Fraction Space Revisited

Бойко Бл. Банчев - Знае се, че рационалните числа образуват интересни и богати на изчислителни възможности структури като редици на Фарей (Феъри) и безкрайни дървета. Малко внимание се обръща на по-общо, систематично излагане на основните свойства на дробите като множество. Понятия биват въвеждани без обосноваване, някои доказателства са ненужно изкуствени, а почти винаги и едните, и другите като че биват отнесени към една или друга особена структура, вместо към множеството на дробите изобщо. Изненадващо е, че някои същностни твърдения изглежда дори не са формулирани в литературата по теория на числата. Тази статия има за цел да подобри състоянието на нещата в това отношение, като предлага общо, подходящо подредено изложение на понятия и свързани с тях твърдения. Като допълнение са представени бележки върху пораждането на множеството от всички дроби – откритие значително по-старо, отколкото е прието да се смята.

On a Stochastic Partial Differential Equation with a Noisy Term

2000 Mathematics Subject Classification: 60H15, 60H40

Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essentially unique example that is invariant under this one-parameter subgroup. On the other hand, when the curvature of the space form is zero, i.e., when the space form is complex 2-space with its standard flat metric, there is an additional `exceptional' example that has no continuous symmetries but is invariant under a lattice of translations. Up to isometry and homothety, this is the unique example with no continuous symmetries.

Colonialism, political unconscious and cognitive mapping in the space of the film "Captain Phillips"

The purpose of this article has been made through a Marxist analysis of the US film "Captain Phillips" (PaulGreengrass, 2013), based on a true story. I have found how the evolution of capitalism in the West continuesto consolidate the belief reified in a historical and geographical superiority of the political and socioeconomicwestern models regarding Africa and Asia lowers models. At the same time, through categories like dialecticalmaterialism, criticism of diffusionist theory and application of cognitive mapping to large geopoliticalspaces located in most poor areas of the world, I have realized a remark about currently being articulatingthe political unconscious of working class in rich countries and the poor in poor countries, establishing arelationship between the ideological representation that takes an individual from his historical reality (ona scale that moves from local to global), and how he has developed a mental ability to escape of the responsibilityto make a critical review of what's happening around him in all areas. Finally, through physicalspace captured in the film, I have realized a materialist critique of globalized business process that takesplace through the carriage of goods, outlining spatial and cognitively limits of the mentality of our time, bothamong "winners"as among the "losers", based on the spatial movement of capital.

Aproximación a la arqueología pública desde las narrativas espaciales contextualizadas en el espacio urbano

El objetivo de este trabajo es analizar la narrativa espacial como género artístico, dentro del Arte en el espacio público y valorar su contextualización en la ciudad donde se ponen en evidencia huellas y restos, al mismo tiempo que queda vinculada a nuevas formas de Arqueología Pública implicando la participación ciudadana. Pretendemos establecer las bases teóricas de una propuesta artística de nuestra Tesis Doctoral, el álbum caminado. Partimos de la hipótesis de que la narración, relato textual o de imágenes ordenados con una relativa coherencia, situada en el espacio real, adquiere una nueva dimensión que extravasa el ámbito literario. De manera similar la excavación arqueológica y exhibición de los restos en el lugar al que pertenecieron formando parte del presente, se aparta del carácter lineal de la Historia. Las narrativas espaciales y distintas formas de Arqueología Pública muestran elementos comunes tales como ubicación en el espacio en el que se contextualizan implicando un desplazamiento in situ para participar de la obra o del resto arqueológico, su estructura narrativa multilineal y multitemporal y su temática social.

Imperative, subjunctive, and the desiderative-appellative space in Spanish

After defining the “enunciative scheme” (sentence type) as a communicative unit, the imperative is characterized as a morphologized modality of appellative kind used when the following conditions occur: appellative meaning, 2nd person, future tense and absence of negation. In Spanish, any variation of any of these requirements determines that the subjunctive is used. We reject the idea that the imperative is a variant of subjunctive specialized in appellative function and that both modes share a desiderative morpheme. Working in this way means attributing to a morphological category of the verb a property that actually corresponds to the enunciative schemes (sentence types). We propose to integrate the imperative and subjunctive in the framework of what we call the “desiderative-appellative space”. This “space” brings together various grammatical or grammaticalized means based on the imperative and the subjunctive. Semantically, it is organized around a component of desirability (action appears as desirable) that, by varying several factors, configures a route that goes from a center (the imperative) to a periphery (the expression of desire).

Liberating the Issue of Present Days. About the Foucaltian Critics of Inflationary Speeches on the Present as “Mass Society” and “Estatalized Space”

With this article we pretend to contribute, in a really modest way, to the liberation of a tenacious image of our society: which operates as an ideological basis of a group of current socio-political pseudocritics, with great success and diffusion. For this we will undertake the exposition and the analysis of the development group of Naissance de la biopolitique in which Foucault accomplishes the critic of all that number of inflationary speeches that represent our society like a “mass society” and a “estatalized space”. Facing these vague and disproportionate forms of consideration, the foucaltian critic, in its exquisite attention to what happens nowadays, it should reveal how our societies function as systems that optimize the difference –radically nominalists-, in which it is produced, beyond any phantasmatic of the oppressor and invasive estate, a regretion of the legal-estate structures that articulate the socio-politic groups, in benefit of the reconstitution and the social tissue as a communitarian network, suitable for the dynamics of market competence that characterise our enterprise societies. That will open to a new idea of the critic, and to a displacement of its object and objectives.

The stochastic geometric machine model

This paper introduces the stochastic version of the Geometric Machine Model for the modelling of sequential, alternative, parallel (synchronous) and nondeterministic computations with stochastic numbers stored in a (possibly infinite) shared memory. The programming language L(D! 1), induced by the Coherence Space of Processes D! 1, can be applied to sequential and parallel products in order to provide recursive definitions for such processes, together with a domain-theoretic semantics of the Stochastic Arithmetic. We analyze both the spacial (ordinal) recursion, related to spacial modelling of the stochastic memory, and the temporal (structural) recursion, given by the inclusion relation modelling partial objects in the ordered structure of process construction.

Building monitoring during the partial implosion stage

The partial collapse of a building in Colombia caused severe damage to its structural components -- An implosion was realized to induce the collapse of 50% of the deteriorated building -- To evaluate the influence of the implosion on the remaining structure, a monitoring survey was realized using triaxial accelerometers -- Time signals associated with ambient, seismic and forced vibration were obtained -- A study of the records in the time and the frequency domain was made -- The analysis of the information allowed determining some structural properties that were useful to calibrate the analytical model of the structure

Bull's eye leaky wave antenna for terrestrial and space applications

This work presents the study of Bull's eye antenna designs, a type of leaky wave antenna (LWA), operating in the 60 GHz band. This band emerged as a new standard for specific terrestrial and space applications because the radio spectrumbecomes more congested up to the millimetre-wave band, starting at 30 GHz. Built on existing Bull's eye antenna designs, novel structures were simulated, fabricated and measured, so as to provide more exibility in the implementation of wireless solutions at this frequency. Firstly, the study of a 60 GHz Bull's eye antenna for straightforward integration onto a CubeSat is presented. An investigation of the design is carried out, from the description of the radiation mechanism supported by simulation results, to the radiation pattern measurement of a prototype which provides a gain of 19.1 dBi at boresight. Another design, based on a modified feed structure, uses a microstrip to waveguide transition to provide easier and inexpensive integration of a Bull's eye antenna onto a planar circuit. Secondly, the design of Bull's eye antennas capable of creating beam deflection and multi-beam is presented. In particular, a detail study of the deflection mechanism is proposed, followed by the demonstration of a Bull's eye antenna generating two separate beams at ±16° away from the boresight. In addition, a novel mechanically steerable Bull's eye antenna, based on the division of the corrugated area in paired sectors is presented. A prototype was fabricated and measured. It generated double beams at ±8° and ±15° from the boresight, and a single boresight beam. Thirdly, a Bull's eye antenna capable of generating two simultaneous orbital angular momentum (OAM) modes l = 3 is proposed. The design is based on a circular travelling wave resonator and would allow channel capacity increase through OAM multiplexing. An improved design based on two stacked OAM Bull's eye antennas capable of producing four orthogonal OAM modes l = (±3,±13) simultaneously is presented. A novel receiving scheme based on discretely sampled partial aperture receivers (DSPAR) is then introduced. This solution could provide a lower windage and a lower cost of implementation than current whole or partial continuous aperture.

Hilbert Space Valued Signal Plus Noise Models: Analysis of Structural Breaks under High Dimensionality and Temporal Dependence

This thesis is concerned with change point analysis for time series, i.e. with detection of structural breaks in time-ordered, random data. This long-standing research field regained popularity over the last few years and is still undergoing, as statistical analysis in general, a transformation to high-dimensional problems. We focus on the fundamental »change in the mean« problem and provide extensions of the classical non-parametric Darling-Erdős-type cumulative sum (CUSUM) testing and estimation theory within highdimensional Hilbert space settings. In the first part we contribute to (long run) principal component based testing methods for Hilbert space valued time series under a rather broad (abrupt, epidemic, gradual, multiple) change setting and under dependence. For the dependence structure we consider either traditional m-dependence assumptions or more recently developed m-approximability conditions which cover, e.g., MA, AR and ARCH models. We derive Gumbel and Brownian bridge type approximations of the distribution of the test statistic under the null hypothesis of no change and consistency conditions under the alternative. A new formulation of the test statistic using projections on subspaces allows us to simplify the standard proof techniques and to weaken common assumptions on the covariance structure. Furthermore, we propose to adjust the principal components by an implicit estimation of a (possible) change direction. This approach adds flexibility to projection based methods, weakens typical technical conditions and provides better consistency properties under the alternative. In the second part we contribute to estimation methods for common changes in the means of panels of Hilbert space valued time series. We analyze weighted CUSUM estimates within a recently proposed »high-dimensional low sample size (HDLSS)« framework, where the sample size is fixed but the number of panels increases. We derive sharp conditions on »pointwise asymptotic accuracy« or »uniform asymptotic accuracy« of those estimates in terms of the weighting function. Particularly, we prove that a covariance-based correction of Darling-Erdős-type CUSUM estimates is required to guarantee uniform asymptotic accuracy under moderate dependence conditions within panels and that these conditions are fulfilled, e.g., by any MA(1) time series. As a counterexample we show that for AR(1) time series, close to the non-stationary case, the dependence is too strong and uniform asymptotic accuracy cannot be ensured. Finally, we conduct simulations to demonstrate that our results are practically applicable and that our methodological suggestions are advantageous.

Patterns in the space use of the Bearded Reedling, Panurus biarmicus, on the Tay Reedbeds, Scotland

This thesis presents research into the space use of a specialist reedbed Passerine, the Bearded Reedling, or Bearded Tit, Panurus biarmicus, with a view to inform the conservation of this species and reedbeds as a whole. How a species uses space, and how space use changes between individuals or over time, can influence: the ability to forage and hunt effectively, breeding success, susceptibility to predation, genetic health, disease spread, robustness against environmental change and ultimately, colonisation or extinction. Thus, understanding the space use of animals can provide critical insight into ecological systems. Birds offer interesting models when studying animal space use, as, by being intrinsically mobile, many bird species can occupy multiple spatial scales. As a consequence of being completely dependent on patchy and ephemeral reedbed habitats, the Bearded Reedling, has a clustered, inhomogeneous distribution throughout its range. This drives the existence of distinct spatial scales upon which space use studies should be characterised. Distribution and movement within a single reedbed can be considered local-scale, while spatial processes between reedbeds can be considered wide-scale. Temporal processes may act upon both of these scales. For example, changing interactions with predators may influence nest positioning at a local-scale, while seasonal changes in resource requirements might drive processes such as migration at a wide-scale. The Bearded Reedling has a wide temperate breeding range, extending over much of Eurasia. On the IUCN’s red list, it is listed as ‘of least concern’, with an estimated European population between 240,000-480,000 breeding pairs. Despite its relatively favourable conservation status, its dependence on reedbed habitats drives a fragmented distribution, with populations being concentrated in small, isolated, stands. Over the last century reedbed wetlands have suffered rapid declines caused by drainage schemes undertaken to improve land for development or agriculture. Additionally, many remaining reed stands are subject to extensive commercial management to produce thatch or biofuel. Conversely, in other areas, management is driven by conservation motives which recognise the present threats to reedbeds, and aim to encourage the diversity of species associated with these habitats. As the Bearded Reedling is fundamentally linked to the quality and structure of a reed stand, understanding the space use of this species will offer information for the direct conservation of this specialist species, and for the effects of reedbed management as a whole. This thesis first presents studies of space use at a local-scale. All local-scale research is conducted at the Tay Reedbeds in eastern Scotland. Mist netting and bird ringing data are used within capture recapture models, which include an explicit spatial component, to gain insight into the abundance of the Bearded Reedling on the Tay. This abundance estimation approach suggests the Tay reedbeds are a stronghold for this species on the British Isles, and that, as a high latitude site, the Tay may have importance for range expansion. A combination of transect surveys and radio-tracking data are then used to establish the local-scale space use of this species during the breeding and autumnal seasons. These data are related to changes in the structure of reed caused by local management in the form of mosaic winter reed cutting. Results suggest that birds exploit young and cut patches of reed as foraging resources when they are available, and that old, unmanaged reed is critical for nesting and winter foraging. Further local-scale studies concern the spatial patterns in the nesting habits of this species. Mosaic reed cutting creates clear edges in a reedbed. Artificial nests placed in the Tay Reedbeds demonstrate increased nest predation rates closer to the edges of cut patches. Additionally, high predation rates become reduced as the cut reed re-grows, suggesting that reed cutting may increase accessibility of the stand to predators. As Bearded Reedling nests are uncommon and difficult to locate, the timing, site selection and structure of a sample of real nests from the Tay is then detailed. These demonstrate an early, and relatively rigid breeding onset in this species, the importance of dense, compacted reeds as nesting sites and a degree of flexibility in nest structure. Conservation efforts will also benefit from studies into wide-scale spatial processes. These may be important when establishing how colonisation events occur and when predicting the effects of climatic change. The Bearded Reedling has been traditionally considered a resident species which only occasionally undertakes wide-scale, between-reedbed, movements. Indeed, the ecology of this species suggests strict year round local residency to reedbeds, with distinct seasonal changes in diet allowing occupation of these habitats year round. The European ringing recoveries of this species, since the 1970s are investigated to better characterise the wider movements of specialist resident. These suggest residency in southern populations, but higher instances of movement than expected in more northerly regions. In these regions wide-scale movement patterns resemble those of partial regular migratory species. An understanding of local and wide-scale spatial processes can offer a strong foundation on which to build conservation strategies. This thesis aims to use studies of space use to provide this foundation for the Bearded Reedling and offer further insight into the ecology of reedbed habitats as a whole. The thesis concludes by proposing an effective strategy for the conservation management of reedbeds that will especially benefit the Bearded Reedling.

Simulation of optical observables for space missions to small bodies

The navigation of deep space spacecraft requires accurate measurement of the probe’s state and attitude with respect to a body whose ephemerides may not be known with good accuracy. The heliocentric state of the spacecraft is estimated through radiometric techniques (ranging, Doppler, and Delta-DOR), while optical observables can be introduced to improve the uncertainty in the relative position and attitude with respect to the target body. In this study, we analyze how simulated optical observables affect the estimation of parameters in an orbit determination problem, considering the case of the ESA’s Hera mission towards the binary asteroid system composed of Didymos and Dimorphos. To this extent, a shape model and a photometric function are used to create synthetic onboard camera images. Then, using a stereophotoclinometry technique on some of the simulated images, we create a database of maplets that describe the 3D geometry of the surface around a set of landmarks. The matching of maplets with the simulated images provides the optical observables, expressed as pixel coordinates in the camera frame, which are fed to an orbit determination filter to estimate a certain number of solve-for parameters. The noise introduced in the output optical observables by the image processing can be quantified using as a metric the quality of the residuals, which is used to fine-tune the maplet-matching parameters. In particular, the best results are obtained when using small maplets, with high correlation coefficients and occupation factors.

Potential theory on metric spaces

This work revolves around potential theory in metric spaces, focusing on applications of dyadic potential theory to general problems associated to functional analysis and harmonic analysis. In the first part of this work we consider the weighted dual dyadic Hardy's inequality over dyadic trees and we use the Bellman function method to characterize the weights for which the inequality holds, and find the optimal constant for which our statement holds. We also show that our Bellman function is the solution to a stochastic optimal control problem. In the second part of this work we consider the problem of quasi-additivity formulas for the Riesz capacity in metric spaces and we prove formulas of quasi-additivity in the setting of the tree boundaries and in the setting of Ahlfors-regular spaces. We also consider a proper Harmonic extension to one additional variable of Riesz potentials of functions on a compact Ahlfors-regular space and we use our quasi-additivity formula to prove a result of tangential convergence of the harmonic extension of the Riesz potential up to an exceptional set of null measure

The Applicability Of Ordered Mesoporous Sba-15 And Its Hydrophobic Glutaraldehyde-bridge Derivative To Improve Ibuprofen-loading In Releasing System.

The mesoporous SBA-15 silica with uniform hexagonal pore, narrow pore size distribution and tuneable pore diameter was organofunctionalized with glutaraldehyde-bridged silylating agent. The precursor and its derivative silicas were ibuprofen-loaded for controlled delivery in simulated biological fluids. The synthesized silicas were characterized by elemental analysis, infrared spectroscopy, (13)C and (29)Si solid state NMR spectroscopy, nitrogen adsorption, X-ray diffractometry, thermogravimetry and scanning electron microscopy. Surface functionalization with amine containing bridged hydrophobic structure resulted in significantly decreased surface area from 802.4 to 63.0 m(2) g(-1) and pore diameter 8.0-6.0 nm, which ultimately increased the drug-loading capacity from 18.0% up to 28.3% and a very slow release rate of ibuprofen over the period of 72.5h. The in vitro drug release demonstrated that SBA-15 presented the fastest release from 25% to 27% and SBA-15GA gave near 10% of drug release in all fluids during 72.5 h. The Korsmeyer-Peppas model better fits the release data with the Fickian diffusion mechanism and zero order kinetics for synthesized mesoporous silicas. Both pore sizes and hydrophobicity influenced the rate of the release process, indicating that the chemically modified silica can be suggested to design formulation of slow and constant release over a defined period, to avoid repeated administration.