Causality linear

In an efficient digital simulation, lumped loss factors of the form Gk (0)) are approximated by a rational frequency response Gk(c,mT). In general, the coefficients of the optimal rational loss filter are obtained by minimizing I Ylk (go) - Gk d r ) I with respect to the filter coefficients or the poles and zeros of the filter. To avoid introducing frequency-dependent delay, the loss filter should be a zero-phase, finite-impluse-response (FIR) filter [Rabiner and Gold, 1975], Restriction to zero phase requires the impulse response g.k(n) to be finite in length (i.e., an FIR filter) and it must be symmetric about time zero, i.e., ) k(-n) = gk(n). In most implementations, the zero-phase FIR filter can be converted into a causal, linear phase filter by reducing an adjacent delay line by half of the impulse-response duration. 

The stress-strain relations for viscoelastic materials are reviewed. The simplest case of intrinsic absorption in polymers is a molecular relaxation mechanism with a single relaxation time. However, the relaxation mechanisms which lead to absorption of sound are usually more complicated, and are characterized by a distribution of relaxation times. Under causal linear response conditions the attenuation and dispersion of sound in a... 

The Kramers-Kronig validation [11] is a well-established method to assess consistency and quality of measured impedance spectra. The Kramers-Kronig relations are integral equations, which constrain the real and imaginary components of the impedance for systems that satisfy the conditions of causality, linearity, and... 

Impedance is only properly defined as a transfer function when the system under investigation fulfils the conditions of causality, linearity, stability, and... 

In the case of our linear, stationary and causal device, input and output are linked by the convolution integral ... 

Where Western science has heretofore been predicated on (1) static partitions of S2 (modulo our co-evolved senses and language), and (2) simple, linear chains of cause o effect, the generalized CA-based physics represents a paradigm shift to (1) causal webs, and (2) fully coevolving object interaction hierarchies and dynamic partitions. 

Marc Van Regenmortel I want to ask Alex whether he believes that explanations must necessarily possess causal efficacy or efficiency. In other words, if you take a reductionist approach, must you necessarily go on believing in linear causality. .. ... 

Marc van Regenmortel. I am asking that question because as you know the complexity jockeys are saying that linear causality is no longer applicable. 

Alex Rosenberg I didn t address your point about linear versus non-linear causality. I guess for the last three generations, opponents of quantitative and other kinds of empirical natural and social sciences have been making heavy... 

Marc Van Regenmortel I think the synthesis that is relevant is a nonlinear synthesis. Linear synthesis and push-pull causality have been given up, because complexity cannot be analysed using linear mathematical tools. 

Active compensation relies on the fact that, to a good approximation, the causal relation between the programmed pulse shape and the resultant pulse shape is linear. Then, it is possible to calculate the pulse shape... 

Fig. B.l Relations between the linear and partial correlation coefficients for two variables and a controlling variable. Lines denote causal relations between the variables.

Unfortunately, even the planning of green biotechnology has now evolved into a wicked problem with complex structures and no obvious causal chains. This applies also to the PA. These problems cannot be determined completely in a quantitative and scientific manner, and there are no existing solutions in the sense of definitive and objective answers alone. Wicked problems have been addressed mainly through formalized (linear) methods that are suitable only for the solution of tame problems. 

We note in passing that a linear relation between e and p, with a slope a 3 is to be expected since both quantities scale with the forth power of either p or T. Causality requires furthermore a > 3. 

In both component and factor analysis, the properties of the system being observed are assumed to be linearly additive functions of the contribution from each of the m causalities that actually govern the system. For example, for airborne particles, the amount of particulate lead in the air could be considered to be a sum of contributions from several sources including automobiles, incinerators and coal-fired power plants, etc. 

Thus, a deterministic answer assumes that the laws of physics and chemistry have causally and sequentially determined the obligatory series of events leading from inanimate matter to life - that each step is causally linked to the previous one and to the next one by the laws of nature. In principle, in a strictly deterministic situation, the state of a system at any point in time determines the future behavior of the system - with no random influences. In contrast, in a non-deterministic or stochastic system it is not generally possible to predict the future behavior exactly and instead of a linear causal pathway the sequence of steps may be determined by the set of parameters operating at each step. 

Although the Kramers-Kronig relations do not follow directly from physical reasoning, they are not devoid of physical content underlying their derivation are the assumptions of linearity and causality and restrictions on the asymptotic behavior of x> As we shall see in Chapter 9, the required asymptotic behavior of x is a physical consequence of the interaction of a frequency-dependent electric field with matter. 

We showed in Section 2.3 that the real and imaginary parts of the electric susceptibility are connected by the dispersion relations (2.36) and (2.37). This followed as a consequence of the linear causal relation between the electric field and polarization together with the vanishing of x(<°) in the limit of infinite frequency to. We also stated that, in general, similar relations are expected to hold for any frequency-dependent function that connects an output with an input in a linear causal way. An example is the amplitude scattering matrix (4.75) the scattered field is linearly related to the incident field. Moreover, this relation must be causal the scattered field cannot precede in time the incident field that excited it. Therefore, the matrix elements should satisfy dispersion relations. In particular, this is true for the forward direction 6 = 0°. But 5(0°, to) does not have the required asymptotic behavior it is clear from the diffraction theory approximation (4.73) that for sufficiently large frequencies, 5(0°, to) is proportional to to2. Nevertheless, only minor fiddling with S makes it behave properly the function... 

Causal quantum theories have been developed to handle the empirical quantum evidence, and some of these theories, such as de Broglie s theory in its linear approximation, are almost as good as the usual orthodox quantum theory. A relative large number of experiments were even developed to test de Broglie s causal theory and other alternative theories as well, but only a few limited number of these proposed experiments were carried out effectively. And even so they were not carried out thoroughly. As a consequence, the results obtained were not conclusive, and no solid conclusion in favor or against the completeness of the usual orthodox interpretation of the Copenhagen School... 

English translation Non-linear Ware Mechanics A Causal Interpretation. F.lsevier, Amsterdam. I960. 

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