrel{(\ref{2.19})}{=}ea(1-t)z^{-2}+(z^{\ast})^{-2}et.
\end{split}
\end{equation}
Therefore,
\begin{equation}\label{2.21}
\begin{split}
    a
    &~\stackrel{(\ref{2.17})}{=}a(1-t)z^{-1}a=a(1-t)e^{-1}(ez^{-1})a\\
    &~\stackrel{(\ref{2.20})}{=}a(1-t)e^{-1}[ea(1-t)z^{-2}+(z^{\ast})^{-2}et]a\\
    &~=a^2(1-t)z^{-2}a\in a^2R.
\end{split}
\end{equation}
According to Lemma~\ref{group-inverse},
equations (\ref{2.15}) and (\ref{2.21}) show that $a\in R^{\#}$ with $a^{\#}=z^{-2}a$.
And from (\ref{2.16}) and Lemma~\ref{e-core-inverse} deducing that $a\in R^{e, \co}$ with
\begin{equation*}
\begin{split}
    a^{e, \co}=a^{\#}aa^{(1, 3e)}=z^{-2}aa(1-t)z^{-1}\stackrel{(\ref{2.15})}{=}z^{-1}a(1-t)z^{-1}.
\end{split}
\end{equation*}

When $n\geqslant 2$,
from $z=a^{n}(1-t)+t\in R^{-1}$ and $t^{\ast}=ete^{-1}$ we get $z^{\ast}=(1-t)^{\ast}(a^{\ast})^{n}+ete^{-1}\in R^{-1}$.
Since $za=a^{n+1}$ and $z^{\ast}ea=(1-t)^{\ast}(a^{\ast})^{n}ea$,
\begin{equation*}
\begin{split}
    a=z^{-1}a^{n+1}\in Ra^{n}
\end{split}
\end{equation*}
and
\begin{equation*}
\begin{split}
    a=(z^{\ast}e)^{-1}(1-t)^{\ast}(a^{\ast})^{n}ea\in R(a^{\ast})^{n}ea.
\end{split}
\end{equation*}
Thus $a\in R(a^{\ast})^{n}ea\cap Ra^{n}$,
and then $a\in R^{e, \co}$ and $a^{e, \co}=a^{n-1}(1-t)(ev)^{-1}e=a^{n-1}(1-t)v^{-1}$ by Theorem~\ref{thm1}.
\end{proof}

When $e=1$,
we get the following result,
which improves Theorem $3.3$ and Theorem $3.4$ in \cite{Li}.

\begin{corollary}
Let $a\in R$,
$n\geqslant 1$ is a positive integer.
The following statements are equivalent: \\
$(i)$ $a\in R^{\co}$; \\
$(ii)$ there exists a unique projection $p$ such that $pa=0$, $u=a^{n}+p\in R^{-1}$;\\
$(iii)$ there exists a Hermitian element $s$ such that $sa=0$, $v=a^{n}+s\in R^{-1}$;\\
$(iv)$ there exists a unique projection $q$ such that $qa=0$, $w=a^{n}(1-q)+q\in R^{-1}$;\\
$(v)$ there exists a Hermitian element $t$ such that $ta=0$, $z=a^{n}(1-t)+t\in R^{-1}$.\\
In this case,
when $n=1$,
$$a^{\co}=u^{-1}(1-p)=v^{-1}av^{-1}=(1-q)w^{-1}=z^{-1}a(1-t)z^{-1},$$
when $n\geqslant 2$,
$$a^{\co}=a^{n-1}u^{-1}=a^{n-1}v^{-1}=a^{n-1}(1-q)w^{-1}=a^{n-1}(1-t)z^{-1}.$$
\end{corollary}

There is an analogous result for the $f$-dual core inverse of $a\in R$,
we omit its proof.

\begin{theorem} \label{thm3}
Let $a\in R$ and let $f\in R$ be an invertible Hermitian element,
$n\geqslant 1$ is a positive integer.
The following statements are equivalent: \\
$(i)$ $a\in R_{f, \co}$; \\
$(ii)$ there exists a unique idempotent $p$ such that $(fp)^{\ast}=fp$, $ap=0$, $u=a^{n}+p\in R^{-1}$;\\
$(iii)$ there exists an element $s$ such that $(fs)^{\ast}=fs$, $as=0$, $v=a^{n}+s\in R^{-1}$;\\
$(iv)$ there exists a unique idempotent $q$ such that $(fq)^{\ast}=fq$, $aq=0$, $w=(1-q)a^{n}+q\in R^{-1}$;\\
$(v)$ there exists an element $t$ such that $(ft)^{\ast}=ft$, $at=0$, $z=(1-t)a^{n}+t\in R^{-1}$.\\
In this case,
when $n=1$,
$$a_{f, \co}=(1-p)u^{-1}=v^{-1}av^{-1}=w^{-1}(1-q)=z^{-1}(1-t)az^{-1},$$
when $n\geqslant 2$,
$$a_{f, \co}=u^{-1}a^{n-1}=v^{-1}a^{n-1}=(1-q)a^{n-1}w^{-1}=(1-t)a^{n-1}z^{-1}.$$
\end{theorem}

When $f=1$,
we get the following result.

\begin{corollary}
Let $a\in R$,
$n\geqslant 1$ is a positive integer.
The following statements are equivalent: \\
$(i)$ $a\in R_{\co}$; \\
$(ii)$ there exists a unique projection $p$ such that $ap=0$, $u=a^{n}+p\in R^{-1}$;\\
$(iii)$ there exists a Hermitian element $s$ such that $as=0$, $v=a^{n}+s\in R^{-1}$;\\
$(iv)$ there exists a unique projection $q$ such that $aq=0$, $w=(1-q)a^{n}+q\in R^{-1}$;\\
$(v)$ there exists a Hermitian element $t$ such that $at=0$, $z=(1-t)a^{n}+t\in R^{-1}$.\\
In this case,
when $n=1$,
$$a_{\co}=(1-p)u^{-1}=v^{-1}av^{-1}=w^{-1}(1-q)=z^{-1}(1-t)az^{-1},$$
when $n\geqslant 2$,
$$a_{\co}=u^{-1}a^{n-1}=v^{-1}a^{n-1}=(1-q)a^{n-1}w^{-1}=(1-t)a^{n-1}z^{-1}.$$
\end{corollary}

In the derivation of $(i)$ from $(ii)$ of Theorem~\ref{thm2},
when $n=1$,
$a^{\co}=u^{-1}(1-p)$.
From the equation (\ref{2.1}) (i.e., $1-p=au^{-1}$) we know that $e(1-p)=eau^{-1}$ is Hermitian,
thus
\begin{equation*}
\begin{split}
    a^{\co}
    &~=u^{-1}(1-p)=u^{-1}au^{-1}=u^{-1}e^{-1}eau^{-1}=u^{-1}e^{-1}(eau^{-1})^{\ast}\\
    &~=(u^{\ast}eu)^{-1}a^{\ast}e=(a^{\ast}ea+ep)^{-1}a^{\ast}e.
\end{split}
\end{equation*}
Through this expression,
we naturally want to know whether $a$ is $e$-core invertible or not when there is a unique idempotent $p$ such that $(ep)^{\ast}=ep$,
$pa=0$,
$a^{\ast}ea+ep\in R^{-1}$.
However,
it is not true.
Here is a counterexample.

\begin{example}\label{eg1}
Let $R$ be an infinite matrix ring over complex filed whose rows and columns are both finite,
let conjugate transpose be the involution and $a=\sum\limits_{i=1}^{\infty}e_{i+1,i}$.
Then $a^{\ast}a=1$,
$aa^{\ast}=\sum\limits_{i=2}^{\infty}e_{i,i}$.
Set $e=1$,
$p=0$,
then $p$ is an idempotent satisfying $(ep)^{\ast}=ep$,
$pa=0$ and $a^{\ast}ea+ep=1\in R^{-1}$.
But $a$ is not group invertible,
thus $a$ is not $e$-core invertible.
\end{example}

The above counterexample shows that even if there is a unique idempotent $p$ such that $(ep)^{\ast}=ep$,
$pa=0$ and $a^{\ast}ea+ep\in R^{-1}$,
$a$ is not necessary to be $e$-core invertible in general rings.
However,
it is true when we take $R$ as a Dedekind-finite ring which satisfies the property that $ab=1$ implies $ba=1$ for any $a, b\in R$.
Let $R^{-1}_r$ and $R^{-1}_l$ denote all right invertible and left invertible elements in $R$,
respectively.
See the following result.

\begin{theorem} \label{D-finite ring}
Let $R$ be a Dedekind-finite ring and $a\in R$,
$e\in R$ is an invertible Hermitian element.
Then the following statements are equivalent: \\
$(i)$ $a\in R^{e, \co}$; \\
$(ii)$ there exists a unique idempotent $p$ such that $(ep)^{\ast}=ep$, $pa=0$, $a^{\ast}ea+ep\in R^{-1}$;\\
$(iii)$ there exists a unique idempotent $p$ such that $(ep)^{\ast}=ep$, $pa=0$, $a^{\ast}ea+ep\in R^{-1}_r$; \\
$(iv)$ there exists a unique idempotent $p$ such that $(ep)^{\ast}=ep$, $pa=0$, $a^{\ast}ea+ep\in R^{-1}_l$.\\
In this case,
\begin{equation*}
\begin{split}
    a^{e, \co}=(a^{\ast}ea+ep)^{-1}a^{\ast}e.
\end{split}
\end{equation*}
\end{theorem}

\begin{proof}
Since $a^{\ast}ea+ep$ is Hermitian,
$a^{\ast}ea+ep$ is one-sided invertible if and only if it is invertible,
hence the statements $(ii)$, $(iii)$ and $(iv)$ are equivalent.
It is sufficient to show that $(i) \Leftrightarrow (ii)$.

$(i)\Rightarrow (ii).$ Suppose that $a\in R^{e, \co}$ and let $p=1-aa^{e, \co}$,
then $a+p\in R^{-1}$ by Theorem~\ref{thm2}.
Moreover,
$e(a+p)=ea+ep\in R^{-1}$,
so $(ea+ep)^{\ast}=a^{\ast}e+ep\in R^{-1}$.
Therefore $a^{\ast}ea+ep=(a^{\ast}e+ep)(a+p)$ is invertible.

$(ii)\Rightarrow (i).$ Let $u=a+p$,
$u^{\ast}eu=a^{\ast}ea+ep\in R^{-1}$.
As $R$ is a Dedekind-finite ring,
thus $u\in R^{-1}$,
which guarantees $a\in R^{e, \co}$ and $a^{e,\co}=(a^{\ast}ea+ep)^{-1}a^{\ast}e$ by Theorem~\ref{thm2}.
\end{proof}

There is a dual result for the $f$-dual core inverse.

\begin{theorem}
Let $R$ be a Dedekind-finite ring and $a\in R$,
$f\in R$ is an invertible Hermitian element.
Then the following statements are equivalent: \\
$(i)$ $a\in R^{e, \co}$; \\
$(ii)$ there exists a unique idempotent $q$ such that $(fq)^{\ast}=fq$, $aq=0$, $af^{-1}a^{\ast}+qf^{-1}\in R^{-1}$;\\
$(iii)$ there exists a unique idempotent $q$ such that $(fq)^{\ast}=fq$, $aq=0$, $af^{-1}a^{\ast}+eqf^{-1}\in R^{-1}_r$; \\
$(iv)$ there exists a unique idempotent $q$ such that $(fq)^{\ast}=fq$, $aq=0$, $af^{-1}a^{\ast}+qf^{-1}\in R^{-1}_l$.\\
In this case,
\begin{equation*}
\begin{split}
    a^{e, \co}=f^{-1}a^{\ast}(af^{-1}a^{\ast}+qf^{-1})^{-1}.
\end{split}
\end{equation*}
\end{theorem}

Let $a\in R$ and $e, f\in R$ be two invertible Hermitian elements.
Zhu and Wang \cite{HHZ} mentioned  that $a\in R^{e, \co}\cap R_{f, \co}$ if and only if $a\in R^{\#}\cap R^{\dagger}_{e, f}$.
Mosi\'{c} et al. \cite{Mosic2} mentioned that $a\in R$ is weighted-$\mathrm{EP}$ with respect to $(e, f)$ if and only if $a\in R^{e, \co}\cap R_{f, \co}$ and $a^{e, \co}=a_{f, \co}$.
By Theorem~\ref{thm2} and Theorem~\ref{thm3},
we obtain the following theorem.

\begin{theorem} \label{EP}
Let $a\in R$ and $e, f\in R$ be two invertible Hermitian elements,
$n\geqslant 1$ is a positive integer.
The following conditions are equivalent: \\
$(i)$ $a\in R$ is weighted-$\mathrm{EP}$ with respect to $(e, f)$; \\
$(ii)$ there exists a unique idempotent $p$ such that $(ep)^{\ast}=ep$, $(fp)^{\ast}=fp$, $ap=pa=0$, $a^{n}+p\in R^{-1}$;\\
$(iii)$ there exists an element $s$ such that $(es)^{\ast}=es$, $(fs)^{\ast}=fs$, $as=sa=0$, $a^{n}+s\in R^{-1}$.\\
\end{theorem}
\begin{proof}
$(i)\Rightarrow (ii).$ Suppose $a$ is weighted-$\mathrm{EP}$ with respect to $(e, f)$,
so $a\in R^{\dagger}_{e, f}\cap R^{\#}$ and $a^{\dagger}_{e, f}=a^{\#}$.
Let $p=1-a^{\#}a=1-a^{\dagger}_{e, f}a$,
it is easily seen that $p$ is an idempotent satisfying $(ep)^{\ast}=ep$, $(fp)^{\ast}=fp$, $pa=ap=0$.
Since
\begin{equation*}
\begin{split}
    (a^{n}+1-a^{\#}a)((a^{\#})^{n}+1-a^{\#}a)=1=((a^{\#})^{n}+1-a^{\#}a)(a^{n}+1-a^{\#}a),
\end{split}
\end{equation*}
thus $a^{n}+1-a^{\#}a$ is invertible.

$(ii)\Rightarrow (iii)$ is trivial.

$(iii)\Rightarrow (i).$ According to Theorem~\ref{thm2} and Theorem~\ref{thm3},
$a\in R^{e, \co}\cap R_{f, \co}$.
It remains to show that $a^{e, \co}=a_{f, \co}$.
Write $v=a^{n}+s$.
When $n=1$,
we have $a^{e, \co}=v^{-1}av^{-1}=a_{f, \co}$.
When $n\geqslant 2$,
$a^{e, \co}=a^{n-1}v^{-1}, a_{f, \co}=v^{-1}a^{n-1}$.
From $pa=ap=0$,
we obtain $av=va$,
thus $av^{-1}=v^{-1}a$.
Therefore,
$a^{e, \co}=a^{n-1}u^{-1}=u^{-1}a^{n-1}=a_{f, \co}$.
As a consequence,
$a$ is weighted-$\mathrm{EP}$ with respect to $(e, f)$.
\end{proof}

 \bigskip

\centerline {\bf ACKNOWLEDGMENTS}
This research is supported by the National Natural Science Foundation of China (No.11871145);
NSF of Jiangsu Province (BK20200944),
Natural Science Foundation of Jiangsu Higher Education Institutions of China (20KJB110001);
the QingLan Project of Jiangsu Province.

redpajama_set_name: RedPajamaArXiv


When Lloyd Steen graduated from SHS in 1978, he left an athletic legacy that included outstanding play as a stopper and goalie in soccer, and record setting performances in indoor and outdoor track. Lloyd's athletic accomplishments earned him the Meade Alcorn Outstanding Athlete at graduation.
Lloyd helped lead SHS to two state semi-finals in soccer. His junior year as a stopper back the team finished with a 14-1-2 record, and, in his senior season he was the goalie on a team that finished with 13-3-3 record, including 9 shutouts.
Lloyd's best sport was track and field. Blessed with both speed and strength, Lloyd excelled in running and field events. He was a sprinter and hurdler and also participated in the shot put, javelin, discus, long jump and pole vault. Never finishing worse than third in every event he entered his senior year, Steen led Suffield to the NCCC Championship. Lloyd was named to the All Conference Team for the second time in 1978. Lloyd's incredible versatility led him to try the decathlon in the State Open where he finished third, setting a school record of over six thousand points. This record still stands.
Lloyd's success in the decathlon took him to Division I University of Rhode Island as one of their top recruits. In 1980, in the decathlon, he finished fifth in the Boston College Relays, fifth in the New Englands, and seventh in IC4A Championship in Philadelphia, and set the decathlon record at URI that stood for 22 years.


Typically when treatment has been completed it is normal to expect some discomfort/soreness from the tooth and the general area.
The reasons for this discomfort are easy to understand. There will be some pain from the injection sites. In addition there will be some localized tissue trauma from the rubber dam clamp and screen. The tooth itself will often be tender to touch or to bite on for several days after the procedure.
These relatively minor problems can be easily counteracted by taking some over the counter pain killers. The best pain killers to take are those that one would take in the event of a bad headache.
It is important to establish before taking any tablet or drug that you are not allergic to the drugs contained within the tablet. If you are unsure then you should not take the tablet and consult your medical doctor.
It is important to establish before you take any tablets that it is safe to do so and that there are no other medical contraindications to taking the tablet. For example during pregnancy (not all pain killers are safe to use during pregnancy), during lactation (for feeding mothers).
It is important that when taking any tablets the safe or recommended dose is not exceeded. This will be clearly written on the back of the packet. Always remember that there may be interactions with other tablets that you are taking. Again if you are unsure you should consult your medical doctor.
In order to get the maximum benefit from the pain killers they need to be taken regularly. Do not wait for the pain to return again, dose regularly. In that way, the pain killer will stay at the optimum level within the body.
It is often recommended to take the tablets with food.
In rare occasions following the root treatment, there can be a lot of pain. This is often termed 'an acute flare up'.
The causes of 'Flare ups' are numerous and multifactorial.
During this process small amounts of debris may be pushed through the end of the root into the surrounding tissues.
There may be some overfilling during the placement of the actual filling itself. All of these will impact on the tissues to some extent causing pain.
Pre-operative status of the tooth: There are two obvious scenarios which tend to be associated with a higher incidence of post operative pain or flare ups.
Teeth with radiographic evidence of significant periapical disease (large area of infection seen on x-ray) have more bacterial strains and are more complicated have a higher incidence of 'flare ups' as a result.
Retreatment cases (re doing a root treatment for a second time) are also associated with a higher incidence of 'flare-ups'. This can be attributed to the difficulty with retreatments and the need to use solvents to remove the old root filling materials, the different micro-organisms that infect these teeth, and the higher chance of iatrogenic problems with these teeth.
Host factors: No two people are the same and their reactions to challenges will be different. The intensity of pre operative pain and the amount of patient apprehension are correlated to the degree of post operative pain. Age, gender, tooth position and presence of allergies are also shown to have a correlation with flare ups. It is impossible to determine in advance who will have the problems following treatment.
If the root treatment has been started but not completed it may benefit from further cleaning and the placement of a dressing.
It certain circumstances the tooth may be extruded (pushed up out of its socket) from the inflammation underneath and a reduction on the temporary filling or tooth may be hugely beneficial easing considerably the associated tenderness on biting.
If there is an associated facial swelling looking to obtain drainage may provide the necessary relief.
Taking antibiotics and pain killers. Antibiotics are really only indicated where there is an overwhelming infection.
NO ALLERGIES TO PARACETAMOL AND ASPIRIN/ANTI INFLAMMATORY (NSAID) RELATED TABLETS.
NO DRUG INTERACTIONS WITH OTHER MEDICATION.
Ibuprofen (200mg) One or two tablets or three tablets.


1. What went wrong? When you upload a new document as a participatory text, you have a preview to check that everything is in order, but if it's not, if there is an error, you don't have the option to go back and reload it again. This means that in order to repeat the operation you have to create a new component of proposals, not being able to delete the first one. And you can end up having 'n' proposal components depending on the errors you make when uploading the file. Also: you can't edit the document title once is published, and this can be also a problem. 2. What did you expect to happen? I expected to have an option to reset and reload the file as long as it hasn't been published yet.
I've noticed that sorting by the most recent doesn't work well. Also, when you select a filter there is no indicator that it is being processed and this causes confusion. To reproduce: 1. Go to "https://meta.decidim.org/processes/bug-report/f/210/" 2. Select "Order proposals by most recent". 3. Scroll down and you will see a proposal created today among older ones. Take a look at the attached gif.
When loading the file it is not known which is the expected format for the import. There should be an example file linked in both Markdown and Open Office formats.
Being able to mention someone is great for encouraging conversation, but right now it's a little cumbersome to do so. Either you copy the username, which is not easy because it is a link and you can accidentally click on it, taking you to the profile page, or you write the username manually and you can mistype it. It would be great to have autocomplete for @usernames mentions. ps. Does anyone have a special trick to mention other people?
Oh no! We need to fix ASAP since this is one of Decidim's most valuable features!
[ES] Establecer un sistema para valorar el impacto de nuevas funcionalidades o cambios en el código. Poder clasificar las mejoras utilizando por ejemplo las mismas categorías del método Semver (major, minor y patch). *MAJOR: cuando se hacen cambios incompatibles con la API *MINOR: cuando se agrega funcionalidad de manera compatible con la versión anterior *PATCH: al hacer correcciones de errores compatibles con versiones anteriores. [EN] Establish a system to assess the impact of new features or changes in the code. To be able to classify the improvements using for example the same categories of the Semver method (major, minor and patch). *MAJOR: when you make incompatible API changes *MINOR: when you add functionality in a backwards-compatible manner *PATCH: when you make backwards-compatible bug fixes.
[ES] El proceso actual de contribución al código no garantiza que, una vez abierto un PR (Pull request), éste termine mergeado en Master (el repositorio principal de código). Uno de los motivos es que cualquier funcionalidad (habiendo sido validada previamente por la comunidad) puede resolverse técnicamente de maneras diferentes, y por tanto la valoración técnica es subjetiva. Publicar las condiciones claras para que un PR sea aceptado y abrir más la comunicación una vez que se abre el PR en github para negociar si es necesario y asegurar que se puede llegar a mergear. [EN] The current process of contribution to the code does not guarantee that, once a PR (Pull request) is opened, it ends up merged in Master (the main code repository). One of the reasons is that any functionality (having been previously validated by the community) can be solved technically in different ways, and therefore technical validation is subjective. Publish clear conditions for a PR to be accepted and open more communication once the PR is opened in github to negotiate if necessary and ensure that it can be merged.
[ES] A la hora de proponer nuevas funcionalidades o desarrollos, aportar algún tipo de evidencia: pueden ser datos, indicadores, evidencia basada en el contexto o en la experiencia de uso. [EN] When proposing new functionalities or developments, provide some kind of evidence: it can be data, indicators, evidence based on context or experience of use.


Article of Interest: If Progressive Democrats Care So Much About the Climate, Why Are They Trying to Kill Nuclear Power?
The Democratic Party has highlighted itself as the environmentally-conscious Party. So, why are so many of these same progressive Democratic leaders strongly against nuclear power?
Environmental Progress Founder and President Michael Shellenberger discusses the Democratic Party's longstanding opposition to nuclear power and his urge to Party leaders to embrace nuclear power for a green energy future.
FORBES: If Progressive Democrats Care So Much About The Climate, Why Are They Trying to Kill Nuclear Power?


text:
lieverthuis
affection for others
Animal charities warn that pets are for life, 'not just for lockdown'
By nikholas 3 months ago
04:16 The COVID-19 crisis not only transformed our lives, it also had an impact on
The COVID-19 crisis not only transformed our lives, it also had an impact on the welfare of animals. Job losses, illness, financial difficulties, and even some people's fear of contracting the virus from pets, led to a rise in animal abandonments in the UK.
When people were furloughed or working from home, the adoption rate went up. During the first week of lockdown Battersea Dogs and Cats Home reported 86 dogs and 69 cats were rehomed, rising from 42 and 29 respectively in the same period last year.
While this might look like a positive trend, and these animals went to good homes, it is too early to say that lockdown united all abandoned animals across the UK with new owners for the long term.
When people go back to work their priorities change and newly-adopted pets can be at risk of ending up in a shelter because of the lack of time and commitment from their owners.
Compared with the same period last year, the Royal Society for the Prevention of Cruelty to Animals (RSPCA) charity received four times more calls from prospective owners when the UK went into lockdown – but now the organization has been receiving calls from those who want to return their new pets.
CLICK: How do dogs detect COVID and which are best at it?
"People have gone back to work and then suddenly realized that this puppy doesn't fit into their life any more," says Herchran Boal, an RSPCA inspector in the West Midlands. "It's almost as if they didn't think about that. And that's very sad because a pet is for life, it's not just for the lockdown period."
During the first three months of the lockdown the RSPCA received almost 3,500 calls – 40 a day – about abandoned animals, including 1,509 dogs, 1,165 cats, 299 small animals such as hamsters and guinea pigs and 275 exotic animals. The closure of RSPCA centers, shortage of staff and a surge of abandoned animals put the charity in a very difficult position.
"I've been an inspector for 20 years and this is the worst that anything has affected the RSPCA," says Boal. "We have a service that was being provided for 24 hours a day but due to the pandemic we've had to close our control centers overnight. We have always been an organization that's gone on 24/7 because animals don't get sick just nine to five. People need us all the time."
As a charity, the RSPCA relies on public donations – but fundraising events had to be stopped and the donations from the public have slowed down due to the COVID-19 crisis.
"The NHS have done an amazing job and they're really great," says Boal. "But let's not forget the animals. The animals are what keep some people going, really. The pets are very important to them."
Video editing: Riaz Jugon
Tags: Animal, charities, life, lockdown, pets, warn
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Categories Select Category Animal Care (39) Animal News (47) Animal Nutrition (54) Pets & Animal (46)
A look inside ADM's Animal Nutrition Technology Center | 2021-01-15
A look inside ADM's new Animal Nutrition Technology Center | 2021-01-15
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Animal Care (39)
Animal Nutrition (54)
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Chania: Man Accused Of Animal Cruelty, Turns Himself In (nikholas) (37)
A 55-year-old man accused of abusing his dog in Chania earlier this week, turned himself
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This course is designed to provide the skills needed to create and maintain SAP Business Objects Universes. The course is focused on technical users to teach how to design universes that are efficient as well as user friendly for report creators. Students are also taught how to maintain and distribute the universes. The course provides a comprehensive coverage of universe development process and techniques, allowing developers to understand the issues that they may encounter in a real world scenario and how to tackle these problems.
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There are lots of accounts of motor vehicle owners who ended up in the hands of inexperienced or unscrupulous mobile vehicle mechanic. Assuming that you fall prey to such mobile vehicle mechanic, you may find yourself having to pay a ridiculously high amount of money above the quote you originally got and in some cases for non-existent repairs. Worse still, you may even be entrusting your vehicle with an unqualified person who possesses neither the know-how nor the skills required to carry out auto repairs on any car. This will not only cost you a lot stress for spending money and not getting any repairs done but will also put your life as well as the lives of other drivers at risk.
Occurrences involving such mobile vehicle mechanic are probably so much more commonplace than you could believe and the prime reason for this is that most states basically only require a business license for one to carry on because mobile vehicle mechanic. The absence of a recognized official certification process makes it very simple for a lot of unprofessional and unskilled individuals to operate as car technicians. Regardless, some the blame goes to the vehicle owners the majority of who take their cars to an auto mechanic without establishing whether or not the auto mechanic is a reputable mobile vehicle mechanic. Often with a little research, selecting and hiring a reliable auto mechanic should not be overly complicated.
If you are trying to find a competent professional mobile vehicle mechanic, below is a checklist of the things to look out for and those you should avoid so that you can pick the best professional to handle your repairs.
This is one of the most effective and fastest methods to find a reliable mobile vehicle mechanic or any other local professional. Odds are one of your friends or trusted relatives know a reputable auto mechanic in your neighborhood. Needless to say, you will still have to make sure the referred auto mechanic still, this can save you a whole lot of hassle and help you find a professional you can trust with your car or truck in a short period of time. If this is absolutely not an alternative for you however, you can take your search online.
A quick Google inquiry for mobile vehicle mechanics registered near your locality will most likely give your more than enough results. Go over for online reviews from the companies' web pages. Observing what other past clients have to express regarding a company gives you an idea of the auto mechanic's standing. You can also check Angie's list or the Better Business Bureau for registered mobile vehicle mechanic near you. However, always keep in mind that online reviews can sometime be misleading as they may be dishonest testimonials from family members, friends, or even the auto mechanics' competitors. Pick about three or four auto mechanics so that you are able to shorten your search and simplify the process.
Any reputable auto mechanic must also gladly hand over you a list of individuals they have worked with in the past without any hesitation. You can contact the references and ask they how long they have utilized the services of the mobile vehicle mechanic, what services they got, as well as the quality of service they got. If the references are not reachable and/or seem to be dubious, trust your hunches and go on with your search.
Requesting for estimations from your chosen mobile vehicle mechanics gives you a leverage when looking for a dependable professional. You will find out the average cost of repairs in the industry and be able to know what is reasonable. After a primary look-over, any honest and experienced professional auto mechanic ought to have the ability to give you a general quotation of the cost of the repairs. Of course, every single auto mechanic may charge you differently for repairs but the cost should certainly range inside of what other car mechanics demand within the neighborhood. If the mobile vehicle mechanic bargains or hesitates to provide you a written estimate upon request, trust your instincts and carry forward your search.
Before picking a mobile vehicle mechanic, it is extremely important to assess your vehicles manufacturer's extended warranty thoroughly. In some instances, taking your vehicle to be repaired by an auto mechanic may void the manufacturer's extended warranty. If your vehicle warranty is already ended, ask the mobile vehicle mechanic if they give warranties for maintenance and repairs and in case they do, make sure to obtain a written warranty form before carrying out any repairs.
Even though there is no established legislation that regulates auto mechanics, any professional is required to have a business license to operate. Any trustworthy auto mechanic ought to be able to provide documents of licensing or certification without any difficulty. You should also choose a mobile vehicle mechanic who is ASE Certified so that you can be sure that they are certified and serious automotive technicians. Only a serious professional will continuously want to remain updated on the latest methods in their niche.
Another method to differentiate professionals from shady people is to find out whether they accept credit card settlements or not. Most genuine companies accept credit cards. Although this does not imply that all auto mechanics who do not accept credit card transactions are bad, it is usually better to be safe than sorry.
Auto maintenance and repairs can be really pricey and without a doubt, it always makes good sense to try to find an auto mechanic who will offer you the most affordable arrangement. Even so, never be entraped to go for an auto mechanic simply because they offer you the most affordable estimate. In fact it is wise to stay clear of anybody who gives you an unreasonably low estimate for repairs since this is a method the majority of unskilled and dishonest auto mechanics use in order to charm naive vehicle owners.
Hopefully these pointers will help you to find a reliable mobile vehicle mechanic in Aldie the next time your vehicle breakdown or simply won't start! Don't pick a mobile vehicle mechanic purely because of price. The qualifications and licensing of a mobile vehicle mechanic is of utmost importance, if you don't want to put the lives of yourself and your family at risk!


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Q: How can I prevent weak customer passwords in Woocommerce? I enforce strong passwords across my WordPress sites using ithemes security; however one of my sites runs Woocommerce; and allows users to create an account. There is seemingly no way that I can prevent users from using '123' or 'password' etc as a password. I tried generating the password but they can still log in and change the password and the change isn't filtered by weak/strong either.
Is there any way to do this, or am I being paranoid thinking that a customer account is something that could be used to hack the site.

A: You can prevent this using user registration action hook.
add_action( 'user_register', 'myplugin_registration_save', 10, 1 );
and writing your restriction functions in  your functions.php
function myplugin_registration_save()
{
           logical code
}

source : Wordpress Codex


Account Spreadsheet Template Accounting Spreadsheet Spreadsheet Templates for Busines Business Account Spreadsheet Template. Accounting Worksheet Template Microsoft Excel. Free Accounting Spreadsheet Templates Excel.
by Vivian M. May at Friday, August 04th 2017 12:16:04 PM.