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Removal of Organics and Inorganics by Activated Carbon
Published in Samuel D. Faust, Osman M. Aly, Chemistry of Water Treatment, 2018
The laboratory-based RSSCTs were effective in prediction of the field-scale breakthrough behavior of NOM and subsequent DBP formation with the three GACs.129a For each parameter evaluated, except TOC, the nonabsorbable fractions measured in the field-scale fractions break through “immediately” and presumably serve as precursors for DBPs. Other parameters that were predicted well by the RSSCT-laboratory scale were the initial rise in the effluent concentration and time to 50% breakthrough. These predictions compared well with the field/pilot-scale observations of the performance of the three carbons with respect to TOC, SAC, TOXSDS, and TTHMSDC. After the initial breakthrough, the shapes of the breakthrough curves for the individual TTHMs were well predicted by the RSSCTs in 9 of 12 runs. For this water, the breakthrough behavior of TOC seems to predict that of TTHMSDC. UV-absorbing substances were removed better by the GACs compared to TOC. SAC “seemed” to predict the breakthrough behavior of TOXSDS. For the individual TTHM species, GAC adsorption worked best in controlling the formation of CHCl3 and worst for CHBr3.
On the connections between two classical notions of multidimensional system equivalence
Published in International Journal of Control, 2021
Mohamed S. Boudellioua, Thomas Cluzeau
Let D be a (not necessarily commutative) noetherian domain of functional operators as, e.g. differential, shift, difference or partial differential operators. In this paper, we consider a linear multidimensional system given by a general description of the form where is the state vector of dimension n, is the input vector of dimension l, is the output vector of dimension m, , , , and . In multidimensional systems theory, the components of the vectors , , and are functions which depend on more than one variable and each variable can be either discrete or continuous. When T is invertible in , the field of fractions of D, the transfer-function matrix of the system (1) is then defined by as we formally have .
Transformation of nonlinear discrete-time system into the extended observer form
Published in International Journal of Control, 2018
Below we recall necessary facts from the linear algebraic approach based on differential forms, focusing on Equation (2) (see Aranda-Bricaire, Kotta, & Moog, 1996 for details). Let denote the field of meromorphic functions (i.e. the field of fractions of the ring of analytic functions) in a finite number of independent system variables from the infinite set , where [−l] denotes the lth backward shift and the variable v can be chosen either to be y or u. The choice can be briefly described as follows. If , then one may choose v = u . In this case, using the i/o equation (2), the variables y[−l], l > 0 can be expressed through the independent variables from . If , then one may set v = y and consider the variables u[−l], l > 0 as dependent. If both and hold, then one has freedom of choice.
Series concatenation of 2D convolutional codes by means of input-state-output representations
Published in International Journal of Control, 2018
Joan-Josep Climent, Diego Napp, Raquel Pinto, Rita Simões
Let be a finite field and let denote the algebraic closure of . Denote by the ring of polynomials in two indeterminates with coefficients in , by the field of fractions of and by the ring of formal powers series in two indeterminates with coefficients in .