Call number: LD2668 .T4 1979 S53 / Master of Science

O estudo das propriedades de regularidade na reta real é tão antigo quanto o surgimento da teoria dos conjuntos no final do século XIX. Essas propriedades indicam bom comportamento para subconjuntos da reta real, sendo os exemplos mais proeminentes a propriedade do conjunto perfeito, a Lebesgue mensurabilidade e a Baire mensurabilidade. Neste trabalho outras propriedades de regularidade são exploradas, como a propriedade de Ramsey, a propriedade doughnut, a Marczewski mensurabilidade, a Miller mensurabilidade, a Laver mensurabilidade, dentre outras. A relação que existe entre propriedades de regularidade e forcing é conhecida desde a década de 70 com os trabalhos de Robert Solovay, que, por exemplo, construiu um modelo de teoria dos conjuntos onde todo subconjunto da reta real é Lebesgue mensurável, Baire mensurável e tem a propriedade do conjunto perfeito. Todas essas propriedades de regularidade são capturadas em uma definição geral recorrendo à poderosa técnica do \\textit{forcing idealizado}, introduzida e explorada por Jindrich Zapletal em 2004. O principal estudo sistemático das propriedades de regularidade via forcing idealizado foi feito por Yurii Khomskii em 2012 em sua tese de doutorado. O resultado de Solovay mencionado acima é provado nesse contexto geral de regularidade. Também são exploradas caracterizações para a regularidade dos conjuntos no segundo nível da hierarquia projetiva via forcing sobre L. Para a maioria dos assuntos abordados é dada alguma nota histórica. / The study of the regularity properties in the real line is as old as the beginning of set theory at the end of the 19th century. These properties indicate well behavior for subsets of the real line, being the Lebesgue measurability, Baire measurability and perfect set properties the most prominent examples. In this work other regularity properties are explored, such as the Ramsey property, the doughnut property, the Marczewski measurability, the Miller measurability, the Laver measurability, among others. The relationship between regularity properties and forcing is known since the 70\'s with the work of Robert Solovay, who, for example, constructed a model of set theory in which every subset of the real line is Lebesgue measurable, Baire measurable, and has the perfect set property. All of theses regularity properties are captured by a general definition making use of the powerful technique of \\textit, introduced by Jindrich Zapletal in 2008. The main systematic study of regularity properties via idealized forcing was done by Yurii Khomskii in 2012 in his Ph.D dissertation. The result of Solovay mentioned above is proved in this general framework. Characterization results for regularity properties of the sets in the second level of the projective hierarchy via forcing over L are also explored. Some historical notes are provided for most of the addressed subjects.

The cooperative communication is one of technologies which can explore the space diversity to resist fading channel. The spatial diversity is achieved by allowing various terminals behaving or a virtual antenna array and forwarding signal for a source terminal in cooperative manner. Under the existence of multiple sources, resource allocation to each source user is even more crucial to enhance the system performance and achieve higher diversity gain. In this work, we proposed a multiuser relaying strategy for a cooperative network with multiple sources sharing the radio resource provided by the cooperative relays simultaneously. Different from the existing work, the set of relays forwards signals of all source users over a common channel to raise spectral efficiency. With full channel information available at relays, the set of sub-optimal precoders and decoders was proposed in terms of maximal the average SNR over all users, subject to eliminating the multiple access interference (MAI) at each destination and satisfying total power constraint among all relays. It shows from the simulation results that, compared with the conventional cooperative strategy and direct transmission, the proposed scheme provides pronounced improvement on the outage capacity. Keywords: user cooperation, multiple access, resource allocation

O estudo das propriedades de regularidade na reta real é tão antigo quanto o surgimento da teoria dos conjuntos no final do século XIX. Essas propriedades indicam bom comportamento para subconjuntos da reta real, sendo os exemplos mais proeminentes a propriedade do conjunto perfeito, a Lebesgue mensurabilidade e a Baire mensurabilidade. Neste trabalho outras propriedades de regularidade são exploradas, como a propriedade de Ramsey, a propriedade doughnut, a Marczewski mensurabilidade, a Miller mensurabilidade, a Laver mensurabilidade, dentre outras. A relação que existe entre propriedades de regularidade e forcing é conhecida desde a década de 70 com os trabalhos de Robert Solovay, que, por exemplo, construiu um modelo de teoria dos conjuntos onde todo subconjunto da reta real é Lebesgue mensurável, Baire mensurável e tem a propriedade do conjunto perfeito. Todas essas propriedades de regularidade são capturadas em uma definição geral recorrendo à poderosa técnica do \\textit{forcing idealizado}, introduzida e explorada por Jindrich Zapletal em 2004. O principal estudo sistemático das propriedades de regularidade via forcing idealizado foi feito por Yurii Khomskii em 2012 em sua tese de doutorado. O resultado de Solovay mencionado acima é provado nesse contexto geral de regularidade. Também são exploradas caracterizações para a regularidade dos conjuntos no segundo nível da hierarquia projetiva via forcing sobre L. Para a maioria dos assuntos abordados é dada alguma nota histórica. / The study of the regularity properties in the real line is as old as the beginning of set theory at the end of the 19th century. These properties indicate well behavior for subsets of the real line, being the Lebesgue measurability, Baire measurability and perfect set properties the most prominent examples. In this work other regularity properties are explored, such as the Ramsey property, the doughnut property, the Marczewski measurability, the Miller measurability, the Laver measurability, among others. The relationship between regularity properties and forcing is known since the 70\'s with the work of Robert Solovay, who, for example, constructed a model of set theory in which every subset of the real line is Lebesgue measurable, Baire measurable, and has the perfect set property. All of theses regularity properties are captured by a general definition making use of the powerful technique of \\textit, introduced by Jindrich Zapletal in 2008. The main systematic study of regularity properties via idealized forcing was done by Yurii Khomskii in 2012 in his Ph.D dissertation. The result of Solovay mentioned above is proved in this general framework. Characterization results for regularity properties of the sets in the second level of the projective hierarchy via forcing over L are also explored. Some historical notes are provided for most of the addressed subjects.

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Given a C*-algebra $\\A$, an irredundant set in $\\A$ is a subset $\\mathcal$ of $\\A$ such that no $a\\in \\mathcal$ belongs to the C*-subalgebra generated by $\\mathcal\\setminus\\{a\\}$. Every separable C*-algebra has only countable irredundant sets and we ask if every nonseparable C*-algebra has an uncountable irredundant set. For commutative C*-algebras, if $K$ is the Kunen line then $C(K)$ is a consistent example of a nonseparable commutative C*-algebra without uncountable irredundant sets. On the other hand, a result due to S. Todorcevic establishes that it is consistent with ZFC that every nonseparable C*-algebra of the form $C(K)$, for a compact 0-dimensional space $K$, has an uncountable irredundant set. By the method of forcing, we construct a nonseparable and noncommutative scattered C*-algebra $\\A$ without uncountable irredundant sets and with no nonseparable abelian subalgebras. On the other hand, we prove that it is consistent that every C*-subalgebra of $\\B(\\ell_2)$ of density continuum has an irredundant set of size continuum. / Given a C*-algebra $\\A$, an irredundant set in $\\A$ is a subset $\\mathcal$ of $\\A$ such that no $a\\in \\mathcal$ belongs to the C*-subalgebra generated by $\\mathcal\\setminus\\{a\\}$. Every separable C*-algebra has only countable irredundant sets and we ask if every nonseparable C*-algebra has an uncountable irredundant set. For commutative C*-algebras, if $K$ is the Kunen line then $C(K)$ is a consistent example of a nonseparable commutative C*-algebra without uncountable irredundant sets. On the other hand, a result due to S. Todorcevic establishes that it is consistent with ZFC that every nonseparable C*-algebra of the form $C(K)$, for a compact 0-dimensional space $K$, has an uncountable irredundant set. By the method of forcing, we construct a nonseparable and noncommutative scattered C*-algebra $\\A$ without uncountable irredundant sets and with no nonseparable abelian subalgebras. On the other hand, we prove that it is consistent that every C*-subalgebra of $\\B(\\ell_2)$ of density continuum has an irredundant set of size continuum.

Thesis (Ph. D.)--York University, 1999. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 87-93). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ43427.

The purpose of following project is to study the effect of dust aerosols on the radiative forcing which is directly related to the surface temperature. A single column radiative convective model is used for simulation purpose. A series of simulations have been performed by varying the amount of dust aerosols present in the atmosphere to study the trends in ground temperature, heating rate and radiative forcing for both its longwave and shortwave components. A case study for dust storm is also performed as dust storms are common in Arabian Peninsula. A sensitivity analyses is also performed to study the relationship of surface temperature minimum and maximum against aerosol concentration, single scattering albedo and asymmetry factor. These analyses are performed to get more insight into the role of dust aerosols on radiative forcing.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 295-332).

Shoot production and in vitro performance of Juglans nigra L and Quercus rubra L. was studied where 0, 3, 10, 30, or 100mM benzyladenine (BA) in a 20% white exterior latex paint diluted with deionized water were applied separately to 40 cm branch segments to determine the most effective concentration of benzyladenine on bud break and shoot growth. Softwood shoot production was maximized in the harvest months of March and April for J. nigra. Softwood shoot production was maximized in the harvest months of April and August for Q. rubra. Both shoot number and shoot length of softwood shoots decreased linearly with increasing BA concentrations applied to the branch segments of both species. Shoot production also decreased for both species during the dormant season September-December. The softwood shoots were surface disinfested and established on either 0 or 5µM Long Preece medium. When all BA treated softwood shoots were compared to the controls, the BA in the medium caused a significant increase in the number of shoots produced by explants obtained from the branch segments painted with BA. Painting with BA also increased shoot production in vitro, only if BA was also in the medium. Nodal explants cultured on 5µM LP medium taken from softwood shoots forced from branch segments painted with 3mM BA produced more shoots than any other BA concentration applied to branch segments except nodal explants on 5µM LP medium taken from softwood shoots forced from branch segments painted with 30mM BA.