Orientador: Maria Angela Fagnani / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Agricola / Made available in DSpace on 2018-08-08T16:23:09Z (GMT). No. of bitstreams: 1 Martins_JoseLuis_D.pdf: 2290824 bytes, checksum: 16399689f4aee5a0a7128cc47568b1e6 (MD5) Previous issue date: 2006 / Resumo: O objetivo deste trabalho foi avaliar um filme para cobertura de casa de vegetação através dos aspectos de produção e qualidade; elementos micrometeorológicos e de envelhecimento do filme plástico, sob as condições impostas pela cobertura plástica com diferentes anos de uso. Para a produção e qualidade foram selecionados 15 vãos de estufa, com plástico de ano de início de uso 1998, 1999, 2002 e 2003 e mais a testemunha com três repetições cada. Dois manejos de produção foram utilizados para a avaliação: o manejo comercial usado na propriedade (primeira etapa) e um manejo específico (segunda etapa) em que houve um corte raso, no início do experimento, em uma área de 1m2 realizado no intuito de avaliar o desenvolvimento do botão floral da poda até a haste comercial pronta. Na primeira etapa foram realizadas 4 coletas ao longo do período do experimento (nos dias 01/03/2004, 17/03/2004, 26/03/2004 e 05/04/2004). Na segunda etapa foi avaliado o aparecimento dos botões florais dos novos brotos em quatro datas (20/02/2004, 07/03/2004, 26/03/2004 e na semana de 28/03 a 06/04/2004) até a formação completa da haste floral comercial. Na primeira etapa foram coletadas 4 hastes florais por tratamento em 5 tratamentos totalizando 60 flores por data de coleta. Na segunda etapa foram coletadas 13 hastes florais por tratamento em 4 tratamentos totalizando 52 hastes florais. Não houve diferença estatística entre os plásticos de ano de início de uso de 1998, 1999, 2002 e 2003 nas variáveis comprimento e diâmetro das hastes, diâmetro e comprimento dos botões florais, massa fresca e seca das pétalas. Para a análise dos parâmetros meteorológicos foram selecionados 12 vãos de estufas com plásticos de ano de uso 1998, 1999, 2002 e 2003, com três repetições cada. Foram estudadas as variáveis temperatura de bulbo seco, temperatura de bulbo úmido, umidade relativa, e intensidade luminosa, com dados coletados durante 35 dias, nos horários das 10, 11, 12, 13, 14, 15, e 16 horas. Para as condições meteorológicas estudadas não houve diferença estatística. Para a análise de envelhecimento do plástico os testes foram divididos em dois componentes distintos: teste de tensão e ruptura e a espectroscopia nas faixas do espectro solar entre 199 e 1500 nm. Para o teste de tensão e ruptura foram selecionadas amostras de plástico de início de uso 1998, 1999 e 2003 (sem uso) onde as variáveis analisadas foram tensão e deformação total. Também para estes itens não houve diferença estatística, sendo que os valores encontrados estão dentro da expectativa de envelhecimento esperado pela fábrica. Para o teste de espectroscopia os plásticos de ano de início de uso de 1998, 1999 e 2003 (sem uso) tiveram duas amostras por ano de uso, uma das quais foi lavada com detergente neutro e outra deixada no estado em que se encontrava. Conclui-se, portanto, que para as condições aqui estudadas não se recomenda a necessidade da troca do plástico de cobertura no período de tempo avaliado devido a não ter havido alterações substanciais na produção da cultura, como conseqüência tanto dos aspectos micrometeorológicos dentro das estufas como quanto aos aspectos funcionais de resistência e transmissividade do plástico / Abstract: The aim of this study is to evaluate a film, which is used as a covering for greenhouses, through the aspects of production and quality, meteorological and aging parameters of the plastic film, under the conditions imposed by the plastic covering with different years of usage. In order to evaluate the production and quality, it was selected 15 greenhouse voids with plastic coverings dating from 1998, 1999, 2002 and 2003 and also a control one with three repetitions each. Two production managements were used in this analyses: the commercial management used in the property (first stage) and a specific management (second stage) in which occurred a clear felling at the beginning of the experiment, in an area of 1 m2 done with the purpose of evaluating the development of the flower buds from the pruning to the commercial flower stalk. On the first stage it was done 4 collections along the experiment period (during the days 01/03/2004, 17/03/2004, 26/03/2004 and 05/04/2004). On the second stage it was evaluated the appearance of the floral buds of the new shoots in four dates (20/02/2004, 07/03/2004, 26/03/2004 and through the weeks of 28/03 to 06/04/2004) until the complete formation of the commercial flower stalks. On the first stage it was collected 4 flower stalks per treatment in 5 treatments making a total of 60 flowers per collecting day. On the second stage it was collected 13 flower stalks per treatment in 4 treatments making a total of 52 flower stalks. There was no statistic difference between the plastics, which began to be used in the years of 1998, 1999, 2002 and 2003, when related to the length and diameter of the stalks, diameter and length of the flower buds, dry and fresh mass of he petal. In order to analyze the meteorological patterns, it was selected 12 greenhouse voids hose plastics dated from of 1998, 1999, 2002 and 2003, each one with three repetitions. The ariables studied were the dry bulb temperature, the relative humidity and the luminous intensity, it datum collected during 35 days, during the period of 10:00, 11:00, 12:00 a.m. and 1:00, :00, 3:00, and 4:00 p.m. There was no statistic difference for the meteorological conditions studied. The tests were divided into two distinct components in order to analyze the plastic aging: ension and rupture tests and the spectroscopy on the areas of solar spectrums between 199 and 4000 nm. For the tension and rupture test it was selected plastic samples which began to be used n 1998, 1999 and 2003 (which has not been used yet) where the variables analyzed were, ension, total deformation. For these items there wasn?t a statistic difference as well, and the values found are in accordance with the aging expectancy expected by the factory. For the studied conditions is not recommended to change the plastic coverture into the evaluated time six years) due to not variations to crop production as consequence of plastic resistance and transmissivity / Doutorado / Agua e Solo / Doutor em Engenharia Agrícola

Sea level rise (SLR) threatens coastal communities, infrastructure, and ecosystems. Worldwide, stakeholders critically depend on SLR projections with the associated uncertainty for risk assessments, decision-making and coastal planning. Recent research suggests that the Antarctic ice sheet mass loss during the 21st century may contribute up to an additional one meter of global SLR by year 2100. While uncertainty still exists, this value would double the ‘likely’ (> 66% probability) range of global SLR (0.52-0.98 m) by the year 2100, as found by Chapter 13 on Sea Level Change in the Fifth Assessment Report by the Intergovernmental Panel on Climate Change. Here, we present three studies that assess mechanisms relevant to 21st century local, regional, and global SLR. Appendix A examines the effect of large-scale oceanic and atmospheric circulation variability on extreme sea levels along the East Coast of North America. Appendices B and C analyze ocean warming on the Antarctic shelf and its implications for future ice shelf basal melt and Antarctic Ice Sheet mass loss. These studies will contribute to more accurate projections of local, regional, and global SLR. In Appendix A, we analyze long-term tide gauge records from the North American eastern seaboard and find an extreme SLR event during 2009-2010. Within this two-year period, coastal sea levels spiked between Montauk, New York and Southern Canada by up to 128 mm. This two-year spike is unprecedented in the tide gauge record and found to be a 1-in-850 year event. We show that a 30% reduction in strength of the Atlantic meridional overturning circulation (AMOC) and a strong negative North Atlantic Oscillation (NAO) index caused the extreme SLR event. Climate models project that the AMOC will weaken and NAO variability will remain high over the 21st century. Consequently, extreme SLR events on the Northeast Coast could become more frequent during the 21st century in response to climate change and SLR. In Appendix B, we use a fine-resolution global climate model (GFDL CM2.6) that resolves an eddying ocean. With this state-of-the-art coupled model, we quantify the mechanisms contributing to ocean warming on the Antarctic continental shelf in an idealized experiment of doubling of the atmospheric CO2 concentration. The results show that the CO2 forcing leads to the shelf region warming both in the upper 100 m ocean and at depths near the sea floor. These warming patterns are controlled by different mechanisms. In the upper 100 m, the heat anomalies are primarily controlled by increased heat transport into the shelf region associated with the warmer near-surface waters from lower latitudes. Below 100 m, the heat anomalies develop due to increased onshore intrusions of relatively warm Circumpolar Deep Water and reduced vertical mixing of heat in the water column. A complete heat budget analysis is performed for the Antarctic shelf region as well as for six subdomains and three depth ranges (0-100 m, 100-700 m, and 700-1000 m). The results show that certain regions of the Antarctic shelf are more susceptible to large CO2-forced warming. These findings have implications for future Antarctic Ice Sheet mass loss and SLR, and can provide more detailed and accurate ocean boundary conditions for dynamical ice sheet models. In Appendix C, we use CM2.6 to examine the connections among ocean freshening and the magnitude and location of ocean warming on the Antarctic shelf. We find that CO2 forcing freshens the Antarctic shelf seas via increases in local precipitation, sea ice loss, liquid runoff, and iceberg calving. The freshening induces three heat budget-relevant responses: (1) reduced vertical mixing; (2) strengthening of the Antarctic Slope Front (ASF); and (3) increased eddy kinetic energy (EKE) near the ASF. First, heat can accumulate at depth (100-1000 m) as freshening increases the vertical stratification on the shelf and reduces upward mixing of heat associated with diffusion and convective processes. Second, freshening near the shelf break strengthens the ASF by increasing the lateral density gradient and by steepening and deepening the associated isopycnals. This response limits cross-ASF onshore heat transport at many locations around Antarctica. Third, EKE increases near the ASF may contribute to shelf warming by increasing cross-ASF onshore eddy heat transport. These results demonstrate the importance of shelf freshening to the development of positive heat anomalies on the Antarctic shelf. The findings provide new insight to the location of future shelf warming and ice shelf basal melting as well as provide significant information for projecting regional and global SLR.

In this dissertation the aim was to investigate the usage of algorithms found in computer science and apply suitable algorithms to the problem of decoding multiple-input multipleoutput (MIMO) space-time-frequency block coded signals. It was found that the sphere decoder is a specific implementation of the A* tree search algorithm that is well known in computer science. Based on this knowledge, the sphere decoder was extended to include a priori information in the maximum a posteriori probability (MAP) joint decoding of the STFC block coded MIMO signals. The added complexity the addition of a priori information has on the sphere decoder was investigated and compared to the sphere decoder without a priori information. To mitigate the potential additional complexity several algorithms that determine the order in which the symbols are decoded were investigated. Three new algorithms incorporating a priori information were developed and compared with two existing algorithms. The existing algorithms compared against are sorting based on the norms of the channel matrix columns and the sorted QR decomposition. Additionally, the zero forcing (ZF) and minimum mean squared error (MMSE) decoderswith and without decision feedback (DF) were also extended to include a priori information. The developed method of incorporating a priori information was compared to an existing algorithm based on receive vector translation (RVT). The limitation of RVT to quadrature phase shift keying (QPSK) and binary shift keying (BPSK) constellations was also shown in its derivation. The impact of the various symbol sorting algorithms initially developed for the sphere decoder on these decoders was also investigated. The developed a priori decoders operate in the log domain and as such accept a priori information in log-likelihood ratios (LLRs). In order to output LLRs to the forward error correcting (FEC) code, use of the max-log approximation, occasionally referred to as hard-to-soft decoding, was made. In order to test the developed decoders, an iterative turbo decoder structure was used together with an LDPC decoder to decode threaded algebraic space-time (TAST) codes in a Rayleigh faded MIMO channel. Two variables that have the greatest impact on the performance of the turbo decoder were identified: the hard limit value of the LLRs to the LDPC decoder and the number of independently faded bits in the LDPC code. / Dissertation (MEng)--University of Pretoria, 2013. / gm2014 / Electrical, Electronic and Computer Engineering / unrestricted

Ce travail de recherche s’inscrit dans le contexte actuel d’accroissement de la vulnérabilité de l’Homme et des activités humaines face aux risques littoraux (aléas érosion et submersion marine), en lien avec les changements environnementaux globaux (élévation du niveau moyen relatif des océans et augmentation de la fréquence et de la virulence des tempêtes) et à la concentration de la population sur le littoral. Suite à la tempête Xynthia du mois de février 2010, l’Etat français s’est doté d’une Stratégie Nationale de Gestion Intégrée du Trait de Côte visant à mettre en place de nouvelles approches en matière de gestion du trait de côte, et notamment, favoriser le repli stratégique contre la défense côtière à tout prix. La mise en place de cette stratégie doit avant tout s’appuyer sur la mise en place d’un réseau d’observation et de suivi de l’évolution du trait de côte à l’échelle de la France. Ce travail s’inscrit dans cette problématique. Il a eu pour objectif d’étudier les dynamiques du trait de côte des plages sableuses et des cordons de galets (formes d’accumulation) de la Bretagne, à différentes échelles spatio-temporelles. Sur le long terme, l’analyse a consisté dans un premier temps à établir une typologie des côtes d’accumulation suivant différents critères morphosédimentaires ; la cinématique du trait de côte a ensuite été analysée à l’échelle des soixante dernières années (1950-2010) à partir d’une étude diachronique par photogrammétrie. Sur le moyen terme, l’analyse s’est faite dans le cadre des suivis topomorphologiques réalisés à l’échelle pluriannuelle à pluridécennale, de plusieurs sites ateliers de l’ODC (IUEM) et/ou du SNO Dynalitt. L’étude des changements morphosédimentaires s’est accompagnée d’une analyse de données de houle, de marée, de vent, et de pression atmosphérique, dans le but d’expliquer la part de ces forçages dans l’alternance de phases d’érosion et de périodes de régénération. Enfin sur le court terme, cette analyse s’est basée sur des levés topomorphologiques à haute fréquence réalisés au cours de l’hiver tempétueux 2013-2014. A cela, s’est ajoutée une étude expérimentale visant à quantifier le runup, dans le but d’analyser l’impact des niveaux d’eau extrêmes à la côte sur l’érosion du trait de côte. De manière globale, la quantification des variations du trait de côte sur le long terme a mis en évidence une tendance à l’érosion (27 % de linéaire étudié), une progradation du trait de côte non négligeable (20,5 % de linéaire) ainsi qu’une importante artificialisation du trait de côte (34,5 % de linéaire). La similitude des réponses morphosédimentaires des cordons littoraux étudiés aux conditions météomarines a permis d’identifier cinq phases distinctes. Trois phases morphogènes (de 1998 à 2003 ; de l’hiver 2006/07 au printemps 2008 ; de l’hiver 2012/13 à aujourd’hui), caractérisées par une érosion importante du trait de côte combinée à une haute fréquence des épisodes tempétueux ; et deux phases au cours desquelles les conditions météomarines ont été plus clémentes (de 2003 à l’hiver 2006/07 ; du printemps 2008 à l’hiver 2012/13), permettant la régénération des cordons littoraux. Au cours de l’hiver 2013-2014, trois tempêtes ont été particulièrement morphogènes en matière d’érosion du trait de côte car elles ont été combinées à de fortes marées de vive-eau : la tempête du 4 et 5 janvier, celle du 1 au 3 février, ainsi que celle du 2 au 3 mars. Durant cet hiver, le recul moyen pour tous les sites étudiés a atteint -6,3 m, avec un maximum d’environ -30,1 m et un minimum de -0,2 m. / This research is part of current context of increasing of human beings and human activities vulnerability face to coastal risks (erosion hazards and marine submersion), linked to global environmental changes (global relative sea level rise and growth of storms’ frequency and intensity) and the current concentration of the population on the coastline. Following the storm Xynthia (February 2010), France has adopted a national strategy dealing with coastal erosion and shoreline retreat, in order to define a new integrated national strategy of coastline management, promoting the relocation of stakes and properties. This strategy focuses on the monitoring of shoreline changes and the identification of coastal risks due to erosion.This work fall within this issue. The main objective was to study sedimentary coasts dynamics (sand dunes and gravel barriers) of Brittany, following different spatial and temporal scales. In the long term, the analysis consisted, first of all, in establishing a typology of sedimentary coasts according to several morpho-sedimentary criteria; then, coastline kinematic has been analyzed over the last sixty years (1950-2010) through a diachronic study using photogrammetry. In the medium term, analysis was carried out as part of topographic surveys performed at multi-annual to multi-decadal scale, on several Observatoire du Domaine Côtier (IUEM) and/or Service National d’Observation - Dynalitt survey sites. The morpho-sedimentary study was combined with a wave, tide, wind and atmospheric pressure analysis, in order to explain the role of these forcing in the erosion and recovery successive phases. Finally, in the short term, analysis was based on high frequency of topomorphological surveys carried out during the 2013-2014 stormy winter. Additionally, an experimental study to quantify runup process, in order to analyze extreme water levels impact on shoreline erosion.Overall, the quantification of coastline variations over the long term revealed an erosion tendency on 27% of the studied linear, a non-negligible progression of the shoreline on 20.5% of the studied linear, and a significant shoreline anthropogenic impact (34.5% of the studied linear). The similarity of the morpho-sedimentary responses of the littoral strands studied to the meteorological conditions allowed to identify five distinct phases. Three morphogenetic phases (1998 to 2003; winter 2006/07 to spring 2008; winter 2012/13 to the present), characterized by severe shoreline erosion combined with a high frequency of storm episodes, and two phases (2003 to winter 2006/07 ; spring 2008 to winter 2012/13) characterized by milder weather conditions, allowing shoreline recovery. During 2013-2014 winter, three storms were particularly morphogenetic for sedimentary coasts, because they were combined with high spring tides: January 4-5, February 1-3, and March 2-3. During this winter, the average retreat for all studied sites reached -6,3 m, with a maximum of -30,1 m and a minimum of -0,2 m.

No description available.

Aerosols are important atmospheric constituents that impact the Earth's radiative balance and climate. The detailed knowledge of the aerosol optical properties is required for a comprehensive analysis of the impacts of aerosols on climate. Mie theory is often used in satellite and ground-based retrieval algorithms to account for atmospheric mineral dust. However, the approximations used in Mie theory are often not appropriate for mineral dust and can lead to errors in the optical properties modeling. Analytic models based on Rayleigh theory that account for particle shapes can offer significant advantages when used to model infrared (IR) extinction of mineral dust. Here, the IR optical properties of some components of mineral dust, authentic dust samples and minerals processed with organic acids were investigated. Detailed characterization of the particles through online and offline methods of analysis that include IR extinction spectroscopy, micro-Raman spectroscopy and scanning electron microscopy was performed. Analysis of the IR extinction spectra and spectral simulations showed that the positions of the peaks and the shapes of the bands of the IR characteristic features are not well simulated by Mie theory in any of the samples studied. The resonance peaks were consistently shifted relative to the experimental spectrum in the Mie simulation. Rayleigh model solutions derived for different particle shapes better predicted the peak positions and band shapes of experimental spectra. To fill the gaps in the refractive index data for atmospherically relevant organic compounds in the IR region optical properties of atmospherically relevant carboxylic acids and humic-like substances using the IR extinction spectra and size distributions measured in the laboratory were determined. In addition to properties of mineral dust this dissertation focuses on properties of sea spray aerosol. Chemical and elemental composition of individual sea spray aerosol particles were studies using micro-Raman spectroscopy, mass-spectrometry and X-ray spectroscopy to provide insights into the biochemical processes that give rise to classes of organic molecules that make up these aerosol particles. The results suggested that degradation of biota (bacteria and diatoms) present in sea water led to lipopolysaccharides and extracellular polymeric substances that further degraded down to carbohydrates and fatty acids. Solubility of the resulting organic species seemed to play a role in their transfer to the aerosol phase. Furthermore, water uptake and hygroscopic growth of multi-component particles were studied. Understanding the interactions of water with atmospheric aerosols is crucial for determining their size, physical state, reactivity, and therefore for aerosol interactions with electromagnetic radiation and clouds. It was determined that particles composed of ammonium sulfate with succinic acid and of mixture of chlorides typical for marine environment show size dependent hygroscopic behavior. Microscopic analysis of the distribution of components within the aerosol particles showed that the observed size dependence is due to the differences in the mixing state. The composition and water uptake properties of sea spray aerosol particles were also measured during a phytoplankton bloom. The results showed that water uptake properties were directly related to the chemical composition of the particles and hygroscopicity decreased with increase in the fraction of water insoluble organic matter emitted during phytoplankton bloom. Finally, multiple methods of particle size, phase and shape analysis were compared and the results showed that the techniques that operate under ambient conditions provide the most relevant and robust measurement of particle size. Additionally, several storage methods for substrate deposited aerosol particles were evaluated and it was determined that storing samples at low relative humidity led to irreversible changes due to sample dehydration while sample freezing and thawing leads to irreversible changes due to phase changes and water condensation. Therefore it is suggested that samples used for single-particles analysis should be stored at ambient laboratory conditions, or near conditions which they were collected, in order to preserve the sample phase and hydration state. The results presented in this dissertation provide insight into physicochemical properties of atmospheric aerosols and help us better understand the role of aerosol particles in the Earth's atmosphere.

Free-space optics (FSO) is an unlicensed communication technology that uses the free space as a propagation medium to connect two communicating terminal wire- lessly [1]. It is an attractive solution to the last-mile connectivity problems in commu- nication networks, mainly when installing optical fibers is expensive or unavailable. A possible idea to increase the throughput of wireless optical links in free space is to use spatial multiplexing (SMM) [2]. Optical beam distortion due to propagation through a turbulent channel is one of the main factors limiting performance of such a system. Therefore, overcoming the effect of turbulence is a major problem for structured light optical communication in free space. Usually, this problem is approached by using adaptive optics systems and various methods of digital signal processing (DSP) on the receiver side [3–5]. Recently, an idea of optical channel pre-compensation to mit- igate inter-modal crosstalk was proposed [6] and experimentally validated [7]. Such a method, if implemented, will allow the use of entirely passive receivers or, in the case of full-duplex transmission, increase throughput. Here, the performance of a zero-forcing precoding technique to mitigate the effects of an optical turbulence in a Laguerre Gaussian mode based SMM FSO is investigated. Equally, details on a close to reality simulation of the atmospheric turbulence and beam propagation are provided.

The zero forcing number is a graph parameter first introduced as a tool for solving the minimum rank problem, which is: Given a simple, undirected graph G, and a field F, let S(F,G) denote the set of all symmetric matrices A=[a_{ij}] with entries in F such that a_{ij} doess not equal 0 if and only if ij is an edge in G. Find the minimum possible rank of a matrix in S(F,G). It is known that the zero forcing number Z(G) provides an upper bound for the maximum nullity of a graph. I investigate properties of the zero forcing number, including its behavior under various graph operations.

Massive MU-MIMO (Multiuser-Multiple Input and Multple Output) is a promising technology for 5G wireless communications because of its spectrum and energy efficiency. To combat the distortion from multipath fading channel, the acquisition of channel state information is essential, which generally requires the training signal that lowers the data rate. In addition, coarse quantization can reduce the high computational energy and cost, yet results in the loss of information. In this thesis, an iterative decision feedback receiver, including iterative Channel Estimation (CE) and equalization, is constructed for a Massive MU-MIMO uplink system. The impact of multipath distortion and coarse quantization can be gradually reduced due to the iterative structure that exploits extrinsic feedback to improve the CE and data detection, so that the data rate is improved by reducing training signals for CE and by using low precision quantization. To observe and evaluate the convergence behaviour, an Extrinsic Information Transfer (EXIT) chart method is utilized to visualize the performance of the iterative receiver. / Graduate

<p>The method of forcing is widely used in set theory to obtain&nbsp;various consistency proofs. Complete Boolean algebras play the main role&nbsp;in applications of forcing. Therefore it is useful to define games on Boolean&nbsp;algebras that characterize their properties important for the method. The&nbsp;most investigated game is Jech&rsquo;s distributivity game, such that the first&nbsp;player has the winning strategy iff the algebra is not (&omega;, 2)-distributive.&nbsp;We define another game characterizing the collapsing of the continuum to&nbsp;&omega;, prove several sufficient conditions for the second player to have a winning&nbsp;strategy, and obtain a Boolean algebra on which the game is undetermined.&nbsp;</p> / <p>Forsing je metod &scaron;iroko kori&scaron;ćen u teoriji skupova za dokaze konsistentnosti. Kompletne&nbsp; Bulove algebre igraju glavnu ulogu u primenama forsinga. Stoga je korisno definisati igre na Bulovim algebrama koje karakteri&scaron;u njihove osobine od značaja za taj metod. Najbolje proučena je Jehova igra, koja ima osobinu da prvi igrač ima pobedničku strategiju akko algebra nije (&omega;, 2)-distributivna. U tezi defini&scaron;emo jo&scaron; jednu igru, koja karakteri&scaron;e kolaps kontinuuma na &omega;, dokazujemo nekoliko dovoljnih uslova da bi drugi igra&scaron; imao pobedničku strategiju, i konstrui&scaron;emo Bulovu algebru na kojoj je igra neodređena.</p>