Generalised prime systems with periodic integer counting function

We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems. I

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Typography papers, 9

This latest issue of the series of Typography papers opens with a beautifully illustrated article by the type designer Gerard Unger on ‘Romanesque’ letters. A further installment of Eric Kindel’s pathbreaking history of stencil letters is published in contributions by him, Fred Smeijers, and James Mosley. Maurice Göldner writes the first history of an early twentieth-century German typefounder, Brüder Butter. William Berkson and Peter Enneson recover the notion of ‘readability’ through a history of the collaboration between Matthew Luckiesh and the Linotype Company. Paul Luna discusses the role of pictures in dictionaries. Titus Nemeth describes a new form of Arabic type for metal composition. The whole gathering shows the remarkable variety and vitality of typography now.

An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0

An example in Beurling's theory of generalised primes

In this paper we prove some connections between the growth of a function and its Mellin transform and apply these to study an explicit example in the theory of Beurling primes.

Gál-type GCD sums beyond the critical line

We prove that ∑k,ℓ=1N(nk,nℓ)2α(nknℓ)α≪N2−2α(logN)b(α) holds for arbitrary integers 1≤n1<⋯

A música em As Báquides, de Plauto: tradução e análise dos cantica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A intersemiose texto-história-cinema na minissérie ROMA da HBO

From August 2005 to March 2007, the two seasons (with 12 and 10 episodes respectively) of the award winning miniseries HBO‟s ROME were aired by the Home Box Office (HBO) channel. With screenplay signed by various writers and directors, the TV series was a coproduction of HBO (USA) and BBC (UK) with support from RAI (Italy), and the show was filmed in multiple locations, but mainly in Cinecittà Film Studios in Rome, very famous for having been headquarters also for Federico Fellini‟s movies. In the first season, the miniseries depicts the conquest of Gaul, made by the military genius of Gaius Julius Caesar, and the political trajectory that made him accumulate power to such an extent that this divided Roman citizens into two factions, one supporting and the other opposing him, the latter focused mainly on the historic figure of General Gnaeus Pompey Magnus. The second season shows the period of civil war following the assassination of Caesar, and the future rise to power of his nephew, adopted son and sole heir, Gaius Octavian Augustus, who was destined to overcome his rivals as well as their allies in the triumvirate that had been formed to pursue and punish Caesar‟s assassins. These facts are well known and usually crowd the mind and imagination of every minimally educated person. The HBO series broke new ground not only for the talent of its writers, directors and actors, not only for its visual effects and locations nor for the vibrancy and grandeur of historical scenes – after all, “historical movies” in general do the same – but it has done so also by the (re)construction of historical events from the perspective of a pair of protagonists of whom too little is known: the centurions Titus Pullo and Lucius Vorenus, who are the only low-rank soldiers mentioned by Caesar in his book Commentaries on the Gallic War (Commentarii de Bello Gallico V.44). Thus, the fictionalization of events also took into account several Roman civilization data which were scattered through historical sources and also those that belong to the modern knowledge of material culture, resulting in a TV series whose filmic aesthetics has rare beauty and creativity. From the survey of textual, historical and cultural data put together in this film, as well as the distance featuring the creative space in the dimension of the gap between them, this paper aims to highlight two pivotal moments of visual and narrative strategies of the show: the opening credits footage and the final scenes of the first season of HBO's Rome.

Transposable elements dynamics in taxa with different reproductive strategies or speciation rate

In recent years the advances in genomics allowed to understand the importance of Transposable Elements (TE) in the evolution of eukaryotic genomes. In this thesis I face two aspects of the TE impact on the in the animal kingdom. The first part is a comparison of the dynamics of the TE dynamics in three species of stick-insects of the Genus Bacillus. I produced three random genomic libraries of 200 Kbps for the three parental species of the taxon: a gonochoric population of Bacillus rossius (facultative parthenogenetic), Bacillus grandii (gonochoric) and Bacillus atticus (obligate parthenogenetic). The unisexual taxon Bacillus atticus does not shows dramatic differences in TE total content and activity with respect to Bacillus grandii and Bacillus rossius. This datum does not confirm the trend observed in other animal models in which unisexual taxa tend to repress the activity of TE to escape the extinction by accumulation of harmful mutations. In the second part I tried to add a contribute to the debate initiated in recent years about the possibility that a high TE content is linked to a high rate of speciation. I designed an evolutionary framework to establish the different rate of speciation among two or more taxa, then I compared TE dynamics considering the different rates of speciation. The species dataset comprises: 29 mammals, four birds, two fish and two insects. On the whole the majority of comparisons confirms the expected trend. In particular the amount of species analyzed in Mammalia allowed me to get a statistical support (p<0,05) of the fact that the TE activity of recently mobilized elements is positively related with the rate of speciation.

Not in the Legends

In writing “Not in the Legends”, one of the images and concepts which constantly returned was that of pilgrimage. I began to write these poems while studying abroad in London, after having passed the previous semester in France and travelling around Europe. There was something in the repetition of sightseeing— walking six miles in Luxembourg to see the grave of General Patton, taking photographs of the apartment where Sylvia Plath ended her life, bowing before the bones of saints, searching through Père Lachaise for the grave of Théodore Gericault— which struck me as numinous and morbid. At the same time, I came to love living abroad and I grew discontent with both remaining and returning. I wanted the opportunity to live everywhere all the time and not have to choose between home and away. Returning from abroad, I turned my attention to the landscape of my native country. I found in the New England pilgrims a narrative of people who had left their home in search of growth and freedom. In these journeys I began to appreciate the significance of place and tried to understand what it meant to move from one place to another, how one chose a home, and why people searched for meaning in specific locations. The processes of moving from student to worker and from childhood to adulthood have weighed on me. I began to see these transitions towards maturity as travels to a different land. Memory and nostalgia are their own types of pilgrimage in their attempts to return to lost places, as is the reading of literature. These pilgrimages, real and metaphorical, form the thematic core of the collection. I read the work of many poets who came before me, returning to the places where the Canon was forged. Those poets have a large presence in the work I produced. I wondered how I, as a young poet, could earn my own place in the tradition and sought models in much the same way a painter studies the brushstrokes of a master. In the process, I have tried to uncover what it means to be a poet. Is it something like being a saint? Is it something like being a colonist? Or is to be the one who goes in search of saints and colonists? In trying to measure my own life and work based on the precedent, I have questioned what role era and generation have on the formation of identity. I focused my reading heavily on the early years of English poetry, trying to find the essence of the time when the language first achieved the transcendence of verse. In following the development of English poetry through Coleridge, John Berryman, and Allison Titus, I have explored the progression of those basic virtues in changing contexts. Those bearings, applied to my modern context, helped to shape the poetry I produced. Many of the poems in “Not in the Legends” are based on my own personal experience. In my recollections I have tried to interrogate nostalgia rather than falling into mere reminiscence. Rather than allowing myself poems of love and longing, I have tried to find the meaning of those emotions. A dominant conflict exists between adventure and comfort which mirrors the central engagement with the nature of being “here” or “there”. It is found in scenes of domesticity and wilderness as I attempt to understand my own simultaneous desire for both. For example, in “Canned Mangoes…” the intrusion of nature, even in a context as innocuous as a poem by Sir Walter Raleigh, unravels ordinary comforts of the domestic sphere. The character of “The Boy” from Samuel Beckett’s Waiting for Godot proved such an interesting subject for me because he is one who can transcend the normal boundaries of time and place. The title suggests connections to both place and time. “Legends” features the dual meaning of both myths and the keys to maps. To propose something “Not in the Legends” is to find something which has no precedent in our histories and our geographies, something beyond our field of knowledge and wholly new. One possible interpretation I devised was that each new generation lives a novel existence, the future being the true locus of that which is beyond our understanding. The title comes from Keats’ “Hyperion, a Fragment”, and details the aftermath of the Titanomachy. The Titans, having fallen to the Olympians, are a representation of the passing of one generation for the next. Their dejection is expressed by Saturn, who laments: Not in my own sad breast, Which is its own great judge and searcher out, Can I find reason why ye should be thus: Not in the legends of the first of days… (129-132) The emotions of the conquered Titans are unique and without antecedent. They are experiencing feelings which surpass all others in history. In this, they are the equivalent of the poet who feels that his or her own sufferings are special. In contrast are Whitman’s lines from “Song of Myself” which serve as an epigraph to this collection. He contends for a sense of continuity across time, a realization that youth, age, pleasure, and suffering have always existed and will always exist. Whitman finds consolation in this unity, accepting that kinship with past generations is more important that his own individuality. These opposing views offer two methods of presenting the self in history. The instinct of poetry suggests election. The poet writes because he feels his experiences are special, or because he believes he can serve as a synecdoche for everyone. I have fought this instinct by trying to contextualize myself in history. These poems serve as an attempt at prosopography with my own narrative a piece of the whole. Because the earth abides forever, our new stories get printed over the locations of the old and every place becomes a palimpsest of lives and acts. In this collection I have tried to untangle some of those layers, especially my own, to better understand the sprawling legend of history.