Time series, importance

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

An important property of the time autocorrelation function CaU) is that by taking its Fourier transform, F CA(t) a, one gets a spectral decomposition of all the frequencies that contribute to the motion. For example, consider the motion of a single particle in a hannonic potential (harmonic oscillator). The time series describing the position of the... 

Much of the variation in these time series for the past 700 kyr can be described by a combination of a 100 kyr cycle plus additional cycles with periods of 20 and 40 kyr. This result immediately suggests that the ice-age cycles are caused by variations in the amount and seasonality of solar radiation reaching the Earth (insolation), because the 20, 40, and 100 kyr periods of climate history match the periods of cyclic variations in Earth s orbit and axial tilt, line hypothesis that these factors control climate was proposed by Milutin Milankovitch in the early part of the 20th century and is widely known as "Milankovitch Theory." It is now generally accepted that the Milankovitch variations are the root cause of the important 20 and 40 kyr climate cycles. The 100 kyr cycle, however, proves to be a puzzle. The magnitude of the insolation variation at this periodicity is relatively trivial, but the 100 kyr cycle dominates the climate history of the last 700 kyr. Further,... 

At Rohm and Haas a committee of several experts contributed to the successes described In this paper. Discussions with Prof. John MacGregor (HcHaster University), Jeff Nathanson, Tom Shannon and Tom Throne were especially Important. Special thanks are due to Chris Altomare, who always had the proper equipment and Instrximentatlon ready for the pilot plant trials. We also would like to acknowledge Prof. Don Watts (Queens University) for assisting with the time series modeling and Prof. 

Numeric-symbolic approaches are particularly important in process applications because the time series of data is by far the dominant form of input data, and they are the methods of choice if annotated data exist to develop the interpretation system. With complete dependence on the annotated data to develop the feature mapping step, numeric-symbolic mappers can be used to assign labels directly. However, as the amount and coverage of available annotated data diminishes for the given label of interest, there is a need to integrate numeric-symbolic approaches with... 

The correlation of values within a time series plays an important role in sampling. It can be characterized by means of the autocorrelation function (Doerffel and Wundrack [1986], Chatfield [1989], Hartung et al. [1991])... 

The correlation coefficients between a 10 year monthly mean time series of volatilisation rates and SST, 1 Om wind speed and pollutant concentration are used to elucidate which of the parameters drives the volatilisation rate changes and causes the deviations from the long term mean. All of the parameters do not vary independently. Since both SST and wind speed influence the volatilisation rate in a nonlinear manner, it is not intuitive whether an increase in wind speed leads to an increase in volatilisation rate. A raise in wind speed that coincides with a decrease of the sea surface temperature can lead to a negative linear correlation coefficient between volatilisation rate and wind speed. For that reason the partial correlation coefficient is calculated in addition to the simple linear correlation coefficients. It explains the relation between a dependent and one or more independent parameters with reduced danger of spurious correlations due to the elimination of the influence of a third or fourth parameter, by holding it fixed. One important feature of the partial correlation coefficient is, that it is equal to the linear correlation coefficient if both variables... 

Seawater reference materials are recommended for nutrients and for trace metals (especially iron). There is an urgent need for a certified reference material for nutrients. Completed global surveys already suffer from the lack of previously available standards, and the success of future surveys as well as the development of instruments capable of remote time-series measurements will rest on the availability and use of good nutrient reference materials. The reference materials for trace metals— though initially characterized only for the important micronutrient, iron— should ultimately be useful for the analysis of the other metals and some dissolved organic materials. The committee also recommends the devel-... 

In order to analyze both systems, some techniques from nonlinear science are burrowed. Firstly, a phase portrait is constructed from delay coordinates, a Poincare map is also computed, FFT is exploited to derive a Power Spectrum Density (PSD) Maximum Lyapunov Exponents (MLE) are also calculated from time series. Although we cannot claim chaos, the evidence in this chapter shows the possible chaotic behavior but, mostly important, it exhibits that the oscillatory behavior is intrinsically linked to the controlled systems. The procedures are briefly described before discuss each study case. 

A set of experiments on gas-liquid motion in a vertical column has been carried out to study its d3mamical behavior. Fluctuations volume fraction of the fluid were indirectly measured as time series. Similar techniques that previous section were used to study the system. Time-delay coordinates were used to reconstruct the underl3ung attractor. The characterization of such attractor was carried out via Lyapunov exponents, Poincare map and spectral analysis. The d3mamical behavior of gas-liquid bubbling flow was interpreted in terms of the interactions between bubbles. An important difference between this study case and former is that gas-liquid column is controlled in open-loop by manipulating the superficial velocity. The gas-liquid has been traditionally studied in the chaos (turbulence) context [24]. 

Yearly water balance time series since 1901 based on measured data have been established and analyzed by [23-25]. Recently, special importance has been attached to the fact that quantification of areal precipitation in mountainous environment remains a very difficult task. With the aim of achieving high spatial resolution, a specific methodology has been developed based on a comprehensive view of the water balance in different spatial and time scales [26]. 

First,one important result of the infrared molecular spectroscopy is a discovery of stationary CO layer in Mira type variable star x Gyg, in which CO lines that stay stationary have been clearly separated from the photospheric CO lines that show cyclic Doppler-shifts by the large amplitude pulsation of the photosphere in time series spectra( Hinkle, Hall, Ridgway, 1982). It was suggested that the stationary CO layer may be located at several stellar radii above the stellar surface, since excitation temperature of the stationary CO layer of x Cyg was found to be 800K. 

Comparison of the depositional fluxes shows that diatoms were the most important particle component transporting P to the sediment surface, accounting for 50-55% of the flux (Table II). Terrigenous material and calcite were also important transport vectors. Deposition varied markedly with season, as shown by the time series plot of the major particle components (Figure 13). The total P flux calculated by using the particle components model agreed with the flux measured by sediment traps (157-227 versus 185 mg/m2). The close agreement indicated that the major particle vectors were represented and associated P concentrations were accurately quantified. 

Another recent trend is to show the importance of hydrophobic profiles rather than molecular hydrophobicity. Giuliani et al. (2002) suggested nonlinear signal analysis methods in the elucidation of protein sequence-structure relationships. The major algorithm used for analyzing hydrophobicity sequences or profiles was recurrence quantification analysis (RQA), in which a recurrence plot depicted a single trajectory as a two-dimensional representation of experimental time-series data. Examples of the global properties used in this... 

Stochastic modeling is used when a measurable output is available but the inputs or causes are unknown or cannot be described in a simple fashion. The black-box approach is used. The model is determined from past input and output data. An example is the description of incomplete mixing in a stirred tank reactor, which is done in terms of contributions of dead zones and short circuiting. In these cases, a sequence of output called a time series is known, but the inputs or causes are numerous and not known in addition, they may be unobservable. Though the causes for the response of the system are unknown, the development of a model is important to gain understanding of the process, which may be used for future planning. 

Variations (usually decrease) in detection limits occur with time, affecting both long-running projects, and the comparison of time-series data or adjacent project areas separated in time. It arises as analytical methods improve, and has its greatest impact on the trace elements, where the natural abundance is low in relation to the lowest measurable concentration. Such improvements can significantly increase the number of sample locations with measurable values in comparison to older data. The ability to make use of all the data acquired to its best potential is important, particularly for national mapping programmes. The data can be levelled as described above, if the standards used fall above the detection limit of the older method. 

It is important to maintain time series of biogeochemical distributions in the Black Sea. Much is learned about the oceanography of a system when you can watch its response to a perturbation. Two important perturbations we want to continue to watch are climatic forcing and eutrophication. 

Wind speed varies over a wide range of time scales. Turbulent fluctuations in the time range of seconds to minutes are important for the assessment of the power quality and the stability of frequency and voltage in an APS. Hourly and daily variations on the other hand, are decisive for the evaluation of the wind potential in a considered site. For the characterisation of wind potential the primary input consists of time series of wind speed measurements. These measurements are usually average values in time steps of 10 min or 1 h. If the height of the meteorological mast used for the acquisition of measurements is lower than the height of the wind turbine tower then a mathematical formula must be used for the transformation of measurements, due to the wind shear effect (Manwell, 1998). 

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