On firmness of the state space and positive elements of a Banach algebra

This paper is an investigation of positive elements in a Banach algebra.Under the firmness of the state space of a Banach algebra, it is shown that even powers of positive Hermitian elements are in fact positive

Space and time in monoidal categories

The use of categorical methods is becoming more prominent and successful in both physics and computer science. The basic idea is that objects of a category can represent systems, and morphisms can model the processes that transform those systems. We can see parts of computational protocols or physical processes as morphisms, which, when appropriately combined using tensor products and categorical composition, model the protocol or process as a whole. However, in doing so, some information about the protocols or processes is forgotten, namely in what location of spacetime did the events involved take place, and what was the causal structure among them. The goal of this thesis is to explore how these categorical models can be enhanced to include information on the spacetime location and causal structure of events. First, we introduce the theory of subunits, which are subobjects of the monoidal unit for which a canonical isomorphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules, and under mild conditions they endow any monoidal category with a topological intuition. We introduce and study well-behaved notions of restriction, localisation, and support. Subunits in general form only a semilattice, but we develop universal constructions completing any monoidal category to one whose subunits universally form a lattice, preframe, or frame.  Afterwards, we introduce a number of constructions to explore how the theory of subunits can be used in practice. Inspired by logical clocks, we define a diagrammatic category where we can capture simple protocols and their causal structure. To progress towards more detailed spacetime and causal information, we define the category of protocols, which formalises the idea of letting a morphism from a category be supported in a different category. This allows us to have one category to model the systems and processes and another one to model spacetime. In particular, we can treat both toy models of spacetime and more realistic ones in the same mathematical footing. A notion of causal structure is defined for monoidal categories, and a generalisation of the usual causal analysis in physics for points to arbitrary regions is provided. We give examples of protocols seen as diagrams and as objects in the category of protocols, both with toy models of spacetime as well as with more realistic ones

Sustainable Functional Food Processing

Functional nutrition is deeply connected with healthy lifestyle and sustainable food production, due to its positive health benefits and the use of economically underexplored and natural raw materials. Expectedly, it appeals to large number of interested consumers while becoming lucrative segment of the food industry with a fast-growing market fueled by new sociodemographic trends. Accordingly, functional juices and beverages made of indigenous fruits are interesting niche for various food market stakeholders. Here, biologically active compounds (BACs) and probiotics that have positive health effects in functional foods (juices) are mostly thermolabile. This is especially important for industry that still employs classical heat treatments (e.g., pasteurization), while being concerned with degradation of food quality in the final products. To prevent this, focus is on designing economic and ecological technologies that are able to preserve nutritional and sensory quality while maintaining microbiological stability in products. Such approaches are based on low-energy consumption and low-impact processing, e.g. “hurdle technology” that combines advanced and conventional methods (e.g., high-power ultrasound, pulse electric field). Food design is another important focus point for consumers’ sensory appeal and economic success of foods. Hence, technologies as 3D food printing can be particularly useful for manufacturing. Based on the above, presented topics are relevant to sustainable functional food production, functional fruit juices, BACs, “hurdle technology,” advanced food processing, 3D food printing, and authentic fruits

Mathematics in literature : modernist interrelations in novels by Thomas Pynchon, Hermann Broch, and Robert Musil

The focus of this thesis is on four novels’ illustrations of the parallels and interrelations between the foundational crisis of mathematics and the political, linguistic, and epistemological crises around the turn to the twentieth century. While the latter crises with their climax in the First World War are commonly agreed to define modern culture and literature, this thesis concentrates on their relations with the ‘modernist transformation’ of mathematics as illustrated in Thomas Pynchon’s Against the Day (2006) and Gravity’s Rainbow (1973), Hermann Broch’s The Sleepwalkers (1930-1932), and Robert Musil’s The Man without Qualities (1930/32). In the revaluation of mathematics during its foundational crisis, the certainty and rationality of this most certain science is challenged, and the novels accordingly employ mathematics as an example for the dramatic transformation of the modern West, the wider loss of absolute truth, and the increasing scepticism towards Enlightenment values. Crisis, however, also implied some freedoms and opportunities for literature and criticism. When the developing modern notion of mathematics is defined by autonomy and independence from the natural world, it bears traits more commonly associated with literary fiction, and the novels examine the possible convergence of mathematics and literature in the freedom of imaginary existence. The novels thus highlight the unique position of the structural science mathematics in the relation of the (natural) sciences and the humanities and suggest it to escape or straddle the perceived divide between the disciplines. The examination and historicising of relations between fiction and mathematical conceptualisations of the world as introduced in the major works by Pynchon, Broch, and Musil thus also contributes to distinguishing the specific conditions of studying mathematics in fiction in the wider field of literature and science

LSU General Catalog 1970-1971

The LSU General Catalog describes all undergraduate and graduate departments and programs with degree requirements and courses offered for each one. The General Catalog includes information on registration and financial aid as well as academic services offered to all students

Reports to the President

A compilation of annual reports including a report from the President of the Massachusetts Institute of Technology, as well as reports from the academic and administrative units of the Institute. The reports outline the year's goals, accomplishments, honors and awards, and future plans

Delaying the image : towards an aesthetics of encounter

This thesis, as part of a movement towards the degree of PhD (a becoming Doctor of Philosophy), is constructed and approached as a philosophical situation, which is always about an encounter between terms that are foreign to each other. In this case, through the exploration of the interplays of space, film and politics, a multiplicity of foreign terms and such encounters will emerge and take us along a journey through places, movies and architectures, to discuss the ways in which architecture and other spatial practices think, imagine and produce the worlds we live in and the ways in which we live together. Quite differently from what has usually been the focus of explorations of the relationships between film and architecture -namely an approach to their connections as formal constructions and compositional techniques- I will approach cinema as a form that thinks, as an apparatus of spatial critique and as a material that is capable of activating a time and a space of encounter: one in which people are enabled to meet reality at a distance from that in which they are presently becoming. Film is here an encounter with otherness, and allows thinking in and through the distance that separates the viewer from the screen and from the spaces and realities presented on it. lt does so by means of its form. lt is a form that thinks. Through its thinking, cinema can change the ways in which we conceive of territories and places; it can change the ways in which we conceive of architecture, helping us move from understanding it as a discipline or an 'it' to seeing it as an action or a verb: to architect. Cinema can help us gain the critical, social, political and utopian impetus we are missing in our 'movement' towards the establishment of the common. Philosophy has, according to Badiou, three tasks in relationship with situations: first, it has to help us clarify the basic choices of our thinking; second, it has to help us clarify the distance between that thinking (truths as creation) and power; and third,it has to help us clarify the importance of the exception, the rupture, the event. Choice, distance, exception. One could also see in that sequence a relationship to the main three parts of this research, the first part is about choices: an archaeology of the present that forces us to choose between different things in order to approach what I will call 'pragmatic dissent'; the second part is about distances: a filmic, spatial and affective journey in which we take a distance from that present in order to encounter reality, and we do so by exploring and developing an 'aesthetics of encounter'; and the third part is about exceptions: an exploration of other images and other spaces, alternatives and events in the conception, thinking and production of spaces and images, a journey through these exceptions that will become a discussion of two interrelated notions: anarchic metapolitics and what I will provisionally call 'ethics of encounter'. Or in other words, a different way of conceiving and addressing our becoming 'of' the world as architects and the responsibilities we have in relationship with its transformation through the thinking, construction and organization of our coexistence.Esta tesis - parte de una trayectoria orientada a la obtención del grado de doctor (un devenir 'philosophi doctor:o PhD) - se ha construido y afrontado como una situación filosófica, siempre un encuentro entre términos ajenos entre sí. En este caso, a través de la exploración de las relaciones de espacio, cine y política, se hacen posibles múltiples encuentros de este tipo, que emergen y nos conducen a lo largo y ancho de lugares, películas y arquitecturas, con el fin de discutir las maneras en las que la arquitectura y otras prácticas espaciales piensan, imaginan y producen los mundos que habitamos y los diversos modos en los que podemos habitarlos juntos. En marcado contraste con las aproximaciones más usuales a las relaciones entre cine y arquitectura -caracterizadas generalmente por enfoques centrados en aspectos formales y técnicas compositivas- la tesis se acerca al cine como forma capaz de pensar, y como aparato de crítica espacial capaz de activar un tiempo y un lugar de encuentro: un espacio y un tiempo en el que encontrarse con la realidad a una cierta distancia con respecto a la que nos separa de nuestro devenir cotidiano. El cine es entonces un encuentro con la alteridad, con el otro, y permite pensar en y a través de la distancia que separa al espectador de la pantalla y de los espacios y realidades que se presentan en ella. El cine es capaz de producir este encuentro gracias a su forma. Una forma capaz de pensar. A través de su pensar, el cine puede cambiar las maneras en que concebimos territorios y lugares; y puede cambiar las formas en las que concebimos la arquitectura, ayudándonos a pasar de entenderla como una disciplina o entidad a verla como una acción o un verbo:'arquitecturar'. El cine puede contribuir a recuperar el ímpetu crítico, social, político y utópico tan necesario en nuestro 'movimiento' hacia el establecimiento de lo común. La filosofía, según Badiou, tiene tres tareas principales en relación con las situaciones:primero, debe ayudarnos a clarificar las decisiones principales de nuestro pensar; segundo,debe ayudarnos a clarificar la distancia entre ese pensamiento (verdades como creación) y el poder;y tercero,debe ayudarnos a clarificar la importancia de la excepción, la ruptura, el acontecimiento. Elección, distancia, excepción. Podría encontrarse en esa secuencia también una relación con las tres partes de esta investigación; la primera parte se centra en la elección: una arqueología del presente que nos obliga a escoger con el fin de aproximarnos a lo que llamaré 'disenso pragmático'; una segunda parte que trata de distancias: un viaje fílmico,espacial y afectivo en el que tomamos distancia sobre ese presente para encontrarnos con la realidad, a través de la exploración y el desarrollo de una 'estética del encuentro'; y una tercera parte que se ocupa de la excepción,una exploración de imágenes y espacios otros y otras, alternativas y acontecimientos en la concepción, pensamiento y producción de espacios e imágenes, una travesía a través de estas excepciones que se convertirá en una discusión de dos nociones interrelacionadas: metapolítica anárquica y lo que denominaré provisionalmente 'ética del encuentro'. Es decir, otra forma de concebir y afrontar nuestro devenir arquitectos 'de' el mundo y las responsabilidades que tenemos en relación con su transformación a través de la concepción, construcción y organización de nuestra coexistenciaPostprint (published version