In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation.

This paper presents the basic concepts of stability in fuzzy linguistic models. Theauthors have proposed a criterion for BIBO stability analysis of fuzzy linguistic modelsassociated to linear time invariant systems [25]-[28]. This paper presents the basic concepts ofstability in the general nonlinear and linear systems. This stability analysis method is verifiedusing a benchmark system analysis.

This paper discusses a method for taking into account rounding errors when constructing stopping criterion the iterative process in gradient minimization methods. The main aim of this work was to develop methods improving quality solutions real applied problems, which require significant amounts calculations and, as result, can be sensitive accumulation errors. However, demonstrates that develo...

Redundancy elimination optimizations avoid repeated computation of the same value by computing the value once, saving it in a temporary, and reusing the value from the temporary when it is needed again. Examples of redundancy elimination optimizations include common subexpression elimination, loop invariant code motion and partial redundancy elimination. We demonstrate that the introduction of ...

this paper presents the basic concepts of stability in fuzzy linguistic models. theauthors have proposed a criterion for bibo stability analysis of fuzzy linguistic modelsassociated to linear time invariant systems [25]-[28]. this paper presents the basic concepts ofstability in the general nonlinear and linear systems. this stability analysis method is verifiedusing a benchmark system analysis.

Uncertainty in pressure sensitive paint (PSP) measurement is investigated from a standpoint of system modeling. A functional relation between the imaging system output and luminescent emission from PSP is obtained based on studies of radiative energy transports in PSP and photodetector response to luminescence. This relation provides insights into physical origins of various elemental error sou...

Investigated is a number system in which the square of a basis number: (w), and the square of its additive inverse: (−w), are not equal. Termed W space, a vector space over the reals, this number system will be introduced by restating defining relations for complex space C, then changing a defining conjugacy relation from conj(z) + z = 0 in the complexes to conj(z) + z = 1 for W space. This cha...