In this paper we introduce the operators of validation and invalidation of a proposition, and we extend the operator of S-denying a proposition, or an axiomatic system, from the geometric space to respectively any theory in any domain of knowledge, and show six examples in geometry, in mathematical analysis, and in topology.

1. Given topological spaces X and Fand two continuous mappings ƒ o and jfi from X to F (denoted by fo, fi : X—> F) we say that ƒ o is homotopic to jfi (denoted by fo—fi) if there exists a continuous family of continuous mappings ht: X—+Y for O^t^l such that ho=fo and h =/ i . Intuitively fo<^fi if the map ƒ o can be continuously deformed into the map jfi. I t is easily seen [4; 7] that the rela...

in this paper, the behavior of free vibrations and buckling of the sandwich panel with a flexible core was investigated using a new improved ‎high-order sandwich panel theory. in this theory, equations of motion were formulated based on shear stresses in the core. first-order shear deformation theory was ‎applied for the procedures. in this theory, for the first time, incompatibility problem of...

A theory is presented for the dispersion relations of the nonlinear phonon-polaritons arising when phonons are coupled to the electromagnetic waves in multilayered structures of nonlinear materials. The calculations are applied to a multilayered structure consisting of a thin film surrounded by semi-infinite bounding media where each layer may have a frequency dependent dielectric function and ...