Physicochemical models which related pig manure nutrient content (ammonium nitrogen, AN; total potassium, TK; total nitrogen, TN; total phosphorus, TP) to its physicochemical properties (specific gravity, dry matter, electrical conductivity, pH) have been reported by previous researchers.
Empirical models which relate LPG composition to its RON and MON are then developed, such that the simplest relationships between the constituent species' mole fractions and the mixture octane rating are achieved.
Then, system identification is applied to derive linear time-invariant reduced-order models, which relate the input process variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output process variables (raffinate concentration and extract concentration).
Results are interpreted using mechanistic models which relate the rate of attrition of the bed material to the hydrodynamic forces in the bed and the mechanical strength of the material.
Then, we formulize the previous assumption into three regression models which relate the predefined closeness to TS, CS and the multiple similarity (MS) information combining TS and CS, named drugCIPHER-TS, drugCIPHER-CS and drugCIPHER-MS respectively (Figure 1).
The last technique relies on kinematic models which relate positions of skin placed markers to joint kinematics.
There are other, less rational or 'causal' adaptive models which relate indoor comfort temperatures to outside conditions based upon data from thermal comfort surveys (e.g. 12).
To gain further insight, we developed mathematical models which relate the shape of the correlation functions to the timing of the underlying molecular processes (see 'Materials and methods').
Continuity in the conditional expectation functions, and, is sufficient for identification of regression parameters across the class of generalized linear models, which relate the conditional expectation (mean, probability, rate) to a linear model via a continuous link function (such as the log or logit).
The results of reactive transport modeling, which related the amount of a passivating iron oxide, hematite (α-Fe2O3), to the reactivity of iron, were generally consistent with the patterns of migration of TCE and nitrate profiles observed in the column experiments.
In the ITSDP model, when the allowable amount of power generation W kt ± and heat generation Y jt ± are known, the above model can be transformed into two branches of deterministic sub-models, which related to the upper and lower bounds of the conceived objective-function value.
