Consider linear systems whose input data are linear functions of uncertain parameters varying within given intervals. We are interested in an explicit description of the so-called AE parametric solution sets (where all universally quantified parameters precede all existentially quantified ones) by a set of inequalities not involving the parameters. This work presents how to obtain explicit desc...

Abstract Consider linear systems whose input data are affine-linear functions of uncertain parameters varying within given intervals. We discuss the so-called AE solution sets of such systems, where the parameters are quantified and all universally quantified parameters precede all existentially quantified ones. Some explicit descriptions of the AE parametric solution sets are derived in the sp...

This paper introduces the emph{interval unilateral quadratic matrix equation}, $IUQe$ and attempts to find various analytical results on its AE-solution sets in which $A,B$ and $CCC$ are known real interval matrices, while $X$ is an unknown matrix. These results are derived from a generalization of some results of Shary. We also give sufficient conditions for non-emptiness of some quasi-solutio...

We consider systems of linear equations, where the elements of the matrix and of the right-hand side vector are linear functions of interval parameters. We study parametric AE solution sets, which are defined by universally and existentially quantified parameters, and the former precede the latter. Based on a recently obtained explicit description of such solution sets, we present three approac...

The work presents a necessary and sufficient condition for the generalized AE-solution sets to interval linear systems of equations to be unbounded. The criterion requires solvability of one of the totality of 2 linear inequalities constructed from the initial interval system. It is shown that the problem of recognizing the boundedness of AE-solution sets is NP-complete in general.

Abstract We consider linear algebraic systems A(p)x = b(p), where the elements of the matrix and the right-hand side vector are linear functions of uncertain parameters varying within given intervals. For the parametric AE-solution set defined for two disjoint index sets A, E by ΣpAE := {x ∈ R n | (∀pA ∈ [pA]) (∃pE ∈ [pE ])(A(p)x = b(p))}, an inner interval estimation [y] ⊆ Σ p AE is sought. In...

The work considers solution of various problems for interval linear systems with nonnegative matrices. Relying on shape monotonicity of the solution sets to such interval systems, we develop a new technique for constructing maximal (with respect to inclusion) inner estimates of the solution sets to nonnegative interval linear equations systems. The main result is extended to general AE-solution...

The descriptors computed by HyperChem® software were employed to represent the solubility of 40 drug molecules in supercritical carbon dioxide using an artificial neural network with the architecture of 15-4-1. The accuracy of the proposed method was evaluated by computing average of absolute error (AE) of calculated and experimental logarithm of solubilities. The AE (±SD) of data sets was 0.4 ...

We consider linear algebraic equations, where the elements of the matrix and of the right-hand side vector are linear functions of interval parameters, and their parametric AE-solution sets, which are defined by universal and existential quantifiers for the parameters. We present how some sufficient conditions for a parametric AE-solution set to have linear boundary can be exploited for obtaini...