text:
Wednesday in Whitsun Week
Semidouble
Veni, sancte Spiritus, reple tuorum corda fidelium, et tui amoris in eis ignem accende.
Come, O Holy Spirit, fill the hearts of thy faithful, and enkindle within them the fire of thy love.
We have seen with what fidelity the Holy Ghost has fulfilled, during all these past ages, the Mission he received from our Emmanuel, of forming, protecting and maintaining his Spouse the Church. This trust given by a God has been executed with all the power of a God, and it is the sublimest and most wonderful spectacle the world has witnessed during the eighteen hundred years of the new Covenant. This continuance of a social body—the same in all times and places—promulgating a precise Symbol of Faith which each of its Members is bound to accept—producing by its decisions the strictest unity of religious belief throughout the countless individuals who compose the society—this, together with the wonderful propagation of Christianity, is the master-fact of History. These two facts are not, as certain modern writers would have it, results of the ordinary laws of Providence; but Miracles of the highest order, worked directly by the Holy Ghost, and intended to serve as the basis of our faith in the truth of the Christian Religion. The Holy Ghost was not, in the exercise of his Mission, to assume a visible form; but he has made his Presence visible to the understanding of man, and thereby he has sufficiently proved his own personal action in the work of man's salvation.
Let us now follow this divine action,—not in its carrying out the merciful designs of the Son of God, who deigned to take to himself a Spouse here below,—but in the relations of this Spouse with mankind. Our Emmanuel willed that she should be the Mother of men; and that all whom he calls to the honor of becoming his own Members should acknowledge that it is she who gives them this glorious birth. The Holy Ghost, therefore, was to secure to this Spouse of Jesus what would make her evident and known to the world, leaving it, however, in the power of each individual to disown and reject her.
It was necessary that this Church should last for all ages, and that she should traverse the earth in such wise that her name and mission might be known to all nations; in a word, she was to be Catholic, that is, Universal, taking in all times and all places. Accordingly, the Holy Ghost made her Catholic. He began by showing her, on the Day of Pentecost, to the Jews who had flocked to Jerusalem from the various nations; and when these returned to their respective countries, they took the good tidings with them. He then sent the Apostles and Disciples into the whole world, and we learn from the writers of those early times that a century had scarcely elapsed before there were Christians in every portion of the known earth. Since then, the Visibility of this holy Church has gone on increasing gradually more and more. If the Divine Spirit, in the designs of his justice, has permitted her to lose her influence in a nation that had made itself unworthy of the grace, he transferred her to another where she would be obeyed. If, at time, there have been whole countries where she had no footing, it was either because she had previously offered herself to them and they had rejected her, or because the time marked by Providence for her reigning there had not yet come. The history of the Church's propagation is one long proof of her ever living and of her frequent migrating. Times and places, all are hers; if there be one when or where she is not acknowledged as supreme, she is at least represented by her Members; and this prerogative, which has given her the name of Catholic, is one of the grandest of the workings of the Holy Ghost.
But his action does not stop here; the Mission given him by the Emmanuel in reference to his Spouse obliges him to something beyond this; and here we enter into the whole mystery of the Holy Ghost in the Church. We have seen his outward influence, whereby he gives her perpetuity and increase; now we must attentively consider the inward direction she receives from him, which gives her Unity, Infallibility, and Holines,—prerogatives which, together with Catholicity, designate the true Spouse of Christ.
The union of the Holy Ghost with the Humanity of Jesus is one of the fundamental truths of the mystery of the Incarnation. Our divine Mediator is called "Christ" because of the anointing which he received; and his anointing is the result of his Humanity's being united with the Holy Ghost. This union is indissoluble: eternally will the Word be united to his Humanity; eternally also will the Holy Spirit give to this Humanity the anointing which makes "Christ." Hence it follows that the Church, being the body of Christ, shares in the union existing between its Divine Head and the Holy Ghost. The Christian, too, receives, in Baptism, an anointing by the Holy Ghost, who from that time forward, dwells in him as the pledge of his eternal inheritance; but while the Christian may, by sin, forfeit this union which is the principle of his supernatural life, the Church herself never can lose it. The Holy Ghost is united to the Church forever; it is by him that she exists, acts, and triumphs over all those difficulties to which, by the divine permission, she is exposed while Militant on earth.
St. Augustine thus admirably expresses this doctrine in one of his Sermons for the Feast of Pentecost: "The spirit, by which every man lives, is called the Soul. Now, observe what it is that our Soul does in the body. It is the Soul that gives life to all the members; it sees by the eye, it hears by the ear, it smells by the nose, it speaks by the tongue, it works by the hands, it walks by the feet. It is present to each member, giving life to them all, and to each one its office. It is not the eye that hears, nor the ear and tongue that see, nor the ear and eye that speak; and yet they all live; their functions are varied, their life is one and the same. So is it in the Church of God. In some Saints, she works miracles; in other Saints, she teaches the truth; in others, she practices virginity; in others, she maintains conjugal chastity; she does one thing in one class, and another in another; each individual has his distinct work to do, but there is one and the same life in them all. Now, what the Soul is to the body of man, that the Holy Ghost is to the Body of Christ, which is the Church: the Holy Ghost does in the whole Church, what the soul does in all the members of one body."
Here we have given to us a clear exposition, by means of which we can fully understand the life and workings of the Church. The Church is the Body of Christ, and the Holy Ghost is the principle which gives her life. He is her Soul—not only in that limited sense in which we have already spoken of the Soul of her Church, that is, of her inward existence, and which, after all, is the result of the Holy Spirit's action within her,—but he is also her Soul, in that her whole interior and exterior life, and all her workings, proceed from Him. The Church is undying, because the love, which has led the Holy Ghost to dwell within her, will last forever: and here we have the reason of that Perpetuity of the Church which is the most wonderful spectacle witnessed by the world.
Let us now pass on, and consider that other marvel, which consists in the preservation of Unity in the Church. It is said of her in the Canticle: One is my dove; my perfect one is One. Jesus would have but One, and not many to be his Church, his Spouse: the Holy Ghost will therefore see to the accomplishment of his wish. Let us respectfully follow him in his workings here also. And firstly; is it possible, viewing the thing humanly, that a society should exist for eighteen hundred years and never change? nay, could it have continued all that time, even allowing it to have changed as often as you will? And during these long ages, this society has necessarily had to encounter, and from its own members, the tempests of human passions, which are ever showing themselves, and which not unfrequently play havoc with the grandest institutions. It has always been composed of nations, differing from each other in language, character, and customs; either so far apart as not to know each other, or when neighbors, estranged one from the other by national jealousies and antipathies. And yet, notwithstanding all this—notwithstanding, too, the political revolutions which have made up the history of the world—the Catholic Church has maintained her changeless Unity: one Faith—one visible head—one worship (at least in the essentials)—one mode for the deciding every question, namely, by tradition and authority. Sects have risen up in every age, each sect giving itself out as "the true Church:"they lasted for a while, short or long, according to circumstances, and then were forgotten. Where are now the Arians with their strong political party? Where are the Nestorians, and Eutychians, and Monothelites, with their interminable cavillings? Could anything be imagines more powerless and effete than the Greek Schism, slave either to Sultan or Czar? What is there left of Jansenism, that wore itself away in striving to keep in the Church in spite of the Church? As to Protestantism—the produce of the principle of negation—was it not broken up into sections from its very beginning, so as never to be able to form one society? and is it not now reduced to such straits that it can with difficulty retain dogmas which, at first, it looked upon as fundamental—such as the inspiration of the Scriptures, or the Divinity of Christ?
While all else is change and ruin, our mother the holy Catholic Church, the One Spouse of the Emmanuel, stands forth grand and beautiful in her Unity. But how are we to account for it? Is it that Catholics are of one nature, and Sectarians of another? Orthodox or heterodox, are we not all members of the same human race, subject to the same passions and errors? Whence do the children of the Catholic Church derive that stability which is not affected by time, nor influenced by the variety of national character, nor shaken by those revolutions that have changed dynasties and countries? Only one reasonable explanation can be given—there is a divine element in all this. The Holy Ghost, who is the soul of the Church, acts upon all the members; and as he himself is One, he produces Unity in the Body he animates. He cannot contradict himself: nothing, therefore, subsists by him which is not in union with him.
Tomorrow, we will speak of what the Holy Ghost does for the maintaining Faith, one and unvarying, in the whole body of the Church; let us today limit our considerations to this single point, namely, that the Holy Spirit is the source of external union by voluntary submission to one center of unity. Jesus had said: Thou art Peter, and upon this Rock I will build my Church: now, Peter was to die; the promise, therefore, could not refer to his person only, but to the whole line of his successors, even to the end of the world. How stupendous is not the action of the Holy Ghost, who thus produces a dynasty of spiritual Princes, which has reached its two hundred and fiftieth Pontiff, and is to continue to the last day! No violence is offered to man's free will; the Holy Spirit permits him to attempt what opposition he lists; but the work of God must go forward. A Decius may succeed in causing a four years' vacancy in the See of Rome; anti-popes may arise, supported by popular favor, or upheld by the policy of Emperors; a long schism may render it difficult to know the real Pontiff amidst the several who claim it: the Holy Spirit will allow the trial to have its course and, while it lasts, will keep up the faith of his Children; the day will come when he will declare the lawful Pastor of the Flock, and the whole Church will enthusiastically acknowledge him as such.
In order to understand the whole marvel of this supernatural influence, it is not enough to know the extrinsic results as told us by history; we must study it in its own divine reality. The Unity of the Church is not like that which a conqueror forces upon a people that has become tributary to him. The Members of the Church are united in oneness of faith and submission, because they love the yoke she imposes on their freedom and their reason. But who is it that thus brings human pride to obey? Who is it that makes joy and contentment be felt in a life-long practice of subordination? Who is it that brings man to put his security and happiness in the having no individual views of his own, and in the conforming his judgment to one supreme teaching—and this too in matters where the world chafes at control? It is the Holy Ghost, who works this manifold and permanent miracle, for he it is who gives soul and harmony to the vast aggregate of the Church, and sweetly infuses into all these millions a union of heart and mind which forms for our Lord Jesus Christ his "One" dearest Spouse.
During the days of his mortal life, Jesus prayed his Eternal Father to bless us with Unity: May they be one, as we also are. He prepares us for it, when he calls us to become his Members; but for the achieving this union, he sends his Spirit into the world—that Spirit who is the eternal link between the Father and the Son, and who deigns to accept a temporal Mission among men, in order to create on the earth a Union formed after the type of the Union which is in God himself.
We give thee thanks, O Blessed Spirit! who, by thy dwelling thus within the Church of Christ, inspirest us to love and practice Unity, and suffer every evil rather than break it. Strengthen it within us, and never permit us to deviate from it by even the slightest want of submission. Thou art the soul of the Church; oh! give us to be Members ever docile to thy inspirations, for we could not belong to Jesus who sent thee, unless we belong to the Church, his Spouse and our Mother, whom he redeemed with his Blood, and gave to thee to form and guide.
Next Saturday, the Ordination of Priests and sacred Ministers is to take place throughout the whole Church. The Sacrament of Orders is one of the principal workings of the Holy Ghost, who comes into the souls of those who are presented for Ordination, and impresses upon them, by the Bishop's hands, the character of Priesthood or Deaconship. The Church prescribes a three days' fast and abstinence; with the intention of obtaining from God's mercy that the grace thus given may fructify in those who receive it, and bring a blessing upon the Faithful. This is the first of the three days.
At Rome, the Station is in the Basilica of Saint Mary Major. It was but right that on one of the days of this great Octave, the Faithful should meet together under the protection of the Mother of God, whose sharing in the mystery of Pentecost was both a glory and a blessing to the infant Church.
We will close this day with one of the finest of Adam of Saint Victor's Sequences on the mystery of the Holy Ghost.
Lux jocunda, lux insignis,
Qua de throno missus ignis
In Christi discipulos
Corda replet, linguas ditat,
Ad concordes nos invitat
Linguæ cordis modulos.
The glad and glorious Light—wherewith the heaven-sent Fire filled the hearts of Jesus' Disciples and gave them to speak in diverse tongues—invites us now to sing our hymns with hearts in concord with the voice.
Christus misit quod promisit
Pignus Sponsæ, quam revisit
Die quinquagesima;
Post dulcorem melleum
Petra fudit oleum,
Petra jam firmissima.
On the Fiftieth day, Christ revisited his Spouse, by sending her the pledge he had promised. After tasting the honeyed sweetness, the Rock (Peter), now the firmest of Rocks, pours forth the unction of his preaching.
In tabellis sexeis,
Non in linguis igneis,
Lex de monte populo;
Paucis cordis novitas
Et linguarum unitas,
Datur in Cœnaculo.
The Law, of old, was given on the Mount to the people, but it was written on tablets of stone, and not on fiery tongues: but in the Cenacle, there was given to a chosen few newness of heart and knowledge of all tongues.
O quam felix, quam festiva
Dies, in ua primitiva
Fundatur Ecclesia!
Vivæ sunt primitiæ
Nascentis Ecclesiæ,
Tria primum millia.
O happy, O festive Day, whereon was founded the primitive Church! Three thousand souls!—oh! how vigorous the first-fruits of the but just born Church!
Panes legis primitivi,
Sub una sunt adoptivi
Fide duo populi:
Se duobus interjecit
Sicque duos unum fecit
Lapis, caput anguli.
The two Loaves commanded to be offered in the ancient Law pre-figured the two adopted people now made one; the Stone, the head of the corner, set himself between the two, and made both one.
Utres novi, non vetusti,
Sunt capaces novi musti:
Vasa parat vidua:
Liquorem dat Eliseus:
Nobis sacrum rorem Deus,
Si corda sint congrua.
New wine may not be put in bottles that are old, but in them that are new:—the Widow prepares her vessels, and Eliseus fills them with oil:—so, too, our God gives us his heavenly dew, if our hearts be ready.
Non hoc musto vel liquore,
Non hoc sumus digni rore,
Si discordes moribus.
In obscuris vel divisis,
Non potest hæc Paraclisis
Habitare cordibus.
If our lives be disorderly, we are not fit to receive the Wine, nor Oil, nor Dew. The Paraclete can never dwell in dark or divided hearts.
Consolator alme, veni:
Linguas rege, corda leni:
Nihil fellis ant veneni
Sub tua præsentia.
Nil jocundum, nil amœnum,
Nil salubre, nil serenum,
Nihil dulce, nihil plenum,
Nisi tua gratia.
O dear Comforter, come! govern our tongues, soften our hearts: where thou art, must be no gall or poison. Nothing is joyous, nothing pleasant, nothing wholesome, nothing peaceful, nothing sweet, nothing full, save by thy grace.
Tu lumen es et unguentum,
Tu cœleste condimentum,
Aquæ ditans elementum
Virtute mysterii.
Nova facti creatura,
Te laudamus mente pura,
Gratiæ nunc, sed natura
Prius iræ filii.
Thou art Light and Unction; thou the heavenly Savor that enrichest the element of water with mysterious power. We praise thee with hearts made pure,—we that have been made a New Creature,—we that once, by nature, were children of wrath, but now Children of Grace.
Tu qui dator es et donum,
Tu qui condis omne bonum,
Cor ad laudem redde pronum,
Nostræ linguæ formans sonum
In tua præconia.
Tu nos purga a peccatis,
Auctor ipse puritatis,
Et in Christo renovatis
Da perfect&aelg; novitatis
Plena nobis gaudia!
O thou, the Giver and the Gift. O thou the Creator of all that is good! make our hearts eager to praise thee, and teach our tongues to sound forth thy glory. Do thou, O Author of purity, purify us from sin! Renew us in Christ; and then, give us the full joy of perfect Newness! Amen.
The Gift of Fortitude
The gift of Knowledge has taught us what we must do and what we must avoid in order that we may be such as Jesus, our divine Master, wishes us to be. We now need another gift of the Holy Ghost, from which to draw the energy necessary for our persevering in the way he has pointed out to us. Difficulties we are sure to have; and our need of support is proved enough by the miserable failures we are daily witnessing. This support the Holy Ghost grants us by the gift of Fortitude, which, if we but faithfully use it, will enable us to master every difficulty, yea, will make it easy for us to overcome the obstacles which would impede our onward march.
When difficulties and trials of life come upon him, man is tempted, sometimes to cowardice and discouragement, sometimes to an impetuosity, which arises either from his natural temperament or from pride. These are poor aids to the soul in her spiritual combat. The Holy Ghost, therefore, brings her a new element of strength—it is supernatural Fortitude, which is so peculiarly his gift, that when our Savior instituted the seven Sacraments, he would have one of them be for the special object of giving us the Holy Ghost as a principle of energy. It is evident that having to fight during our whole lives against the devil, the world, and ourselves, we need some better power of resistance than either pusillanimity or daring. We need some gift which will control both our fear and the confidence we are at times inclined to have in ourselves. Thus gifted by the Holy Ghost, man is sure of victory; for grace will supply the deficiencies and correct the impetuosities of nature.
There are two necessities which are ever making themselves felt in the Christian life;—the power of resistance, and the power of endurance. What could we do against the temptations of Satan if the Fortitude of the Holy Spirit did not clad us with heavenly armor and nerve us to the battle? And is not the World, too, a terrible enemy? Have we not reason to dread it when we see how it is every day making victims by the tyranny of its claims and its maxims? What, then, must be the assistance of the Holy Ghost, which is to make us invulnerable to the deadly shafts that are dealing destruction around us?
The passions of the human heart are another obstacle to our salvation and sanctification; they are the more to be feared, because they are within us. It is requisite that the Holy Ghost change our heart, and lead it to deny itself as often as the light of grace points out to us a way other than that which self-love would have us follow. What supernatural Fortitude we need in order to hate our life, as often as our Lord bids us make a sacrifice, or when we have to choose which of the two Masters we will serve. The Holy Spirit is daily working this marvel by means of the Gift of Fortitude: so that, we have but to correspond to the Gift, and not stifle it either by cowardice or indiscretion—and we are strong enough to resist even our domestic enemies. This blessed Gift of Fortitude teaches us to govern our passions and treat them as blind guides; it also teaches us never to follow their instincts, save when they are in harmony with the law of God.
There are times when the Holy Spirit requires from a Christian something beyond interior resistance to the enemies of his soul:—he must make an outward protestation against error and evil, as often as position or duty demands it. On such occasions, one must bear to become unpopular, and console one's self with the words of the Apostle: If I yet pleased men, I should not be the servant of Christ. But the Holy Ghost will be on his side; and finding him resolute in using his Gift of Fortitude, not only will he give him a final triumph, but he generally blesses that soul with a sweet and courageous peace, which is the result and recompense of a duty fulfilled.
Thus does the Holy Ghost apply the gift of Fortitude, when there is question of a Christian's making resistance. But as we have already said, it imparts also the energy necessary for bearing up against the trials, which all must go through who would save their souls. There are certain fears, which damp our courage, and expose us to defeat. The gift of Fortitude dispels them and braces us with such a peaceful confidence that we ourselves are surprised at the change. Look at the Martyrs; not merely at such a one as St. Mauritius, the leader of the Theban Legion, who was accustomed to face danger on the battlefield, but at Felicitas, a mother of seven children, at Perpetua, a high-born lady with everything this world could give her, at Agnes, a girl of thirteen, and at thousands of others like them; and say, if the gift of Fortitude is not a prompter to heroism? Where is the fear of death—that death, the very thought of which is sometimes more than we can bear? And what are we to say of all those lives spent in self-abnegation and privation, with a view to make Jesus their only treasure and be the more closely united with him? What are we to say of those hundreds and thousands of our fellow creatures who shun the sight of a distracted and vain world, and make sacrifice their rule? whose peacefulness is proof against every trial, and whose acceptance of the cross is as untiring as the cross itself is in its visit? What trophies are these of the Spirit of Fortitude! and how magnificent is the devotedness he creates for every possible duty! Oh! truly, man, of himself, is of little worth; but how grand when under the influence of the Holy Ghost!
It is the same Divine Spirit who also gives the Christian courage to withstand the vile temptation of human respect, by raising him above those worldly considerations which would make him disloyal to duty. It is He that leads man to prefer, to every honor this world could bestow, the happiness of never violating the law of his God. It is the Spirit of Fortitude that makes him look upon the reverses of fortune as so many merciful designs of Providence; that consoles him when death bereaves him of those who are dear to him; that cheers him under bodily sufferings, which would be so hard to bear but from his taking them as visits from his heavenly Father. In a word, it is He, as we learn from the Lives of the Saints, that turns the very repugnances of nature into matter for heroic acts, wherein man seems to go beyond the limits of his frail mortality and emulate the impassible and glorified spirits of heaven.
O divine Spirit of Fortitude! take full possession of our souls, and keep us from the effeminacies of the age we live in. Never was there such lack of energy as now, never was the worldly spirit more rife, never was sensuality more unbridled, never were pride and independence more the fashion of the world. So forgotten and unheeded are the maxims of the Gospel, that when we witness the Fortitude of self-restraint and abnegation, we are as surprised as though we beheld a prodigy. O Holy Paraclete! preserve us from this anti-christian spirit, which is so easily imbibed! Suffer us to present to thee, in the form of prayer, the advice given by St. Paul to the Christians of Ephesus: Give us, we beseech thee, "the armor of God, that we may be able to resist in the evil day, and to stand in all things perfect. Gird our reins with truth; arm us with the breastplate of justice; let our feet be shod with the love and practice of the Gospel of peace; give us the shield of Faith, wherewith we may be able to extinguish all the fiery darts of the most wicked one; cover us with the helmet of the hope of salvation; put into our hand the spiritual sword, which is the Word of God," and by which we, as did our Jesus in the Desert, may defeat all our enemies! O Spirit of Fortitude! hear, we beseech thee, and grant our prayer!


enter now his courts with praise.
that Christ has made known to us your wisdom, O Lord.
to glorify you, our God, through Christ.
we seek your promised guidance, Lord God.
we commit ourselves to this endeavour.
together in your purposes in this land in this time.
facing injustice, disunity, violence and death.
in our hearts and our trusting.


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La municipalità regionale di contea di Le Fjord-du-Saguenay è una municipalità regionale di contea del Canada, localizzata nella provincia del Québec, nella regione di Saguenay-Lac-Saint-Jean.

Il suo capoluogo è Saint-Honoré.

Suddivisioni
Municipalità
Bégin
Ferland-et-Boilleau
L'Anse-Saint-Jean
Larouche
Petit-Saguenay
Rivière-Éternité
Saint-Ambroise
Saint-Charles-de-Bourget
Saint-David-de-Falardeau
Saint-Félix-d'Otis
Saint-Fulgence
Saint-Honoré
Parrocchie
Sainte-Rose-du-Nord
Territori non organizzati
Lac-Ministuk
Lalemant
Mont-Valin

Altri progetti

Collegamenti esterni

Le Fjord-du-Saguenay

redpajama_set_name: RedPajamaWikipedia


text:
Home > Opinion > Governor playing partisan role in Arunachal
Governor playing partisan role in Arunachal
Barun Das Gupta22 Dec 2015 10:05 PM GMT
Arunachal Pradesh, the sensitive north-eastern State bordering China, is currently in the throes of a political crisis. The Governor's controversial role in handling – if not actually precipitating – the crisis has reached the Gawhati High Court.
But first a quick look at the series of recent events. On December 17, 33 members of the state Assembly, including 20 from Congress, 11 from opposition BJP and two Independents, removed the Speaker, Nabam Rebia, from his post at a composite session of the Assembly. The composite session' that took place outside the assembly building, in a makeshift venue, with the full knowledge and consent of Governor Jyoti Prasad Rajkhowa.
Deputy Speaker Tenzing Norbu Thongdok presided over the session but abstained from voting. Chief Minister Nabam Tuki and 26 Congress MLAs loyal to the party, did not attend the session. The MLAs present elected Kalikho Pul as the 'Leader of the House. Incidentally, Pul, a senior Congress leader, had resigned from the Tuki cabinet about a year ago, alleging financial irregularities.
The Congress immediately took the matter to the Gauhati High Court. Rebia moved a writ petition challenging the notification issued by the Governor, advancing the Assembly session from January 14, 2016, to December 16, 2015. It was in pursuance of this impugned order of the Governor that the rebels held a parallel House session the following day elsewhere, as the doors of the Assembly had been locked under the orders of the Speaker. Justice Roy of the High Court kept 'in abeyance' the impugned decision passed by the Assembly the previous day and fixed February 1, 2016, as the next date of hearing. Meanwhile, the Governor has threatened to challenge the order of the High Court, without clarifying whether he would approach a division bench of the High Court or go to the Supreme Court. That is how the matter stands now.
As pointed out earlier, the political crisis has been in the making for quite some time. There is no doubt that Chief Minister Tuki had alienated a sizeable section of Congress legislators who took their grievances to the party High Command in Delhi, but without much success. The High Command gave them a patient hearing but did not disturb Tuki. The Congress president summoned Tuki but what transpired between them is not known. The rebel Congress MLAs felt frustrated.
The charge against Tuki is that he is encouraging and indulging in corruption. Most of the top jobs in the administration have gone to his relations or cronies. The State's revenue has fallen. The crime has graph risen, resulting in a sharp drop in the number of tourists in a State which promotes tourism as a major revenue earner.
Meanwhile, as dissidence against Tuki rose, six Cabinet ministers criticized him for his alleged misgovernance. Five of them were sacked in mid-October. Three political heavyweights, heading three State sector corporations, also resigned. They were Techi Lama, Tani Loffa and Toko Anil who headed the Monitoring and Vigilance Committee.
New Delhi was keenly watching the crisis brewing in Arunachal and the growing dissidence against Chief Minister Tuki. The BJP-led Centre decided to strike. It chose Jyoti Prasad Rajkhowa, a 1968-batch IAS officer who retired as Chief Secretary of Assam, to be the key actor in Operation Topple Tuki. The appointment of Rajkhowa as Governor of Arunachal Pradesh in June surprised many except those who knew his proximity to the BJP leadership.
His career as an administrator was undistinguished. For some time during the 1979-85 Assam agitation, which had a strong secessionist trend in it, Rajkhowa was the district head or Deputy Commissioner of Kamrup. It surprised many then that as a government servant he did not try to conceal his support and sympathy for the movement.
After Rajkhowa entered Raj Bhavan at Itanagar as its new tenant (his predecessor, Nirbhay Sharma, was quietly dispatched to Mizoram) things started moving quickly in Arunachal Pradesh. The suborning of dissident Congress MLAs began in right earnest. Congress dissidents and BJP legislators formed an unannounced united front for Operation Topple Tuki.
Acting in close concert with the legislators in the anti-Tuki camp (both Congress and BJP), the Governor advanced the scheduled date of the Assembly session and, when the Speaker locked the House, blessed the holding of the session in a 'makeshift' Assembly outside the precincts of the Assembly building.
In his writ petition before the Gauhati High Court, Chief Minister Tuki has challenged the impugned order of the Governor as being violative of Articles 174 and 175 of the Constitution. The ball is now literally in the court. It remains to be seen at whose door the Governor knocks next – a division bench of the Gauhati High Court or the Supreme Court.
Whatever the denouement, the recent political developments in Arunachal Pradesh have sent a strong message to 24 Akbar Road – be more responsive to and more accommodative of dissidents in the party. Don't allow dissidence to snowball.
(The views expressed are strictly personal)
Barun Das Gupta

redpajama_set_name: RedPajamaCommonCrawl


• Wetted surface 26.8 sq.ft.
The Prospector models built by the Chestnut Canoe Company were made in lengths from 12 to 18 ft. filling a need for a canoe with greater carrying capacity than the Pleasure and Cruiser models but not as large as the Freight canoes.
This model, the 15' 'Ranger' is a sweet shape and Ron Frenette of Canadian Canoes decided we should have it in our catalogue. It has the same end shape and highly rockered hull of our 16' Prospector. With a flattened shallow arch bottom and full ends, the Ranger is stable, strong and a good load carrier. If you are looking for a canoe in the fifteen foot range with some history and good all round paddling characteristics, this might be the one you are looking for.
Lines taken and drawn by Steve Killing for Ron Frenette, Canadian Canoes Ltd.


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As the holidays roll on, we took Lyla to a couple of holiday parties Friday. The first was at Uncle Arthur's office. Lyla had fun playing with the other kids there and showing Uncle Arthur how to revise his fiscal strategies to increase returns on investments. She also liked drawing with crayons and having a snack.
After partying in mid-town, we headed downtown for dinner. Lyla enjoyed a grilled cheese sandwich at Soup N' Burger. Dinner became a stalling tactic between parties before we headed down to the Muppet Workshop for their holiday party.
Lyla quickly discovered where her muppet friends were hanging out. She was thrilled to spend some time exchanging hugs, kisses and tickles with Ernie, Telly and Oscar (or Grouch as she calls him). Within a couple of hours, Lyla was a pro, showing everyone where the muppets were. She was a little disappointed she didn't get to meet Elmo, but was thrilled to celebrate with the muppets in attendance.
I can't believe it's actually been a month since the last post! Since then we've been to Massachusetts for Thanksgiving. I don't have quite so many pictures as I thought I had, but if you check out the latest gallery you can see some of the family at Aunt Emmy's house on Thanksgiving and at my mom's house the Saturday after. Lyla loved hanging out and playing with all of her family. She was glad to finally be able to tell everyone that she's going to be a big sister in June, too.
Back home in Astoria, we got ready for Hannukah as I started frying up 12 pounds of potatoes and onions who were willing to sacrifice themselves to the glory of latkes! We had a smaller Hannukah party this year, but were happy to have a close group of friends come and celebrate the holiday with us. Lyla really liked the potato latkes and seems to have made the bold choice of apple sauce over sour cream.
We've been lighting our Hannukiah (Hannukah menorah) every night and Lyla loves it! As soon as we say, "it's time for the lights!" she points to the menorah and gets ready for me to light them and Erin and I sing the blessings over the candles. Then we sit together and open presents. Lyla likes to hand presents to Mamma and Dadda, regardless of who they belong to and then help open everyone's presents. She's had plenty of presents between her parents, her Mima and her cousin Arlyne.
Lyla also experienced her first big "owie" as she was running around with daddy, she missed a step and face planted into the dining room floor. Ow! She bounced back remarkably well and actually seemed to enjoy dunking her pacifiers in a bowl of ice water to try and keep the swelling down from her split lip. You might be able to notice the swelled lip in this picture. Of course, later in the day, she was still quick to play her favorite chase/run away from Daddy game. We happened to have a doctor's appointment for her follow-up flu shot and the doctor checked out her lip and said all would be well soon enough, but she might prefer soft, mushy food for a little while.
That's it for now, but we're heading into Christmas in Wisconsin and the New Year in Astoria, so we'll have more in the New Year! Happy Holidays to all of our friends and family and we hope you have a very happy 2008!
At Lyla's recent doctor's appointment, the doctor asked how many words Lyla can say. We said about "a ton... about a half a million". The doctor then asked if she said more than 10 words. We assured him that she does. Later, Erin decided to count up how many words she actually has in her vocabulary. The tally came to over 50!! She also loves to pick up the phone and say, "hello". I'm dead when she's a teenager.
I wanted to take this chance to point out that those of you who read this blog are no longer mere recipients of Lyla's life. You can be an active part by posting comments! Click the "comments" link below each blog post and type away!


Thanks for sharing, CA. Matt does a great job of breaking it all down.
L8U obviously changed the offensive count in a vain attempt to slow Bama down.
Maybe they did change the count or cadence, but the players seemed to get awful excited when an OL was called for a false start. Made me think they were being drawn offsides.
I'll have to watch it again, but on the Tua run, it's true Irv broke open in the middle of the field. But I think Tua had made the decision to run the instant before that happened. Just another second, and I'm sure he would have saw him.
Yep. Tua wasn't in a spot to make the throw by the time Irv was clearly open. He would have had to throw on the run without planting his feet. If he tried to plant and squareup, the DL would have gotten him.
it looked like on the first td to ruggs, that najee would have had a pretty much open run to the end zone had he been given the ball. he is really hard to bring down once he gets past the line.
In addition, we also knew they were doing nothing but trying to pass to put up at least one score to get the goose egg off the board. So our guys were just pinning their ears back. They smelled blood in the water!
I bet 1/3 of their total offense for the game occurred on the last couple of drives when one of them ended by the missed short fg attempt.
Probably closer to 1/2 of their total offense. They had 67 at halftime IIRC and they did nothing in the 3rd qtr.
I'll take Ruggs 1v1 on a DB over Najee breaking through 2 layers defenders even with big gaps. The numbers matchup is just better on that 1st read IMO.
[/B]Probably closer to 1/2 of their total offense. They had 67 at halftime IIRC and they did nothing in the 3rd qtr.
The missed FG drive started with 1:41 left in the third quarter. It went for 64 yards. The last drive went for 63 yards. 127 of their yards came on the last two drives.
Really love the Matt Wyatt film studies. The guy knows his football.
Quinnen Williams is an alien. No human can beat double teams consistently. He's absolutely amazing. I don't know where Quinnen is on the NFL draft boards, but if I were an NFL GM he be at the top of my list.


text:
El taller F. Arthur Uebel
Sistema alemán
Sistema francés
Artistas>
Xiaoting Ma
PrevEugene Mondie
Boja KraguljNext
Xiaoting Ma, actualmente es profesora adjunta de clarinete en la Universidad de Soochow Music College en China.
A versatile clarinetist and champion of music from the past, present, and future, Dr. Ma has developed an international reputation as a virtuosic and prolific soloist, chamber musician and orchestral player. Ma was awarded first prize in the Northern Illinois University Concerto Competition and was a winner of the Yale Chamber Music Competition. She is also the recipient of numerous awards, including Jiangsu Provence Entrepreneur Innovation Award, Wilbur Smith Clarinet Scholarship, Northern Illinois University Graduate Woodwind Quintet Scholarship and Graduate Fellowship and Shanghai Conservatory of Music People's Academic Scholarship. Dr. Ma was featured as soloist on the Copland Concerto with the Northern Illinois Philharmonic Orchestra, and also performed as a soloist on the E-flat clarinet with the Clarinet Cornucopia Choir Ensemble. She has also appeared in concerts at festivals and societies, including the Stony Brook University Staller Center, the Yale Center for British Art, the International Ensemble Modern Academy, the Klangspuren Festival in Austria, the Clarinet Festival at Griffith University in Australia, the international Clarinet Festival in Beijing and Chongqing, Shanghai New Music Week, the International Workshop on Computer Music and Audio Technology in Taiwan and The 6th Shenyang Musical Cultural Exchange Between China and Foreign Countries. She has collaborated with distinguished artists and ensembles such as Andreas Ottensamer, David Shifrin, Alan Kay, Gil Kalish, members of the Emerson Quartet and the Tokyo Quartet. Dr. Ma was the second / E-flat and bass clarinetist of the Shanghai Philharmonic Orchestra, appointed by Music Director Zuo-Huang Chen. In addition, she also performed as a guest clarinetist with the New Britain Symphony Orchestra, Connecticut Virtuosi Chamber Orchestra, Shenzhen Symphony Orchestra and Shanghai Radio Symphony Orchestra, Suzhou Symphony Orchestra, Macao Orchestra, Hong Kong Philharmonic Orchestra and Shanghai Contemporary Music Ensemble. Dr. Ma's multifaceted career has taken her through the United States, China, Australia, Austria and Italy. Dr. Ma earned a Doctor of Musical Arts Degree from the State University of New York at Stony Brook, an Artist Diploma from Yale School of Music, a Master of Music Degree from Northern Illinois University, and a Bachelor of Music Degree from Shanghai Conservatory of Music. She is an Assistant Professor of Clarinet at Soochow University School of Music, an Uebel artist since 2019 and a Légère Artist. Her primary teachers include Gregory Barrett, Alan Kay, David Shifrin, Ran Tao and Zengmao Zhao.
F. Arthur Uebel GmbH
Tel.: +49 37422 401 972
Web: www.uebel-klarinetten.de
E-Mail: info@uebel-klarinetten.de


text:
\section{Introduction}
Graphs in this paper are simple and finite.  The vertex set of a graph $G$ is denoted by $V(G)$, and the edge set by $E(G)$.
A signed graph $(G,\sigma)$ is a graph $G$ and a function $\sigma : E(G) \rightarrow \{ \pm 1 \}$,
which is called a signature of $G$. The set $N_{\sigma} = \{e : \sigma(e) = -1\}$ is the set of negative edges of $(G,\sigma)$ and
$E(G) - N_{\sigma}$ the set of positive edges. For $v \in V(G)$, let $E(v)$ be the set of edges which are incident to $v$.
A switching at $v$ defines a graph $(G,\sigma')$ with $\sigma'(e) = -\sigma(e)$ for $e \in E(v)$ and $\sigma'(e) = \sigma(e)$ otherwise.
Two signed graphs $(G,\sigma)$ and $(G,\sigma^*)$ are {\em equivalent} if they can be obtained from each other by a sequence of switchings. We also say that
$\sigma$ and $\sigma^*$ are equivalent signatures of $G$.

A circuit in $(G,\sigma)$ is balanced, if it contains an even number of negative edges; otherwise it is unbalanced. The graph
$(G,\sigma)$ is unbalanced, if it contains an unbalanced circuit; otherwise $(G,\sigma)$ is balanced.
It is well known (see e.g.~\cite{Raspaud_Zhu_2011})
that $(G,\sigma)$ is balanced if and only if it is equivalent to the signed graph with no negative edges, and $(G,\sigma)$ is antibalanced if
it is equivalent to the signed graph with no positive edges.
Note, that a balanced bipartite graph is also antibalanced. The underlying unsigned graph of $(G,\sigma)$ is denoted by $G$.

In the 1980s Zaslavsky \cite{Zaslavsky_1982, Zaslavsky_1982_2, Zaslavsky_1984} started studying vertex colorings of signed graphs.
The natural constraints for a coloring $c$ of a signed graph $(G,\sigma)$ are, that (1) $c(v) \not= \sigma(e) c(w)$ for each edge $e=vw$,
and (2) that the colors can be inverted under switching, i.e.~equivalent signed graphs have the same chromatic number.
In order to guarantee these properties of a coloring, Zaslavsky \cite{Zaslavsky_1982} used the set $\{-k, \dots, 0, \dots ,k\}$ of $2k+1$ "signed colors" and studied the
interplay between colorings and zero-free colorings through the chromatic polynomial.

Recently, M\'a\v{c}ajov\'a, Raspaud, and \v{S}koviera \cite{MRS_2014}
modified this approach. If $n = 2k+1$, then let $M_n = \{0, \pm 1, \dots,\pm k\}$, and
if  $n = 2k$, then let $M_n = \{\pm 1, \dots,\pm k\}$.
A mapping $c$ from $V(G)$ to $M_n$ is a {\em signed $n$-coloring} of $(G,\sigma)$, if $c(v) \not= \sigma(e) c(w)$ for each edge $e=vw$.
They  define $\chi_{\pm}((G,\sigma))$ to be the smallest number $n$ such that $(G,\sigma)$ has a signed $n$-coloring.
We also say that $(G,\sigma)$ is {\em signed $n$-chromatic}.

In \cite{KS_2015} we study circular coloring of signed graphs. The related integer $k$-coloring of a signed graph $(G,\sigma)$ is defined as follows.
Let $\mathbb{Z}_k$ denote the cyclic group of integers modulo $k$, and the inverse of an element $x$ is denoted by $-x$.
A function $c : V(G) \rightarrow \mathbb{Z}_k$ is a $k$-coloring of $(G,\sigma)$ if $c(v) \not= \sigma(e) c(w)$ for each edge $e=vw$. Clearly,
such colorings satisfy the constrains (1) and (2) of a vertex coloring of signed graphs.
The {\em chromatic number} of a signed graph $(G,\sigma)$ is the smallest $k$ such that $(G,\sigma)$ has a $k$-coloring.
We also say that $(G,\sigma)$ is {\em $k$-chromatic}.

The following proposition describes the relation between these two coloring parameters for signed graphs.

\begin{proposition} [\cite{KS_2015}] \label{pm}
If $(G,\sigma)$ is a signed graph, then $\chi_{\pm}((G,\sigma)) - 1 \leq \chi((G,\sigma)) \leq \chi_{\pm}((G,\sigma)) + 1$.
\end{proposition}

Let $G$ be a graph and $\Sigma(G)$ be the set of pairwise non-equivalent signatures on $G$.

The {\em chromatic spectrum} of $G$ is the set $\{\chi((G,\sigma))\colon\ \sigma \in \Sigma(G)\}$, which is denoted by $\Sigma_{\chi}(G)$.
Analogously,
{\em signed chromatic spectrum} of $G$ is the set $\{\chi_{\pm}((G,\sigma))\colon\ \sigma \in \Sigma(G)\}$. It is denoted by $\Sigma_{\chi_{\pm}}(G)$.
 Let $M_{\chi}(G) = \max\{\chi((G,\sigma))\colon\ \sigma \in \Sigma(G)\}$ and $m_{\chi}(G) = \min\{\chi((G,\sigma))\colon\ \sigma \in \Sigma(G)\}$.
Analogously, $M_{\chi_{\pm}}(G) = \max\{\chi_{\pm}((G,\sigma))\colon\ \sigma \in \Sigma(G)\}$ and $m_{\chi_{\pm}}(G) = \min\{\chi_{\pm}((G,\sigma))\colon\ \sigma \in \Sigma(G)\}$.

The following theorems are our main results.

\begin{theorem} \label{cs}
If $G$ is a graph, then $\Sigma_{\chi}(G) = \{ k : m_{\chi}(G) \leq k \leq M_{\chi}(G)\}$.
\end{theorem}

\begin{theorem} \label{cs_pm}
If $G$ is a graph, then $\Sigma_{\chi_{\pm}}(G) = \{k : m_{\chi_{\pm}}(G) \leq k \leq M_{\pm}(G)\}$.
\end{theorem}

Theorems \ref{cs} and \ref{cs_pm} will be proved in Sections \ref{chrom_spec} and \ref{sig_chrom_spec}, respectively.

\section{The chromatic spectrum of a graph}  \label{chrom_spec}

We start with the determination of $m_{\chi}(G)$.

\begin{proposition} \label{bipartite}
	Let $G$ be a nonempty graph. The following statements hold.
	\begin{enumerate}
		\item $\Sigma_{\chi}(G) = \{1\}$ if and only if $m_{\chi}(G) = 1$ if and only if $E(G)= \emptyset$.
		\item if $E(G) \not = \emptyset$, then
		$\Sigma_{\chi}(G) = \{2\}$ if and only if $m_{\chi}(G) = 2$ if and only if $G$ is bipartite.
		\item If $G$ is not bipartite, then $m_{\chi}(G) = 3$.
	\end{enumerate}
\end{proposition}

\begin{proof}
Statements 1. and 2. are obvious. For statement 3 consider $(G,\sigma)$ where $\sigma$ is the signature with all edges negative.
Then $c : V(G) \rightarrow \mathbb{Z}_3$ with $c(v)=1$ is a 3-coloring of $G$. Since
$G$ is not bipartite the statement follows with statements 1. and 2.
\end{proof}

If $(G,\sigma)$ is a signed graph and $u \in V(G)$, then $\sigma_u$ denotes the restriction of $\sigma$ to $G-u$.
A $k$-chromatic graph $(G,\sigma)$ is {\em $k$-chromatic critical} if $\chi((G-u,\sigma_u)) < k$,  for every $u \in V(G)$.
In the following proposition, we will give some basic facts on $k$-chromatic critical graphs.
The complete graph on $n$ vertices is denoted by $K_n$.

\begin{proposition}\label{basic_p}
Let $(G,\sigma)$ be a signed graph.
\begin{enumerate}
	\item $(G,\sigma)$ is 1-critical if and only if $G = K_1$
	\item $(G,\sigma)$ is 2-critical if and only if $G = K_2$.
	\item $(G,\sigma)$ is 3-critical if and only if $G$ is an odd circuit.
\end{enumerate}
\end{proposition}
\begin{proof}
Statements 1. and 2. are obvious. An odd circuit with any signature is 3-critical. For the other direction let $G$ be a 3-critical graph.
Note, that  (*) $G-u$ is bipartite for every $u \in V(G)$ by Lemma \ref{bipartite}.
Since $G$ is not bipartite it follows that every vertex of $G$ is contained in all odd circuits of $G$,
and by (*) every odd circuit $C$ is hamiltonian. $C$ cannot contain a chord, since for otherwise $G$ contains a non-hamiltonian odd circuit,
a contradiction.
Hence, $G$ is an odd circuit.

\end{proof}

\begin{lemma}\label{lem_remove'}
Let $k \geq 1$ be an integer. If $(G,\sigma)$ is $k$-chromatic, then $\chi((G-u,\sigma_u))\in \{k,k-1\}$, for every $u \in V(G)$. In particular,
if $(G,\sigma)$ is $k$-critical, then $\chi((G-u,\sigma_u)) = k-1$.
\end{lemma}

\begin{proof}
For $k\in \{1,2\}$, the statement follows with Proposition \ref{bipartite}. Hence, we may assume that $k\geq3$.
Clearly, $\chi((G-u,\sigma_u)) \leq \chi((G,\sigma)) = k$.
Suppose to the contrary that $\chi((G-u,\sigma_u))\leq k-2$, and
let $\phi$ be a $(k-2)$-coloring of $(G-u,\sigma_u)$.
We extend $\phi$ to a $(k-1)$-coloring of $(G,\sigma)$.
If $k$ is odd, then change color $x$ to $x+1$ for each $x\geq \frac{k-1}{2}$ and assign color $\frac{k-1}{2}$ to vertex $u$, and we are done.
If $k$ is even, then change color $x$ to $x+1$ for each $x\geq \frac{k}{2}$, and assign color $\frac{k}{2}$ to vertex $u$.
If $\phi(v)=\frac{k-2}{2}$ for a vertex $v$ and $\sigma(uv)=-1$, then recolor $v$ with color $\frac{k}{2}$ to obtain
a $(k-1)$-coloring of $(G,\sigma)$. Hence $\chi((G,\sigma)) \leq k-1 < k$, a contradiction.
Clearly, if $(G,\sigma)$ is $k$-critical, then $\chi((G-u,\sigma_u)) = k-1$.
\end{proof}

The following statements are direct consequence of Lemma \ref{lem_remove'}.

\begin{theorem} \label{critical}
Let $(G,\sigma)$ be a signed graph and $k \geq 1$. If $\chi((G,\sigma)) = k$, then
$(G,\sigma)$ contains an induced $i$-critical subgraph for each $i \in \{1, \dots,k\}$.
\end{theorem}

\begin{lemma}\label{lem_subgraph_reachable'}
Let $k \geq 3$ be an integer and $H$ be an induced subgraph of a graph $G$. If $k \in {\Sigma_{\chi}(H)}$, then $k\in{\Sigma_{\chi}(G)}$.
\end{lemma}

\begin{proof}
If $k\in{\Sigma_{\chi}(H)}$, then there is a signature $\sigma$ of $H$ such that $\chi((H,\sigma))=k$. Let
$\phi$ be a $k$-coloring of $(H,\sigma)$. Define a signature $\sigma'$ of $G$ as follows. Let $e \in E(G)$ with $e=uv$.

If $e\in E(H)$, then $\sigma'(e)=\sigma(e)$,

if $u,v\notin V(H)$ or if  $u\in V(H), v\notin V(H)$ and $\phi(u)=1$, then $\sigma'(e)=-1$,

if $u\in V(H), v\notin V(H)$ and $\phi(u)\neq 1$, then $\sigma'(e)=1$.

	It follows that $\phi$ can be extended to a $k$-coloring of $(G,\sigma')$ by assigning color 1 to each vertex of $V(G)\setminus V(H)$.
	Thus $\chi((G,\sigma'))\leq k$.
	Moreover, $(G,\sigma')$ has $(H,\sigma)$ as a subgraph with chromatic number $k$, hence, $\chi((G,\sigma'))\geq k$.
	Therefore, $\chi((G,\sigma'))=k$ and thus, $k\in{\Sigma_{\chi}(G)}$.
\end{proof}

\begin{theorem} \label{thm_reachable'}
Let $k \geq 4$ be an integer and $G$ be a graph. If $k\in{\Sigma_{\chi}(G)}$, then $k-1\in{\Sigma_{\chi}(G)}$.
\end{theorem}

\begin{proof}
By Theorem \ref{critical}, $(G,\sigma)$ contains an induced $k$-critical subgraph $(H,\sigma')$, where $\sigma'$ is the restriction of
$\sigma$ to $H$. Since $k \geq 4$, it follows that $|V(H)| > 3$. Hence, there is $u \in V(H)$ such that $\chi(H-u,\sigma'_u)= k-1$.
Furthermore, $H-u$ is an induced subgraph of $G$.
Thus,  $k-1\in{\Sigma_{\chi}(H-u)}$, and hence, $k-1\in{\Sigma_{\chi}(G)}$ by Lemma \ref{lem_subgraph_reachable'}.

Note that if $k=3$, then by Proposition \ref{bipartite}, $G$ is not a bipartite graph and thus $k$ can not be decreased to 2.
\end{proof}

Theorem \ref{cs} follows from Proposition \ref{bipartite} and Theorem \ref{thm_reachable'}.

\section{The signed chromatic spectrum of a graph} \label{sig_chrom_spec}

\begin{proposition} \label{char_pm_color}
Let $G$ be a nonempty graph. The following statements hold.
\begin{enumerate}
\item $\Sigma_{\chi_{\pm}}(G) = \{1\}$ if and only if $E(G)= \emptyset$.
\item if $E(G) \not = \emptyset$, then $m_{\chi_{\pm}}(G) = 2$.
\end{enumerate}
\end{proposition}

\begin{proof}
Statement 1. is obvious. For statement 2, since $G$ has at least one edge it can not be colored by using only one color,  hence $m_{\chi_{\pm}}(G) = 2$.
\end{proof}

A signed $k$-chromatic graph $(G,\sigma)$ is {\em signed $k$-chromatic critical} if $\chi_{\pm}((G-u,\sigma_u)) < k$,  for every $u \in V(G)$.
In  \cite{Stiebitz_2015} Schweser and Stiebitz defined a graph $(G,\sigma)$ to be critical with respect to $\chi_{\pm}$ if
$\chi_{\pm}((H,\sigma')) < \chi_{\pm}((G,\sigma))$ for every proper signed subgraph $(H,\sigma')$ of $(G,\sigma)$, where $\sigma'$ is the restriction of $\sigma$ to $E(H)$.
However, for trees and circuits the two definitions coincide.
The analog statement to Proposition \ref{basic_p} for signed colorings is due to Schweser and Stiebitz in \cite{Stiebitz_2015}.

\begin{proposition}  [\cite{Stiebitz_2015}]  \label{basic_p'}
Let $(G,\sigma)$ be a signed graph.
\begin{enumerate}
		\item $(G,\sigma)$ is signed 1-critical if and only if $G = K_1$
		\item $(G,\sigma)$ is signed 2-critical if and only if $G = K_2$.
		\item $(G,\sigma)$ is signed 3-critical if and only if $G$ is a balanced odd circuit or an unbalanced even circuit.
	\end{enumerate}
\end{proposition}

\begin{lemma}\label{lem_remove}
Let $k \geq 1$ be an integer. If $(G,\sigma)$ is signed $k$-chromatic, then $\chi_{\pm}((G-u,\sigma_u))\in \{k,k-1\}$, for every $u \in V(G)$. In particular,
if $(G,\sigma)$ is signed $k$-critical, then $\chi_{\pm}((G-u,\sigma_u)) = k-1$.
\end{lemma}

\begin{proof}
For $k\in \{1,2\}$, the statement follows with Proposition \ref{char_pm_color}. Hence, we may assume that $k\geq3$.
Clearly, $\chi_{\pm}((G-u,\sigma_u)) \leq \chi_{\pm}((G,\sigma)) = k$.
Suppose to the contrary that $\chi_{\pm}((G-u,\sigma_u))\leq k-2$ and let $\phi$ be a
$(k-2)$-coloring of $(G-u,\sigma_u)$.
We shall extend $\phi$ to a $(k-1)$-coloring of $(G,\sigma)$.
If $k$ is even, then assign color 0 to vertex $u$, we are done.
If $k$ is odd, then assign color $\frac{k-1}{2}$ to vertex $u$, and for each vertex $v$ such that $\phi(v)=0$ and $\sigma(uv)=-1$, recolor $v$ with color $\frac{k-1}{2}$, and for each vertex $v$ such that $\phi(v)=0$ and $\sigma(uv)=1$, recolor $v$ with color $-\frac{k-1}{2}$ to obtain a $(k-1)$-coloring of $(G,\sigma)$.
Hence $\chi_{\pm}((G,\sigma))\leq k-1<k$, a contradiction. Clearly, if $(G,\sigma)$ is signed $k$-critical, then $\chi_{\pm}((G-u,\sigma_u))=k-1$.
\end{proof}

\begin{theorem} \label{s_critical}
	Let $(G,\sigma)$ be a signed graph and $k \geq 1$. If $\chi_{\pm}((G,\sigma)) = k$, then
	$(G,\sigma)$ contains an induced signed $i$-critical subgraph for each $i \in \{1, \dots,k\}$.
\end{theorem}

\begin{lemma}\label{lem_subgraph_reachable}
	Let $k\geq 2$ be an integer and $H$ be an induced subgraph of a graph $G$. If $k\in \Sigma_{\chi_{\pm}}(H)$, then $k\in \Sigma_{\chi_{\pm}}(G)$.
\end{lemma}
The proof is similar to the proof of Lemma \ref{lem_subgraph_reachable'}.

\begin{theorem} \label{thm_reachable}
Let $k\geq3$ be an integer and $G$ be a graph. If $k\in \Sigma_{\chi_{\pm}}(G)$, then $k-1\in \Sigma_{\chi_{\pm}}(G)$.
\end{theorem}

\begin{proof}

By Theorem \ref{s_critical}, $(G,\sigma)$ contains an induced signed $k$-critical subgraph $(H,\sigma')$, where $\sigma'$ is the restriction of
$\sigma$ to $H$. Since $k \geq 3$, it follows that $|V(H)| \geq 3$. Hence, there is $u \in V(H)$ such that $\chi_{\pm}(H-u,\sigma'_u)= k-1$.
Furthermore, $H-u$ is an induced subgraph of $G$.
Thus,  $k-1\in{\Sigma_{\chi_{\pm}}(H-u)}$, and hence, $k-1\in{\Sigma_{\chi_{\pm}}(G)}$ by Lemma \ref{lem_subgraph_reachable}.
\end{proof}

Theorem \ref{cs_pm} follows from Proposition \ref{char_pm_color} and Theorem \ref{thm_reachable}.

redpajama_set_name: RedPajamaArXiv


text:
De mantel (pallium) is het dorsale lichaamsoppervlak bij weekdieren. Dit fungeert ten dele als een soort huid, maar vervult afhankelijk van de groep van weekdieren verschillende functies. In de mantel zit de mantelholte, die de kamvormige kieuwen bevat en de ademhaling verzorgt. De mantel dient als bescherming door de slijmcellen en speelt een grote rol bij de voortbeweging bij slakken, de mantel produceert het skelet bij vrijwel alle weekdieren en zorgt voor de opname van voedsel bij tweekleppigen. Bij sommige weekdieren wordt de mantel ook gebruikt voor de voortbeweging, maar veel soorten verplaatsen zich met de voet.

Aan de buitenzijde van de mantel zijn cellen aanwezig die bij de meeste soorten een hard pantser aanmaken, de schelp.

Anatomie van weekdieren


text:
Q: Ratio in first quarter of transformed sine graph Take a standard sine graph with a period of $4$ such that the first peak is at $x = 1$. Take also the graph $y = x$. Take also a line $y = c - x$.

*

*What is the value of $c$ such that the graph it is part of passes through both other graphs and is perpendicular to both at their respective intersections (points $A$ and $B$ for the $\sin$ graph and $y = x$ graph respectively)?

*What is the ratio between the distance $(0, 0)$ to $(1, 1)$ and $AB$?

Thanks for any help.

A: Since the line $y=c-x$ is always orthogonal to $y=x$, the problem reduce to find $c$ such that the line $y=x$ passes through the points $(x_P,y_P)$ of the function $y=\sin(\frac{\pi}{2}x)$ where the slope of the tangent is $m=y'(x_P)=1$.
we have:
$$y'=\frac{\pi}{2}\cos(\frac{\pi}{2}x)=1  $$
so, in the period $[0,4]$ we have the two solutions:
$$x_P=\frac{2}{\pi}\cos^{-1}\left(\frac{2}{\pi}\right)$$
$$
x_{P'}=4-\frac{2}{\pi}\cos^{-1}\left(\frac{2}{\pi}\right)
$$
as you can see in the figure.

From these we can find the value of $c$ for the lines $y=c-x$ that passes through these points (the red lines in the figure).

redpajama_set_name: RedPajamaStackExchange


text:
First NART Spyder to be Auctioned
By VR Staff on	 July 1, 2005 2005, July '05, News–Racecar, North America, Region, Vintage Racecar Archives, Vintage Racecar Articles
Gooding and Company will be offering the first 275 GTS/4 Ferrari built during its August 21 auction following the Pebble Beach Concours d'Elegance.
This Ferrari, carrying serial number 09437, was the brainchild of Luigi Chinetti, Snr., the American Ferrari distributor and New York City dealer whose North American Racing Team activities lent these cars their NART designation.
This car, the prototype, is one of two built with alloy bodies while the 3rd and 4th examples were crafted with all-steel bodies. All four bodies were constructed individually by Scaglietti but the final six cars, also steel bodied, were converted to Spyders from coupe bodywork.
This first NART Spyder, completed in January, 1967 was delivered to Chinetti Motors the following month. Meanwhile, motoring writer and racecar driver Denise McCluggage had approached Chinetti for a car to drive in the Sebring 12-hour that year. She and co-driver Marianne "Pinkie" Rollo were offered this car by Luigi Chinetti. Seven Ferraris took the green flag at Sebring but only one finished; the McCluggage/Rollo NART Spyder scoring a very creditable 2nd place in the GT class and 17th overall. This victory would mark the only time a NART Spyder was raced in contemporary competition.
1947 Rolls-Royce Silver Wraith by Inskip (1 of 2)
The Silver Wraith presented here is an extraordinary Rolls-Royce, and it should come as no surprise that its first owner…


text:
The Pixel Painter: Art making is accessible to everyone
by wolfejg | Jun 13, 2019 | TLT
The Pixel Painter from The Pixel Painter on Vimeo.
As an instructional technologist and digital artist, I've taught people of all ages how to be creative with computer software. I see no distinction between using a mouse, crayon or sculptor's chisel to make something new. Technology need not replace older art making tools, and digital art has its own aesthetic that can be appreciated alongside traditional media like painting, sculpture and printmaking.
Computers and assistive devices can also make creation possible for those with physical impairments who might not otherwise be able to use handheld tools. Influential guitarist Jason Becker has had ALS for 30 years, yet he continues to compose music digitally and communicate via a custom eye-tracking system. He released his latest album Triumphant Hearts in 2018 to critical acclaim.
To illustrate the power of digital literacy and the idea that art should be accessible to everyone, I highly recommend watching The Pixel Painter. Below is a description of the artist depicted in the short film:
Pixel by Pixel. That's how Hal Lasko made his masterpieces. Each one, tediously and lovingly crafted on Microsoft Paint, some taking hundreds of hours to complete. "Grandpa Hal", as he was better known, did all of his work despite suffering from wet macular degeneration, an age-related, chronic eye disease which severely limited the center of his field of vision. It was a formidable handicap for anyone, but especially someone who'd made a living off his artist's eye.
Long before age began to take its toll on Lasko, he'd enjoyed a successful career as an artist. He started out as a graphic designer, working in the military during World War II drafting maps and eventually retired from American Greetings in the 1970s. Throughout it all he would paint at home to satisfy his artistic urges, but the older Lasko got, the harder it became for him to paint. That all changed for Hal when his family gave him a computer as an 85th birthday present. His new PC came loaded with Microsoft Paint software, a program developed in the 1980's. In today's "Age of the iPad", the program is more kitsch than cutting edge, but its easy interface and pixel precision allowed Lasko to journey down a new artistic path with a style many consider "retro cool".
In his last year of life, Hal sold his first piece of artwork, had international gallery showings and was featured in Microsoft's 2013 Super Bowl commercial. He passed away just shy of his 99th birthday in 2014, leaving us with a legacy that passion knows no age, and for Hal, the proof of that is surely in the pixels.
– Jack Wolfe, Instructional Technologist


Twice a year, the inner precincts of the Imperial Palace are opened to the general public, who turn up in a flag-waving mass to catch a glimpse of the Emperor and his family. If you missed out on the Emperor's birthday on December 23, you can head there on January 2 instead to receive a customary New Year greeting. The Imperial family are scheduled to make five appearances on the palace balcony during the morning and afternoon: at 10.10am, 11am, 11.50am, 1.30pm and 2.20pm.


If you have been looking for a quality Bachelor's degree program then we can highly recommend Capella University. We have received some great feedback from prospects regarding this university. They offer a Bachelor of Science in Management and Leadership degree fully online. In order to compete in today's business environment you'll need the proper training. One of the advantages of attending Capella is when you take your Bachelor's degree you have the option of taking a combined Bachelor's-to-Master's degree option. This will save you thousands of dollars by earning master level credits once you complete your Bachelor's degree.
One thing you don't have to worry about is if Capella is accredited. Accreditation as you know if the most important thing to verify before you enroll. Accreditation protects students and Capella University is accredited by the Higher Learning Commission.
Capella offers concentrations within their degree programs. One could for example have concentrations in finance, marketing or project management. You can also take individual courses. When talking to an enrollment counselor they can go over your career and educational goals and provide the best fit for your education.
Have you attended another school in the past? If so you might be able to transfer some or all of the credits you have completed and apply them to your new degree program at Capella. Restrictions can apply but you could transfer up to 135 credits. One criteria is that the courses were taken from an accredited school. Talk to your enrollment counselor for more info.
When you attend Capella most of their students take 1-2 courses at a time. Each course is divided into 10 weekly units where you'll be responsible for reading about the subject matter and participate in discussions and other activities. Your assignments are then all due on Sunday each week. Another option that Capella University offers is a FlexPath learning option. This option allows you to take programs at yoru own pace and the homework assignments are due at the end of the course. There's no limit to the number of courses you can complete per quarter for a flat tuition price. This allows you to save money and complete your degree program quicker.


text:
Slovo kompozice nebo komposice (z lat. compositio = složení, skladba) se užívá ve smyslu skladba, složenina, rozmístění, rozvržení, uspořádání, a to konkrétně:

 v jazykovědě
 skládání respektive tvoření slov

v umění
 obrazová kompozice ve výtvarném umění barevná a světelná skladba obrazu, sepětí s tvary obsaženými v obrazu apod.
 kompozice v literatuře značí jednak uspořádání syžetu ve vztahu k fabuli, jednak uspořádání textových segmentů, např. předmluvy, dedikace, motta, kapitol apod.
 v hudbě – komponování resp. skládání hudebního díla
 hudební dílo jako takové (hotová hudební skladba)
 zahradní architektuře (sadovnická tvorba) – je například zřetelně vymezen styl komponování (kompozice krajinářského parku).

ve školství
 větší písemná zkouška – lidově řečeno velká písemka

v chemii a metalurgii
 složenina, smíšenina, směs, slitina více různých látek. Ne však roztok nebo eutektikum!

v technice
 ložisková kompozice – slitina cínu, olova a dalších kovů pro výrobu ložiskových pánví velkých kluzných ložisek (např. u čepů parních lokomotiv)


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On the other hand, you will additionally have to check the odds being offered by various sports books to be able to feel the pulse of the bookies and the bettors within the fray. You might easily need to work for around 50 hours in a week polishing up on your handicapping skills while you collect and process each piece of vital information.
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The fact that an excessive amount of effort and time goes into the making of an expert handicapper is the reason that we now have hardly any genuine handicappers with a pulse on each aspect of the sport. Should you be confident about sharpening your handicapping skills and are also ready to make the required effort then you too can jump over other experts to become the best sports handicapper. You do not have to contest with anyone but yourself whilst your own record will quickly justify if you have attained the top slot.


text:
Home / News / Amazigh Woman and The Tribal Identity.
Amazigh Woman and The Tribal Identity.
The Amazigh woman's identity in garments is arguably one of the most preserved aspect of the explicit relationship between the women's fertility and nature's elements.
Throughout history, each tribe has vowed in one way or another to differentiate itself from other neighboring tribes.
Before the introduction of Islam to the northern African Imazighen tribes, tattoos were widely used by women to express their appertainance to a certain tribal congregation. Albeit the tradition has been increasingly disapearing over the years due to the arrival of the colonization and the settling of several tribes into several areas of the Atlas Mountains.
These tribes had to give up their nomadic life style and share a space with the Arab population. The Islamic teachings look at tattoos as a disgrace to the body which is supposed to be a gift from God that shouldn't be altered since it doesn't belong to the person but to the creator.
Thus, in order to fit into their new invironement, Amazigh women had to give up the tradition of tattooing and substitute it with displaying their identity via their garments and accessories.
One of the best examples of such an adjustment is the Ait-Atta, an enormous tribal congregation located southeast of Morocco around the Tafilalt oasis.
The women of Ait-Atta are known for their incomparable knotting and embroidery skills. Just like the Tuaregues, they chose an indigo died cotton fabric headcover to deferentiate themselves from other tribes: the Tahruyt.
This unique garment is made of two lengths of clothes joined together at the selvedges creating a line called Tanammast. The Ait-Atta women place it over the head and upper body while draping one end over the left shoulder. Sequins and tassels are added to the two short ends and arranged so when the garment is worn it frames the women's forehead.
When you take a closer look to the embroidery, you can notice the intimate relationship between Amazigh women and mother nature. The goal is to make the Tahruyt link the women's reproductive ability to nature's fertility.
The Tahruyt embroidery is made to look as a three dimensional representation of nature. In order to achieve such an effect, women have chosen to use contrasting colors to project the 3D effect by mirroring each motif using its complementary color in each side of the tanammast, and circular motives using yellow and red to represent the sun.
While the general outsider conception of the Amazigh woman is that she's confined to the restricted space of her house, the tribal expectation is for her to display publicaly the identity of her tribe within her body, clothing and accessories, making her the carrier of a message and the curator of continuity.


alinaghizadeh, elahe and Pakpour HA, Amir and Javadi, maryam and Soleimani, Mohammad Ali (2017) The effectiveness of family-based intervention model health action process approach to a healthy diet in primary school students of Tehran District No.5. Masters thesis, Qazvin University of Medical Sciences,Qazvin,Iran.
Dehghankar, Leila (2014) Physical Activity's Related Factors Based on Transtheoretical Model in Older Adults Guilan In 2013. Journal of applied environmental and biological sciences.
Khorasani, Maryam and Mohammadpoorasl, Asghar and Javadi, Javadi (2016) The survey of association between metabolic measurements and anthropometrics with sleep quality in Petrochemical staff in Tehran, 2015. Masters thesis, Qazvin university of medical science,Qazvin,Iran.
Maryam, shahidi Motlagh and Maryam, Javadi and Ameneh, Barikani and parvin, mirmiran (2017) Comparison of Sleep Hours and Dietary Diversity Based on Body Mass Index in Type 2 Diabetic Patients با توجه به اهمیت تنوع رژیم غذایی و وضعیت خواب در کنترل و پیشگیری از بیماری های مزمن، مطالعه حاضر با هدف مقایسه ساعات خواب و تنوع غذایی با نمایه توده بدنی بیماران دیابتی نوع 2 انجام شد. Masters thesis, Department of Nutrition, Faculty of Health, Qazvin University of Medical Sciences, Qazvin, Iran.
Pouragahi, Samiie (2016) Evaluation of Myelin Basic Protein (MBP)'s antigenicity; as a valuable biomarker; for susceptibility prognostic in Multiple Sclerosis (MS). Other thesis, QAZVIN UNIVERSITY OF MEDICAL SCIENCE,QAZVIN,IRAN.
zehni moghadam, Sayed Amir hossein and Javadi, Maryam and Mohammadpoor Asl, Asghar (2016) Study of Correlation between food security, combined with glucose and boold lipids in type II diabetic over 25 years of diabetes center in southern and eastern. Masters thesis, Qazvin university of medical science,Qazvin,Iran.
فیض اله, فتاح and امام جمعه, محمد مهدی (2017) مقایسه عملکرد منعقد کننده های متداول در حذف کدورت و رنگ از منابع آب های سطحی مطالعه موردی: تصفیه خانه آب شهر ارومیه. Masters thesis, Qazvin University of Medical Sciences Qazvin Iran.
مركز سلامت محيط و كار, پزوهشكده محيط زيست راهنماي كنترل سرب در محل كار. انتشارات دانشگاه علوم پزشكي تهران.
This list was generated on Fri Apr 26 04:24:05 2019 +0430.


text:
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text:
"Royal Chocolate Flush" is the eighteenth single by Japanese recording artist Misia. It was released on December 5, 2007 as the second single from Misia's eighth studio album Eighth World.

Background

The single was released simultaneously with the Hoshizora no Live IV Classics tour DVD. It is Misia's first EP-length single, which consists of three other tracks. The A-side, "Royal Chocolate Flush," was written by Misia, composed by Sakoshin and Shusui, and produced by Sakoshin. In an interview with OCN's Talking Japan, Misia explained the theme of the lyrics, "The song is for all the girls who have ever had to choose between either love or work. It's about tossing away the negativity and putting in double the effort in order to have both."

The main B-side of the single, "Taiyō no Chizu," was also written by Misia, composed by Gomi and Shusui, and produced by Gomi. It served as theme song for the Fuji TV morning show Mezamashi TV, from October 2007 to March 2008. The single also includes "Chandelier," which was first performed during the Hoshizora no Live IV Classics tour, and "Kiss and Hug," the theme song for the J-Wave radio show of the same name.

Chart performance
"Royal Chocolate Flush" debuted on the Oricon Daily Singles chart at number 4 and peaked at number 10 on the Oricon Weekly Singles chart, with 11,670 copies sold in its first week. The single charted for seven weeks and sold a total of 19,576 copies.

Track listing

Charts

Release history

References

External links

2007 singles
Misia songs
Songs written by Misia
2007 songs


text:
Q: How to prevent horizontal scrolling of text in input field with blackberry5 I am creating a html form that needs to work for users of older mobile devices.
The problem I have is when using an older Blackberry device, such as a 2 year old 9300, if you use the trackpad to move to the right of the text field, then the text scrolls off to the left and becomes hidden.
Is there any way to prevent this behaviour, or even to realign the text after the input has lost focus?
The problem is apparent even with a form as simple as this.
<form>
<input type="text" name="testit" />
</form>

A: In case it helps anyone else, I have found a way to fix this - but if anyone can think of a better solution I'd love to hear it.
I simply clear the textfield and then rewrite the value to the textfield when the mouse leaves the input.
<script type="text/javascript">
function updateTheText()
{
  var boxVal = $('#testit').val();
  $('#testit').val('');
  $('#testit').val(boxVal);
}
</script>

and then add an onmouseout to the input
<form>
<input type="text" id="testit" name="testit" onmouseout="updateTheText()" />
</form>


Corn maize polenta is available from most supermarkets, it is a satisfying and weight loss friendly product, easy to cook, and you do not need too much to feel full. Here it is served with tasty blue cheese, mushrooms and peppers, but you can combine it with lots of different veggies and use a different cheese if blue is not your colour.
Heat the oil in a griddle or frying pan then sauté the mushrooms and peppers until tender with the garlic, herbs and seasoning.
While the mushrooms and peppers are cooking, make the polenta according to packet instructions with water and omit any butter if it is included in the instructions, next divide the polenta between two gratin dishes and top with the cooked mushrooms and peppers.
Finally sprinkle with crumbled cheese then place under a hot grill for 2–5 minutes, until cheese melts, delicious with a spinach and rocket side salad.


Hi all, just wanted to let you know about the latest release of our Aggregator module. Stop by www.dnnstuff.com and download a free trial.
container or localization container for 1 or more modules.
Tab look and feel are only limited by your imagination.
just a few of the many looks you can achieve.
Faulting application grpwise.exe, version 6.0.1.0, faulting module grpwise.exe, version 6.0.1.0, fault address 0x0000ff90.
How to change .Net framework from Version=3.5.0.0 back to Version=2.0.0.0 ?
Aggregators and Content Aggregation : Is there an open source content aggregation platform?
A new law in Spain passed requires news aggregators such as Google News to pay publishers a fee if they link to their content.


text:
Q: Using regex and pscp on AIX servers I've been having lots of troubles using pscp and regex on AIX server.
As you can see, I am trying to use Putty's pscp to transfer file "stdout" to my local folder.
This usually works fine, but my problem is that I won't know exact same folder name so I need to use REGEX.
I've been told that possibly my regex was written for grep and that it wasn't supported by pscp.
What would be alternative then to write regex for pscp.
Error message is: "multiple-level wildcards unsupported"
pscp.exe -P 22 -pw krt_345 testuser@testserver5:"/app/log/s500/20201023/.\*/20201023-02\.2[0-9]\.[0-5][0-9]_s500_testuser.\*"/stdout C:\logs

regex only:
"/app/log/s500/20201023/.\*/20201023-02\.2[0-9]\.[0-5][0-9]_s500_testuser.\*"/stdout

A: With SCP protocol, the filemask in the path is resolved by the server. With a typical OpenSSH scp "server", you can use standard Linux glob masks. Definitely not regex. Though your mask is simple enough, that a simple glob mask 20201023-02.2[0-9].[0-5][0-9]_s500_testuser* would. But you can use glob mask for the last path component only. Not for the parent directory. What is what the "multiple-level wildcards unsupported" error message is trying to tell you.
So what you are doing is not doable with SCP. You would have to obtain the folder name using other means. Like using a shell commands over SSH.
And I belive you have asked for this already:
Finding folder name on a server using batch file
And based on your comments to the answer, you already know what you need to combine a shell command like find with scp. So I do not understand, why don't you ask for that.


text:
\section{Introduction}

The Higgs sector of the Standard Model (SM) contains an instability
due to the radiative corrections to the Higgs boson mass;
this is known as the hierarchy problem. Various theories and models
have been designed to solve this problem. One of them is called
the Little Higgs model and was proposed a few years ago \cite{ACG}.
This is an effective model in which the Higgs
is a pseudo-Goldstone boson resulting from a spontaneously broken global
symmetry at a very high scale. Such a Higgs boson remains light, protected
by the approximate global symmetry.
Here we concentrate on one of the several implementations
of the model, called the {\it Littlest Higgs} model \cite{littlest}.
This particular model includes a $SU(5)$ to $SO(5)$ breaking,
and the following heavy new particles:
scalar particles $\phi^0$, $\phi^+$, $\phi^{++}$,
new 2/3 charge heavy quark (\T),
and heavy partners of the electroweak gauge bosons \ah,\ \zh \ and \whpm.

\section{Phenomenology at the LHC}
The Higgs boson (\h) properties remain those of the SM.
Production cross sections and branching ratios of the heavy new particles
have been computed in \cite{Burdman,Hanetal},
leading to the following search strategy:
\begin{itemize}
\item
The $\phi^{++}$ scalar is produced in $W^+W^-$ fusion. The dominant decay mode
is $\phi^{++}\to W^+W^-$. The corresponding cross section is small and the SM background large,
so this particle would be difficult to observe. Nevertheless, the prospects for its detection
have been studied and reported in \cite{Azuelosetal}.
\item
The heavy quark \T can be produced singly in the $bq\to Tq'$ channel via \W exchange.
The \T \ then decays to $tZ$ or $th$. The corresponding cross section is small as well,
although larger than the cross section for the QCD production of a $T\bar T$ pair.
How well the \T \ could be detected by ATLAS was studied in \cite{Azuelosetal}.
\item
The gauge bosons \zh \ and \wh \ are produced via $q\bar q^{(\prime )}$ annihilation
and the cross section is much higher than for the $\phi^{++}$ and \T. Once their mass is fixed
(they are approximatly degenerate),
the only parameter is $\theta$, the mixing angle between the $W$ triplets,
and the cross section is proportional to $(\cot\theta )^2$.
The production cross section for the \ah \ boson is more difficult to predict
since the couplings are not entirely fixed by the model. Nevertheless,
some results on its search are shown in~\cite{Azuelosetal}.
\end{itemize}

In the following, we concentrate on the experimental search of \zh \ and \wh \
using the ATLAS detector. The \texttt{PYTHIA} event generator\cite{pythia} was used
to generate signal and background events. The events were passed through the ATLAS
fast simulation\cite{atlfast} which provides a parameterized response of the detector
to jets, electrons, muons, isolated photons and missing transverse energy.
The integrated luminosity is assumed to be 300~fb$^{-1}$, which corresponds
to data collected during three years of running at high luminosity.
The event selection includes the ATLAS trigger criteria.

\section{Heavy gauge boson searches}

Once produced, the heavy \zh \ and \wh \ bosons can have two types of decays:
the fermionic channels, which are the same channels as their SM partners,
and the bosonic channels. Denoting \vh \ for both \zh \ and \wh \ (and \V \ for \Z \ and \W),
these are $V_H\to V h$ and $Z_H\to W^+W^-$, $W_H\to Z W$.

Among the fermionic channels, $Z_H\to l^+l^-$ and $\W_H\to l\nu$
are clearly the discovery channels. It was shown in~\cite{Azuelosetal}
that \vh \ can be discovered at masses of up to 6~TeV if $\cot\theta$ is large.
On the other hand, the  $V_H\to q\bar q^{(\prime )}$ channel is expected to be more difficult,
because of the high level of background. It was studied however, and the results are reported below.

The observation of the $V_H\to V h$ decay is essential to test Little Higgs models.
Besides, it is dominant at low values of $\cot\theta$. A first study was performed
assuming that the Higgs boson is discovered with a mass $m_h=120$~GeV \cite{Azuelosetal}.
The resulting exclusion contour in the $(M_{V_H},\cot \theta)$ plane is shown on Fig~\ref{fig:mh120200}~(left).
In the next subsection, we report on the results of a more recent study of this decay,
which assumes $m_h=200$~GeV.

\begin{figure}
  \includegraphics[height=.3\textheight]{mh120_col}
  \includegraphics[height=.3\textheight]{mh200_col}
  \caption{Discovery region with the $V_H\to V h$ channel (left: $m_h=120$~GeV, right: $m_h=200$~GeV) as a function of $M_{V_H}$ and $\cot\theta$.}
  \label{fig:mh120200}
\end{figure}

\subsection{Search for the decays $V_H\to Vh$ assuming $m_h=200$~GeV.}

When $m_h=200$~GeV, the main Higgs decays are $h\to W^+W^-$ (73\%) and $h\to ZZ$ (26\%). Various $Zh$ and $Wh$ final states
have been chosen, as listed in Table~\ref{tab:mh200}, resulting from a compromise between cross section and signature~\cite{mh200+recap}.
\begin{table}
\begin{tabular}{cclll}
\hline
    \tablehead{1}{r}{b}{Mode}
  & \tablehead{1}{r}{b}{BR ($10^{-4}$)}
  & \tablehead{1}{c}{b}{Decay}
  & \tablehead{1}{l}{b}{Signature}
  & \tablehead{1}{l}{b}{$\epsilon$} \\
\hline
A1 & 1.0 & $Z_H\to Zh\to l^+l^-W^+W^-\to l^+l^- l^+\nu l^-\nu$ & 4 leptons + $E_T^{miss}$ & 34\%\\
A2 & 3.0 & $W_H\to Wh\to l\nu-W^+W^-\to l\nu l^+\nu l^-\nu$    & 3 leptons + $E_T^{miss}$ & 12\%\\
A3 & 0.4 & $Z_H\to Zh\to jjZZ\to jjl^+l^- l^+l^-$              & 4 leptons + jets & 26\%\\
A4 & 0.4 & $W_H\to Wh\to jjZZ\to jjl^+l^- l^+l^-$              & 4 leptons + jets & \\
B1 & 6.8 & $Z_H\to Zh\to l^+l^-W^+W^-\to l^+l^- jjl\nu$        & 3 leptons + jets + $E_T^{miss}$ & 22\%\\
B2 & 0.8 & $Z_H\to Zh\to l^+l^-ZZ\to l^+l^- jjl^+l^-$          & 4 leptons + jets & 17\%\\
B3 & 2.4 & $W_H\to Wh\to l\nu ZZ\to l\nu jjl^+l^-$             & 3 leptons + jets & 15\%\\
\hline
\end{tabular}
\caption{\zh \ and \wh \ final states under study. The branching ratios are computed assuming $\cot\theta=0.5$,
the selection efficiencies $\epsilon$ assume a gauge boson mass of 1~TeV.}
\label{tab:mh200}
\end{table}
In all the modes, the main background is inclusive top pair production, where both tops decay semi-leptonically
and a third lepton can arise from a $b$ jet.
In the A1 and A2 modes, the missing transverse momentum is used to reconstruct the Higgs momentum,
assuming that the neutrino is colinear to the leptons. In addition, the \W \ mass constraint is applied
in the B1 and B3 mode. The A3 and A4 modes have indistinguishable final state.
The hadronic decay of high $p_T$ \W \ or \Z \ are reconstructed by looking for two high $p_T$ jets
with mass close to the \W/\Z \ mass or, if it fails, by taking the jet with the largest $p_T$.

The corresponding discovery reach is summarised on
Fig~\ref{fig:mh120200}(right); it is similar to the $m_h=120$~GeV case, but the
bound on the \vh \ mass is weaker (6~TeV versus 2~TeV).

\subsection{Search for hadronic decays }

For $\cot\theta\approx 1$, BR($V_H\to Vh$) vanishes and the branching ratios to heavy quarks are\cite{Hanetal}:
BR($Z_H\to b\bar b$)=BR($Z_H\to t\bar t$)=1/8 and BR($W_H\to tb$)=1/4.
It was shown\cite{hadronic} that no convincing signal can be seen in the \zh \ case. However, the $W_H\to tb$
appears visible in the channel where the top decays to the $W(l\nu )b$ final state.
One isolated lepton is searched for, and two $b$-jets tagged, one close to the lepton,
one recoiling against the lepton. The neutrino 3-momentum is estimated from the reconstructed missing transverse
momentum and assuming it is parallel to the lepton momentum.

The discovery reach is shown on Fig~\ref{fig:hadronic} in the same plane as before,
together with earlier results on the $Z_H\to l^+l^-$ and $W_H\to l\nu$ discovery channels~\cite{Azuelosetal}.
The $\cot\theta=1$ region which was missing in the $V_H\to Vh$ analyses
is well covered up to $M_{W_H}=2.5$~TeV.

\begin{figure}
  \hspace{-1cm}
  \includegraphics[height=.29\textheight]{WH_tb_Alpgen_invmass_2TeV}
  \includegraphics[height=.29\textheight]{WZHiggsless_col}
  \caption{Left: reconstructed mass peak for $W_H\to tb$ ($M_{W_H}=2$~TeV). Right: discovery region with the fermionic channels as a function of $M_{V_H}$ and $\cot\theta$.}
  \label{fig:hadronic}
\end{figure}

\section{Summary}
We have shown the latest examples of channels which can be used to test the predictions of Little Higgs models.
The discovery reach is found to be rather good, in particular for
the new gauge bosons.
However, we are aware that the model family of the particular implementation studied here
is actually disfavoured by precision electroweak constraints.
The introduction of a discrete symmetry called T-parity would allow to escape them.
Unfortunately, since it implies that the heavy partners can only be produced in pairs,
the phenomenology is drastically modified and would therefore require a new analysis.

\begin{theacknowledgments}
Thanks are due to the authors of these analyses:
J.E.~Garcia, S.~Gonz\'alez de la Hoz, M.~Lechowski,
L.~March, E.~Ros and, last but not least, D.~Rousseau.
\end{theacknowledgments}

\bibliographystyle{aipproc}


Caviar -is not just for eating ... its now a nail art ! for those of us ready to take that aspiration of livable luxury to the next level there's Ciaté Caviar Manicure, (A PROUD uk BRAND) .. is the latest craze in nail décor. The system was created by Ciaté's creative director Charlotte Knight, who wanted three-dimensional nails for a magazine cover shoot that were delicate and feminine—and totally indulgent.
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Do you like playing strategy board games? Or have you heard about Ticket to Ride or Catan and wondered how to play? Check out our board game night at HEPL where we'll have a wide variety of games to play for all skill levels. So, whether you're into strategy games which last for hours or want to learn a quick card game, check out our game night at HEPL! This program is open to teens and adults.