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Process Control for Thermal Processing
Published in Gauri S. Mittal, Computerized Control Systems in the Food Industry, 2018
A block diagram of the heating or cooling process of canned food subjected to sterilization is shown in Fig. 4. The transfer operator or model of the process characterizes the dynamic and physical properties of the process. If the transfer operator is known, the response of the process to a known input can be predicted. Ryniecki and Jayas [10] assumed the most general mth-order exponential lag transfer function (including a dead-time delay) for the transfer operator: () G(s)=Ke−sτ1(1+sτ2)m
Intermediately trimmed strong laws for Birkhoff sums on subshifts of finite type
Published in Dynamical Systems, 2020
Marc Kesseböhmer, Tanja I. Schindler
Let be a measure theoretical dynamical system with T-invariant probability measure μ and denoting the transfer operator of T, i.e. the uniquely defined operator such that for all and we have see, e.g. [18, Section 2.3] for further details. The norms in and will be denoted by and , respectively. Furthermore, let be a Banach space with respect to the norm and let be -measurable.
A central limit theorem for the Birkhoff sum of the Riemann zeta-function over a Boolean type transformation
Published in Dynamical Systems, 2020
We first give the basic definition of the transfer operator. If is a mixing, probability preserving dynamical system, then we denote by the transfer operator of T, i.e. the (up to almost sure equivalence) uniquely defined operator such that for all and we have Furthermore, we will need the notion of quasi-compactness given as follows: is a quasi-compact operator if there exists a direct sum decomposition and with ρ the spectral radius where G, H are closed and U-invariant, i.e. , , and all eigenvalues of have modulus larger than τ, and.