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Showing 1 to 20 of 36 for “"Rational function"”.
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Rational Function Approximation of Polynomials With Equiripple Error
Made available in DSpace on 2014-12-04T21:03:35Z (GMT). No. of bitstreams: 1 6305104.pdf: 2610002 bytes, checksum: 1ef0dfa34041ab96c8f80296994a627c (MD5) Previous issue date: 1963
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Black Box Modeling of Passive Systems by Rational Function Approximation
… efficiency and accuracy compared to existing rational function approximation methods.
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Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data
Item marked as restricted to the 'Administrator' Group (id=1) by Timothy Donohue (tdonohue@illinois.edu) on 2009-06-04T16:03:37Z Item is restricted until 2010-06-04T16:03:37Z
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Noncommutative rational functions and their finite-dimensional representations
Noncommutative rational functions form a free skew field, a universal object in the category of skew fields. They emerge in various branches of pure and applied mathematics, such as noncom-mutative algebra, automata theory, control theory, free analysis, free real algebraic geometry and free …
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Approximation of Elements of Exponentials of Differential Operators With Rational Quadrature
… of differential operators, by using a rational function, instead of a polynomial function, as the interpolating function. Since a rational function behaves more like a decaying exponential function, it seems logical that the approximation should be more accurate. Through the use of high …
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Dynamics and Measures for Semigroups of Rational Functions
In addition in Chapter 6 we provide examples of rational semigroups where the Fatou set contains an arbitrary finite number of components. The Fatou set of a single rational function must contain zero, one, two or infinitely many components.
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Passive Rational Fitting of a Passive Network Transfer Function From Its Real Part
A methodology is presented to generate a rational function approximation of a passive network transfer function that makes use of sampled values of the transfer function's real part at a set of frequencies over the bandwidth of interest. For passive networks, real-part sufficiency describes the …
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Broadband Macromodeling via a Fast Implementation of Vector Fitting with Passivity Enforcement
… This often involves the generation of passive rational function representations of the system from the measured port responses. In this thesis, we will employ the vector fitting algorithm to generate a rational function representation of the system along with its state space model. Various …
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A global Boettcher's theorem
We prove a global result for rational functions that is analogous to a local theorem of L. E. Boettcher (1904). Under the hypotheses that f is a complex rational function with a superattractive fixed point $\alpha$ of order $p \ge 2$ and that $\alpha$ is the only critical point of f in the …
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The fine structure of translation functors, the triangle function and a construction of R-matrices
… character chi( au + <br>u). This is a rational function in au and we <br>calculate its poles and zeros. <br>We then apply this result in order to compare translation functors. <br>We also describe a transformation for quantum dynamical R-matrices.
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Efficient and physically consistent electromagnetic macromodeling of high-speed interconnects exhibiting geometric uncertainties
… in macromodeling techniques pertinent to the rational function interpolation of broadband electromagnetic responses of linear, passive, multiport, high-speed interconnect networks. First, we propose and demonstrate a new methodology that combines the efficiency of low-frequency and …
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Numerical Modeling of Multi-Conductor Interconnects for High Speed Integrated Circuits
… RLCG extractor. The methodology relies upon a rational fitting algorithm called VECTFIT to express the parameters as a rational function expression, a form suitable for equivalent circuit generation using a commercial circuit simulator like HSPICE. The methodology has been numerically verified …
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On congruence function fields with many rational places
In this thesis, we study congruence function fields, in particular those with many rational places. This thesis consists of three parts, the first two parts present our results in two different aspects of function fields with many rational places, namely maximal function fields and asymptotically …
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Volterra Systems with Realizable Kernels
… integral to be realizable as an impulse response function. We discover that when applicable, the internal state method is orders of magnitude more efficient than the direct numerical method. However, constructing state representation for realizable kernels can be challenging at times; therefore, …
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Some Extensions of the Skolem-Mahler-Lech Theorem
… Taylor series expansion (about the origin) of a rational function has infinitely many zero coefficients, then the set of indices of these zero coefficients forms a finite union of arithmetic progressions modulo a finite set. Since rational functions satisfy linear differential equations of order …
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Box approximation and related techniques in spectral theory
… presents a study of a family of spectral shift functions [xi]r, each associated with a pair of self-adjoint Schrödinger operators on a finite interval (0, r). Specifically, we investigate the limit behavior of the functions [xi]r when the parameter r approaches infinity. We prove that an …
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Prime Rational Functions and Integral Polynomials
Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for …
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Fractional parts of powers and related topics
… We are generally concerned with constructing rational function approximations to certain polynomials and to the exponential and other related functions. From these systems, we deduce arithmetic information about the original problem. Chapter 0 is an introduction to the field and contains …
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Effective integrality results in arithmetic dynamics
Given a rational function f defined over a number field K, S. Ih conjectured the finiteness of f-preperiodic points which are S-integral relative to a given non-preperiodic point β. This conjecture remains open, but certain special cases have been proved. We formulate a generalisation of Ih's …
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