Exercise sheet 3 pdf

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Exercise sheet 3

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MA17xexam01pdf

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Java-XSC : módulo complexo e complexo intervalar

This work aims to develop modules that will increase the computational power of the Java-XSC library, and XSC an acronym for "Language Extensions for Scientific Computation . This library is actually an extension of the Java programming language that has standard functions and routines elementary mathematics useful interval. in this study two modules were added to the library, namely, the modulus of complex numbers and complex numbers of module interval which together with the modules original numerical applications that are designed to allow, for example in the engineering field, can be used in devices running Java programs

Visualização das funções complexas e do Teorema Fundamental da Álgebra

Pós-graduação em Matemática Universitária - IGCE

Discours sur la nature des grandeurs négatives et imaginaires,

Mode of access: Internet.

A treatise on the geometrical representation of the square roots of negative quantities /

Mode of access: Internet.

GeoPlexo: um material manipulável para o ensino dos números complexos

This study aims to develop a manipulative material to assist the teaching and learning of Complex Numbers. Primarily, It tries to define the status of the current teaching of Complex Numbers, having as guide the bias of the research produced in dissertations and published on the website of Capes and the Virtual Library of Profmat from 2004 to 2014. It presents historical aspects of the theme, a mathematical foundation and a discussion of the use of manipulative materials as teaching resources for the teaching of mathematics. It introduces the manipulative material called GeoPlexo and a sequence of activities of potentiation and settling of complex numbers, explaining its use. It concludes with the importance of manipulative materials as a teaching resource for the teaching of Complex Numbers, especially regarding the geometric visualization of this mathematical object.

Construction of the transcomplex numbers from the complex numbers

A geometrical construction of the transcomplex numbers was given elsewhere. Here we simplify the transcomplex plane and construct the set of transcomplex numbers from the set of complex numbers. Thus transcomplex numbers and their arithmetic arise as consequences of their construction, not by an axiomatic development. This simplifes transcom- plex arithmetic, compared to the previous treatment, but retains totality so that every arithmetical operation can be applied to any transcomplex number(s) such that the result is a transcomplex number. Our proof establishes the consistency of transcomplex and transreal arithmetic and establishes the expected containment relationships amongst transcomplex, complex, transreal and real numbers. We discuss some of the advantages the transarithmetics have over their partial counterparts.

Paraconsistent Multivalued Logic and Coincidentia Oppositorum: Evaluation with Complex Numbers

Paraconsistent logic admits that the contradiction can be true. Let p be the truth values and P be a proposition. In paraconsistent logic the truth values of contradiction is . This equation has no real roots but admits complex roots . This is the result which leads to develop a multivalued logic to complex truth values. The sum of truth values being isomorphic to the vector of the plane, it is natural to relate the function V to the metric of the vector space R2. We will adopt as valuations the norms of vectors. The main objective of this paper is to establish a theory of truth-value evaluation for paraconsistent logics with the goal of using in analyzing ideological, mythical, religious and mystic belief systems.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Synthesis of optically complex core-shell colloidal suspensions: Pathways to multiplexed biological screening

The ability to generate enormous random libraries of DNA probes via split-and-mix synthesis on solid supports is an important biotechnological application of colloids that has not been fully utilized to date. To discriminate between colloid-based DNA probes each colloidal particle must be 'encoded' so it is distinguishable from all other particles. To this end, we have used novel particle synthesis strategies to produce large numbers of optically encoded particle suitable for DNA library synthesis. Multifluorescent particles with unique and reproducible optical signatures (i.e., fluorescence and light-scattering attributes) suitable for high-throughput flow cytometry have been produced. In the spectroscopic study presented here, we investigated the optical characteristics of multi-fluorescent particles that were synthesized by coating silica 'core' particles with up to six different fluorescent dye shells alternated with non-fluorescent silica 'spacer' shells. It was observed that the diameter of the particles increased by up to 20% as a result of the addition of twelve concentric shells and that there was a significant reduction in fluorescence emission intensities from inner shells as an increasing number of shells were deposited.

A Hexanuclear Mixed-Valence Oxovanadium(IV,V) Complex as a Highly Efficient Alkane Oxidation Catalyst

The new hexanuclear mixed-valence vanadium complex [V3O3(OEt)(ashz)(2)(mu-OEt)](2) (1) with an N,O-donor ligand is reported. It acts as a highly efficient catalyst toward alkane oxidations by aqueous H2O2. Remarkably, high turnover numbers up to 25000 with product yields of up to 27% (based on alkane) stand for one of the most active systems for such reactions.

Hepatitis C viral load does not predict disease outcome: going beyond numbers

The analysis of 58 patients with chronic hepatitis C without cirrhosis and treated with interferon-alpha demonstrated that hepatitis C viral (HCV) load does not correlate with the histological evolution of the disease (p = 0.6559 for architectural alterations and p = 0.6271 for the histological activity index). Therefore, the use of viral RNA quantification as an evolutive predictor or determinant of the severity of hepatitis C is incorrect and of relative value. A review of the literature provided fundamental and interdependent HCV (genotype, heterogeneity and mutants, specific proteins), host (sex, age, weight, etc) and treatment variables (dosage, time of treatment, type of interferon) within the broader context of viral kinetics, interferon-mediated immunological response (in addition to natural immunity against HCV) and the role of interferon as a modulator of fibrogenesis. Therefore, viral load implies much more than numbers and the correct interpretation of these data should consider a broader context depending on multiple factors that are more complex than the simple value obtained upon quantification.

Dissociation of thymic positive and negative selection in transgenic mice expressing major histocompatibility complex class I molecules exclusively on thymic cortical epithelial cells.

Thymic positive and negative selection of developing T lymphocytes confronts us with a paradox: How can a T-cell antigen receptor (TCR)-major histocompatibility complex (MHC)/peptide interaction in the former process lead to transduction of signals allowing for cell survival and in the latter induce programmed cell death or a hyporesponsive state known as anergy? One of the hypotheses put forward states that the outcome of a TCR-MHC/peptide interaction depends on the cell type presenting the selecting ligand to the developing thymocyte. Here we describe the development and lack of self-tolerance of CD8(+) T lymphocytes in transgenic mice expressing MHC class I molecules in the thymus exclusively on cortical epithelial cells. Despite the absence of MHC class I expression on professional antigen-presenting cells, normal numbers of CD8(+) cells were observed in the periphery. Upon specific activation, transgenic CD8(+) T cells efficiently lysed syngeneic MHC class I(+) targets in vitro and in vivo, indicating that thymic cortical epithelium (in contrast to medullary epithelium and antigen-presenting cells of hematopoietic origin) is incapable of tolerance induction. Thus, compartmentalization of the antigen-presenting cells involved in thymic positive selection and tolerance induction can (at least in part) explain the positive/negative selection paradox.