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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 35 for “"complex numbers"”.
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On the Necessity of Complex Numbers in Quantum Mechanics
… quantum system admits a representation in real, complex or quaternionic Hilbert spaces as established by Solèr’s theorem (1995) closing a long standing problem that can be traced back to von Neumann’s mathematical formulation of quantum mechanics. However up to now there are no examples of …
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Finite Solvable Subgroups of the General Linear Group of Prime Degree Over the Field of Complex Numbers
Made available in DSpace on 2014-12-09T22:17:37Z (GMT). No. of bitstreams: 1 6711875.pdf: 2000961 bytes, checksum: 9c6dc3b74bed4c4eae4cc4d170820180 (MD5) Previous issue date: 1967
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Números complexos graduados e avaliação de desempenho de classificadores
… a linguistic approach based in Fuzzy Complex Numbers for the multi-criteria evaluation of classification algorithms was proposed. However, when the absolute values are very close, this approach suggests a ranking with a large number of ties. In order to solve this problem, this work …
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On the Theory of Quaternions
… can be defined on pairs consistent with the complex numbers. However, as this paper will show, one cannot define a multiplication on triplets which is consistent with the complex numbers.
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Conditionally convergent vector series
… we propose to study the behavior of series of complex numbers, or of vectors in two dimensions; and to generalize this study to the case of vectors in n dimensions. The particular properties to be studied are described on page 7. We shall firsts state a few well-known properties of series, both …
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Topological uniqueness results for the special linear and other classical Lie Algebras.
… local fields (up to isomorphism) are the real, complex, and p-adic numbers, finite extensions of the p-adic numbers, and fields of formal power series over finite fields. We establish the topological uniqueness of the special linear Lie algebras over local fields other than the complex numbers …
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Classifying expansions of the real field by complex subgroups
… real field by multiplicative subgroups of the complex numbers. We first consider expansions by a subgroup generated by an element of the unit circle and a positive real number. We then consider expansions by a subgroup generated by a complex number and a positive real number. In both of these …
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IMPLEMENTATION OF A NOVEL INTEGRATED DISTRIBUTED ARITHMETIC AND COMPLEX BINARY NUMBER SYSTEM IN FAST FOURIER TRANSFORM ALGORITHM
… approach for computing and representing complex numbers as a single entity without the use of any dedicated multiplier for calculating the fast Fourier transform algorithm (FFT), using the Distributed Arithmetic (DA) technique and Complex Binary Number Systems (CBNS). The FFT algorithm is …
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Algebraically closed fields with characters; differential-henselian monotone valued differential fields
… field of characteristic p, C is the field of complex numbers and χ ∶ F → C is an injective, multiplication preserving map. In the second project we study the model theory of the differential-henselian monotone valued differential fields. We also consider definability in differential-henselian …
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Lifting Module Maps Between Different Noncommutative Domain Algebras
… a<sub>1</sub>, . . . , a<sub>N</sub> be complex numbers, and <strong>D</strong> the unit disk. When does there exist an analytic function F : <strong>D</strong> → <strong>C</strong> and complex numbers a<sub>N+1</sub>, a<sub>N+2</sub>, . . . such that F(z) = a<sub>0</sub> + a<sub>1</sub>z …
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Arithmetic properties and decomposability of Jacobians
… decomposability of Jacobians of curves over the complex numbers. This involves studying the action of a finite group on an abelian variety in general. Next, we use methods for point counting properties of curves over finite fields to study the decomposability of Jacobians over number fields and …
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On Berglund-Hübsch-Krawitz Mirror Symmetry
… they are orbifold K3 surfaces, both over the complex numbers and fields of positive characteristic. Finally, we provide a conjectural framework that unifies the toric mirror construction of Batyrev and Borisov with the BHK construction in the context of Kontsevich's Homological Mirror Symmetry …
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Applications of the Pauli algebra and other geometric algebras.
Relationships among the complex numbers, quaternions, and the Pauli algebra are developed by presenting them as geometrical (Clifford) algebras. Rotations are examined using both quaternions and the Pauli algebra, and in particular, algorithms that are used in three-dimensional simulations and …
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Fully-coupled fluid-structure analysis of a baffled rectangular orthotropic plate using the boundary element and finite element methods
… materials the analysis of these structures is complex and usually cannot be adequately performed using classical methods. In this dissertation the formulation of the fully coupled fluid-structure interaction of a laminated composite plate and its surrounding fluid medium is presented. The …
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Space-variant incoherent optical processing using color
… optical processing techniques. However, the complex amplitude linearity exhibited by coherent optical systems that provides a natural means for performing operations on complex functions, is lacking with incoherent optical systems. Bipolar values, as well as complex values, must be …
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Discrete Quantum Theories and Computing
… models are based on the continuum of real numbers, while classical digital computers faithfully realize only discrete computational models. Analog computers appear to be an option, but in reality are far weaker than would be needed for computational models requiring real numbers. One …
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Spectral Properties of Quaternionic Unit Gain Cycles
… a non-commutative division ring that extends the complex numbers. A gain graph is a simple graph together with a gain function that assigns a value from an arbitrary group to each edge of the graph. We can define certain concepts on these graphs such as adjacency and Laplacian matrices, gains of …
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A History of Complex Simple Lie Algebras
… In this paper, we focus on Lie algebras over the complex numbers, and how simplicity and the related notion of semisimplicity, as well as root spaces and their representations, reveal that there are, up to isomorphism, surprisingly few simple complex Lie algebras, a result which Killing examined …
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The Irreducible Representations of D2n
… on the m-dimensional space V over the field K of complex numbers and if U is an invariant subspace of φ, then U has a complementary reducing subspace W .</p> <p>The objective of this thesis is to find all irreducible representations of the dihedral group D2n. The reason we will work with the …
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Octonions and the Exceptional Lie Algebra g_2
… This approach parallels the realization of the complex numbers as ordered pairs of real numbers. The rest of the thesis is devoted to following a paper by N. Jacobson written in 1939 entitled "Cayley Numbers and Normal Simple Lie Algebras of Type G". We prove that the algebra of derivations on …
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