scholarly journals Chromatic roots as algebraic integers

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Adam Bohn

International audience A chromatic root is a zero of the chromatic polynomial of a graph. At a Newton Institute workshop on Combinatorics and Statistical Mechanics in 2008, two conjectures were proposed on the subject of which algebraic integers can be chromatic roots, known as the ``$α +n$ conjecture'' and the ``$nα$ conjecture''. These say, respectively, that given any algebraic integer α there is a natural number $n$ such that $α +n$ is a chromatic root, and that any positive integer multiple of a chromatic root is also a chromatic root. By computing the chromatic polynomials of two large families of graphs, we prove the $α +n$ conjecture for quadratic and cubic integers, and show that the set of chromatic roots satisfying the nα conjecture is dense in the complex plane. Une racine chromatique est un zéro du polynôme chromatique d'un graphe. A un atelier au Newton Institute sur la combinatoire et la mécanique statistique en 2008, deux conjectures ont été proposées dont le sujet des entiers algébriques peut être racines chromatiques, connus sous le nom ``la conjecture $α + n$'' et ``la conjecture $n α$ ''. Les conjectures veulent dire, respectivement, que pour chaque entier algébrique $α$ il y a un nombre entier naturel $n$, tel que $α + n$ est une racine chromatique, et que chaque multiple entier positif d'une racine chromatique est aussi une racine chromatique . En calculant les polynômes chromatiques de deux grandes familles de graphes, on prouve la conjecture $α + n$ pour les entiers quadratiques et cubiques, et montre que l'ensemble des racines chromatiques qui confirme la conjecture $nα$ est dense dans le plan complexe.

10.37236/6578 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Peter J. Cameron ◽  
Kerri Morgan

A chromatic root is a root of the chromatic polynomial of a graph.  Any chromatic root is an algebraic integer. Much is known about the location of chromatic roots in the real and complex numbers, but rather less about their properties as algebraic numbers. This question was the subject of a seminar at the Isaac Newton Institute in late 2008.  The purpose of this paper is to report on the seminar and subsequent developments.We conjecture that, for every algebraic integer $\alpha$, there is a natural number n such that $\alpha+n$ is a chromatic root. This is proved for quadratic integers; an extension to cubic integers has been found by Adam Bohn. The idea is to consider certain special classes of graphs for which the chromatic polynomial is a product of linear factors and one "interesting" factor of larger degree. We also report computational results on the Galois groups of irreducible factors of the chromatic polynomial for some special graphs. Finally, extensions to the Tutte polynomial are mentioned briefly.


Author(s):  
Marina Aleksandrovna Neglinskaya

The subject of this research is the art of Cai Guo-Qiang (born in 1957) – the modern Chinese painter who lives and works in China and the United States (New York). The object of this research is the storyline fireworks of Cai and his innovative technique of “gunpowder painting”. The first works of the painter were canvasses in oil painting, and by 1980’s he invented a new “gunpowder” technique, which was first applied in combination with oil on the canvas, and since 1990’s – with ink on the paper, as a version of modern traditional painting guo-hua. His works evolved from social realism to a distinct variation of modern expressionism, as demonstrated the first in Russia retrospective exhibition of the works of Cai Guo-Qiang that took place in the Phuskin State Museum of Fine Arts (“October”, Moscow, 2017). Authors of the exhibition catalogue justifiably note the “cosmopolitan mission” of his art, but leave out of account the traditional context. The proposed methodology, which integrates art and culturological analysis, allows seeing in the works of this prominent modern painter the version of mass art that retains mental and reverse connection with the Chinese tradition. The scientific novelty of the article is defined by the following conclusions: the art of Cai Guo-Qiang is addressed to the international audience, but concords with the traditional paradigm due to Buddhist mentality deeply rooted in the painter’s consciousness. The traditional aspect is his proclivity for harmonization of social environment. This mass art that possesses formal and substantive novelty is associated with the modern international artistic market, as well as market version of “Chinese style” (Chinoiserie) of the XVIII century.


2021 ◽  

This volume presents, for the first time, an assemblage of contributions on the philosophical dimensions of the impersonal, the multiplicity of its linguistic, social, scientific, religious and artistic perspectives, as well as initial approaches to its unified definition. Linguistic and logical impersonality The “It" in K. Kraus “Impersonality” in the subject and in events The impersonal ontology of H. Rombach Levinas on the “Il y a” Organisation in non-egological consciousness The witness of consciousness in the Vedānta traditions Anonymous self-consciousness G. Deleuzes figures of the impersonal The impersonal in G. Agamben's Philosophy Formal and collective thought in Spinoza Cusanus and the person as stake in the game of life Impersonal subjectivity and the comedy of solipsism Dimensions of the impersonal in T. Nagel, E. Husserl and H. Plessner On the figure of the impersonal in the Anthropocene Language and mask in F. Nietzsche Theodoros Terzopoulos on impersonality and theatre With contributions by Michael Astroh, Eric Ebner, Eric Eggert, Rolf Elberfeld, Katrin Felgenhauer, Ralf Gisinger, Annika Hand, Stefan Lang, Robert Lehmann, Enrico Müller, Daniel Neumann, Frank Raddatz, Christian Rößner, Thomas Schmaus, Fabian Strobel and Theodoros Terzopoulos.


2009 ◽  
Vol 61 (2) ◽  
pp. 264-281 ◽  
Author(s):  
J. P. Bell ◽  
K. G. Hare

Abstract. Let q be an algebraic integer of degree d ≥ 2. Consider the rank of the multiplicative subgroup of ℂ* generated by the conjugates of q. We say q is of full rank if either the rank is d − 1 and q has norm ±1, or the rank is d. In this paper we study some properties of ℤ[q] where q is an algebraic integer of full rank. The special cases of when q is a Pisot number and when q is a Pisot-cyclotomic number are also studied. There are four main results.(1)If q is an algebraic integer of full rank and n is a fixed positive integer, then there are only finitely many m such that disc `ℤ[qm]´ = disc `ℤ[qn]´.(2)If q and r are algebraic integers of degree d of full rank and ℤ[qn] = ℤ[rn] for infinitely many n, then either q = ωr′ or q = Norm(r)2/dω/r′ , where r ′ is some conjugate of r and ω is some root of unity.(3)Let r be an algebraic integer of degree at most 3. Then there are at most 40 Pisot numbers q such that ℤ[q] = ℤ[r].(4)There are only finitely many Pisot-cyclotomic numbers of any fixed order.


Author(s):  
John Mraz

Photography, film, and other forms of technical imagery were incorporated quickly into Mexican society upon their respective arrivals, joining other visual expressions such as murals and folk art, demonstrating the primacy of the ocular in this culture. Photojournalism began around 1900, and has formed a pillar of Mexican photography, appearing in illustrated magazines and the numerous picture histories that have been produced. A central bifurcation in the photography of Mexico (by both Mexicans and foreigners) has been that of the picturesque and the anti-picturesque. Followers of the former tendency, such as Hugo Brehme, depict Mexicans as a product of nature, an expression of the vestiges left by pre-Columbian civilizations, the colony, and underdevelopment; for them, Mexico is an essence that has been made once and for all time. Those that are opposed to such essentialism, such as Manuel Álvarez Bravo, choose instead to posit that Mexicans are a product of historical experiences. The Mexican Revolution has been a central figure in both photography and cinema. The revolution was much photographed and filmed when it occurred, and that material has formed the base of many picture histories, often formed with the archive of Agustín Víctor Casasola, as well as with documentary films. Moreover, the revolution has been the subject of feature films. With the institutionalization of the revolution, governments became increasingly conservative, and the celebrity stars of “Golden Age” cinema provided models for citizenship; these films circulated widely throughout the Spanish speaking world. Although the great majority of photojournalists followed the line of the party dictatorship, there were several critical photographers who questioned the government, among them Nacho López, Héctor García, and the Hermanos Mayo. The Tlaltelolco massacre of 1968 was a watershed, from which was born a different journalism that offered space for the critical imagery of daily life by the New Photojounalists. Moreover, the representation of the massacre in cinema offered sharply contrasting viewpoints. Mexican cineastes have received much recognition in recent years, although they do not appear to be making Mexican films. Television in Mexico is controlled by a duopoly, but some programs have reached an international audience comparable to that of the Golden Age cinema.


Literator ◽  
2003 ◽  
Vol 24 (2) ◽  
pp. 59-82
Author(s):  
J. Koch

The face of war – the face of the Other: Epiphany of the visage in Die son struikel by Dolf van Niekerk Traumatic war experiences are crucial in shaping the identity of Diederik Versveld, the main character in Dolf van Niekerk’s Die son struikel (The sun stumbles). In this article I want to explore the war experience that the protagonist has to deal with, its literary adaptation, and the construction of the protagonist’s identity. I indicate that the three stages of Diederik’s development are closely connected to the concrete philosophic contents of the novel. The thought of Emmanuel Lévinas serves as my interpretative framework. Central to Diederik Versveld’s experience of war is the reduction of the subject to merely and impersonally existing, to il y a (“there is”). In my opion Lévinian concepts are useful in outlining the route to a better understanding of the protagonist’s experience of the war. In analysing the processing of the trauma of war Lévinas’ notion of the epiphany of the face of the Other can be helpful. The encounter with the Other in the faces of other people plays a crucial role in Diederik’s attempt to come to terms with his experiences of war and death. In Totalité et Infini (Lévinas, 1961:188) the French philosopher wrote: “The epiphany of the face unlocks humanity”.


2003 ◽  
Vol 34 (2) ◽  
pp. 231-247 ◽  
Author(s):  
Phillip Deery

Although Cold War propaganda is now the subject of close scholarly scrutiny, the main method by which it was communicated – language – has been overlooked. The Malayan Emergency illustrates how the British government grappled with the issue of political terminology within the broader context of anti-communist propaganda. This article will analyse the use of political language; the change from ‘bandit’ to ‘communist terrorist’; and the problems of delineating the Malayan from the international audience.


2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Aaron Meyerowitz

International audience It is known the one dimensional prototile $0,a,a+b$ and its reflection $0,b,a+b$ always tile some interval. The subject has not received a great deal of further attention, although many interesting questions exist. All the information about tilings can be encoded in a finite digraph $D_{ab}$. We present several results about cycles and other structures in this graph. A number of conjectures and open problems are given.In [Go] an elegant proof by contradiction shows that a greedy algorithm will produce an interval tiling. We show that the process of converting to a direct proof leads to much stronger results.


Slovo ◽  
2017 ◽  
Vol The autobiographical... (Russia in its margins>) ◽  
Author(s):  
Catherine Géry

International audience Red Cavalry is an ambiguous and unstable literary text, an oneiric and mystifying reconstruction in which reality as it was lived by the author/narrator goes through several distorting prisms. The reader has to experience the same feeling of disorientation as Isaac Babel experienced during the Polish campaign in 1920. The War experience is translated into an experience of otherness. Lioutov, the narrator of Red Cavalry and Babel’s alter ego, is the “absolute stranger”: he is a Jew among Cossacks, an Intellectual among Soldiers, and a Bolshevik among Hasids. He looks at the world with external eyes, which prevents him from recognition and from subjection to identitarianism. The outsider’s look is a way of renewing perception, which is, according to Viktor Shklovsky, one of the main principles of the “defamiliarization” as a narrative technique that achieves singularity. Here we are talking about the irreducible singularity of the subject who is thinking of himself as an outsider and, consequently, resists all kinds of social determinism and normative forms of power and knowledge. Cavalerie rouge est un texte instable et ambigu, une reconstruction onirique et mystificatrice où le réel vécu par l’auteur-narrateur passe par toute une série de prismes déformants, faisant subir au lecteur une expérience de la désorientation analogue à celle éprouvée par Isaac Babel lors de la campagne de Pologne en 1920. Aussi, l’expérience de la guerre est rendue comme une expérience de l’altérité. Lioutov, le narrateur de Cavalerie rouge et alter ego de Babel est l’étranger absolu : Juif chez les Cosaques, intellectuel chez les combattants, bolchevique chez les Hassidim, il contemple le monde d’un regard extérieur avec une distance qui empêche toute identification mais aussi tout assujettissement identitaire. Le regard de l’étranger est propre à renouveler profondément la perception, ce qui est, selon Viktor Chklovski, l’un des principes majeurs de l’étrangéisation comme dispositif narratif visant à gêner les processus de reconnaissance ou d’appartenance, pour atteindre la singularisation. Cette singularité irréductible, c’est celle du sujet qui se pense lui‑même comme un autre et qui, de ce fait, résiste à toutes lesdéterminations sociales et à toutes les formes normatives de pouvoir et de savoir. Конармия Исаака Бабеля – двусмысленное и «нестабильное» литературное произведение, в котором жизненный опыт повествователяпроходит сквозь целый ряд искажающих призм. Следовательно, читатель испытывает то же ощущение дезориентации, что и испытывал Бабель-Лютов во время польской кампании в 1920-ом году. В Конармии военный опыт превращается в столкновение с «инакостью». «Абсолютным чужаком» является Кирилл Лютов – еврей среди казаков, интеллигент среди боевиов, большевик среди хасидов. Он смотрит на окружающий мир с внешним взглядом постоянно чужого человека. Эта дистанция мешает процессу опознавания и даже формирования индентичности. К тому же взгляд чужого человека позволяет обновить восприятие – один из основных принципов «остранения» по Виктору Шкловскому. Способ видеть вещи выведенными из их контекста имеет своей целью индивидуализацию не только предметов но и самого субъекта. Я здесь имею в виду ту неотъемлемую единственность индивида, мыслящего себя как «чужого» и, следовательно, противостоящего всякой социальной детерминированности или нормативным видам власти и знания.


Slovo ◽  
2019 ◽  
Vol To the East of Pixar :... ◽  
Author(s):  
Pascal Vimenet

International audience Новый Гулливер (1935), первый черно-белый советскиймультипликационно-игровой фильм, режиссера Александра Птушко, не былдо сих пор предметом специального исследования. Нижеследующее являетсяего контекстуальным, биографическим, равно как и кинематографическим анализом. Творческий путь Птушко (1900-1973) дается в новом освещении, особенно 1920-30 годы, на которые приходится становление его кино.Осуществив постановку Это случилось на стадионе (1928) и Властелинбыта (1932), Птушко принял руководство секцией мультипликационногофильма на студии Совкино, ставшей Москинокомбинат, затем Мосфильм.Подробно рассматривается политико-культурный контекст, в период созданияего игрового фильма, между 1927 и 1935 годами, который сводит воедино всёмногообразие советского авангарда, но и является свидетелем торжествадогмы соцреализма. Фильм Птушко оказался восприимчив к теориям бурлескаоснователей Фабрики эксцентрического актера (ФЭКС). Превращениеперсонажей фильма Птушко в кукол-марионеток, символическое обыгрываниемасштабов могло зародиться в недрах этого движения. Но как сумел «НовыйГулливер», этот «фильм-сказка» обмануть политический контекст ипротивостоять сиренам соцреализма или отклониться от известныхшаблонных кодов? Птушко избирает философскую повесть, усугубленнуюполитическим памфлетом, что дает ему законное основание привязать чудесноек политическому. Смелая экранизация Свифта, московский дорогостоящийкинофильм, с его полуторатысячей шарнирных кукол, сотнями пластилиновыхфигурок, их сочетание с игровым кино, и два десятка массовых сцен претендуетна соперничество с «Кинг Конгом». Своим остроумием и развлекательностьюфильм Птушко вызывал восхищение Чарли Чаплина. Данное исследованиепрепарирует аллегорию – держащий каркас фильма, и стремитсяидентифицировать в кинопостановке всё то, в чем отголоском дают о себе знатьсоветские времена. И когда оказывается, что гимн лиллипутов, это воспеваниеотвратительного монархизма, жутковатым образом предвосхищает ОдуСталину 1939 года, то совершенно внятно становится, что Новый Гулливерне столько выставляет на показ всепобедительность homo sovieticus, сколькоделает из истории опасный аттракцион падений и взлетов и внедряет в неёсубверсивное понятие ухронии. The New Gulliver (1935), the first black and white Soviet animatedfeature film directed by Alexander Ptusko, has not been the subject of a specific studyso far. The following is contextual, biographical, as well as filmic analysis. It offers anew light on the route of Ptusko (1900-1973), especially on the 1920-1930 whichsees emerge his cinema. After having realized It Arrived at the Stadium (1928)and The Master of Everyday Life (1932), Ptusko took the lead of the section of theanimated film of the Sovkino studios become Moskinokombinat, then Mosfilm. Thepolitico-cultural context of the emergence of his feature film, 1927 and 1935, whichbrings together all the diversity of the Soviet avant-garde but sees the triumph of thedogma of socialist realism, is examined at length. Ptusko’s film seems receptive to theburlesque theories of the founders of the FEKS. The puppetisation of the characters inPtusko’s film, the symbolic games of scale, may have originated in this movement. Buthow could The New Gulliver, this « film-tale », have imposed itself in the politicalcontext and resist the realistic socialist sirens or divert certain codes? Ptusko choosesa philosophical tale doubled by a political pamphlet that authorizes him to link themarvelous to the political. An audacious adaptation of Swift, a Muscovite spectacular,The New Gulliver aims to compete, with its 1 500 puppets articulated, hundreds ofplastic figurines, their combination to the real shot and its 20 sets, with King Kong.Ptusko’s film provokes Chaplin’s admiration for his facetiousness. The study dissects theallegory that structures the film and seeks to identify in the staging of everything thatechoes the Soviet present. And when it appears that the Lilliputian hymn, the songof the hated kingship, anticipates in an unsettling way The Ode to Stalin of 1939, itbecomes certain that The New Gulliver, more than to demonstrate the invincibility ofthe homo sovieticus, transforms the history in a roller coaster and makes penetrate theexplosive concept of uchronia. Le Nouveau Gulliver (1935), premier long métrage d’animationsoviétique noir et blanc, réalisé par Aleksandr Ptouchko, n’a pas fait l’objetd’études spécifiques jusqu’ici. Celle qui suit est contextuelle, biographique, toutautant qu’analyse filmique. Elle propose un nouvel éclairage sur l’itinéraire dePtouchko (1900-1973), particulièrement sur les années 1920-1930 qui voitémerger son cinéma. Après avoir réalisé C’est arrivé au stade (1928) et Le Maîtredu quotidien (1932), Ptouchko prend la tête de la section du film animé des studiosSovkino devenus Moskinokombinat, puis Mosfilm. Le contexte politico-cultureld’émergence de son long métrage, entre 1927 et 1935, qui met en présence toutela diversité de l’avant-garde soviétique mais voit triompher le dogme du réalismesocialiste, est longuement examiné. Le film de Ptouchko semble réceptif aux théoriesburlesques des fondateurs de la FEKS. La marionnettisation des personnages dufilm de Ptouchko, les jeux symboliques d’échelle ont peut-être pris leur sourcedans ce mouvement. Mais comment Le Nouveau Gulliver, ce « ciné-conte », a-t-ilpu s’imposer dans le contexte politique et résister aux sirènes réalistes socialistesou en détourner certains codes ? Ptouchko choisit un conte philosophiquedoublé d’un pamphlet politique qui l’autorise à lier le merveilleux au politique.Audacieuse adaptation de Swift, superproduction moscovite, Le Nouveau Gulliverambitionne de rivaliser, avec ses 1 500 marionnettes articulées, ses centaines defigurines en plastiline, leur combinaison à la prise de vue réelle et ses vingt décors,avec King-Kong. Le film de Ptouchko provoque l’admiration de Chaplin, quien apprécie l’esprit facétieux. L’étude dissèque l’allégorie qui structure le film ets’attache à repérer dans la mise en scène tout ce qui fait écho au présent soviétique.Et quand il apparaît que l’hymne lilliputien, chant de la royauté honnie, anticipede manière troublante L’Ode à Staline de 1939, il devient certain que Le NouveauGulliver, plus que de démontrer l’invincibilité de l’homo sovieticus, transformel’histoire en montagnes russes et y fait pénétrer le concept explosif de l’uchronie.


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