2,615,993 research outputs found

    Characterising linear spatio-temporal dynamical systems in the frequency domain

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    A new concept, called the spatio-temporal transfer function (STTF), is introduced to characterise a class of linear time-invariant (LTI) spatio-temporal dynamical systems. The spatio-temporal transfer function is a natural extension of the ordinary transfer function for classical linear time-invariant control systems. As in the case of the classical transfer function, the spatio-temporal transfer function can be used to characterise, in the frequency domain, the inherent dynamics of linear time-invariant spatio-temporal systems. The introduction of the spatio-temporal transfer function should also facilitate the analysis of the dynamical stability of discrete-time spatio-temporal systems

    Transfer Function Synthesis without Quantifier Elimination

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    Traditionally, transfer functions have been designed manually for each operation in a program, instruction by instruction. In such a setting, a transfer function describes the semantics of a single instruction, detailing how a given abstract input state is mapped to an abstract output state. The net effect of a sequence of instructions, a basic block, can then be calculated by composing the transfer functions of the constituent instructions. However, precision can be improved by applying a single transfer function that captures the semantics of the block as a whole. Since blocks are program-dependent, this approach necessitates automation. There has thus been growing interest in computing transfer functions automatically, most notably using techniques based on quantifier elimination. Although conceptually elegant, quantifier elimination inevitably induces a computational bottleneck, which limits the applicability of these methods to small blocks. This paper contributes a method for calculating transfer functions that finesses quantifier elimination altogether, and can thus be seen as a response to this problem. The practicality of the method is demonstrated by generating transfer functions for input and output states that are described by linear template constraints, which include intervals and octagons.Comment: 37 pages, extended version of ESOP 2011 pape

    Transfer functions for infinite-dimensional systems

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    In this paper, we study three definitions of the transfer function for an infinite-dimensional system. The first one defines the transfer function as the expression C(sIA)1B+DC(sI-A)^{-1}B+D. In the second definition, the transfer function is defined as the quotient of the Laplace transform of the output and input, with initial condition zero. In the third definition, we introduce the transfer function as the quotient of the input and output, when the input and output are exponentials. We show that these definitions always agree on the right-half plane bounded to the left by the growth bound of the underlying semigroup, but that they may differ elsewhere

    Testing the stability of the benefit transfer function for discrete choice contingent valuation data

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    We examine the stability of the benefit transfer function across 42 recreational forests in the British Isles. A working definition of reliable function transfer is put forward, and a suitable statistical test is provided. The test is based on the sensitivity of the model log-likelihood to removal of individual forest recreation sites. We apply the proposed methodology on discrete choice contingent valuation data and find that a stable function improves our measure of transfer reliability, but not by much. We conclude that, in empirical studies on transferability, function stability considerations are secondary to the availability and quality of site attribute data. Modellers’ can study the advantages of transfer function stability vis-à-vis the value of additional information on recreation site attributes

    Synthesis of electro-optic modulators for amplitude modulation of light

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    Electro-optical modulator realizes voltage transfer function in synthesizing birefringent networks. Choice of the voltage transfer function is important, the most satisfactory optimizes the modulator property

    The transfer functions of rocket nozzles

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    The transfer function is defined as the fractional oscillating mass flow rate divided by the fractional sinusoidal pressure oscillation in the rocket combustion chamber. This is calculated as a function of the frequency of oscillation. For very small frequencies, the transfer function is approximately 1 with a small "lead component." For very large frequencies, the transfer function is considerably larger than 1, and is approximately 1 + (γM_1)^(-1) where γ is the ratio of specific heats of the gas, and M_l is the Mach nUlllber at entrance to the nozzle
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