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The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered.
A methodology for assessment, seismic verification and strengthening of existing masonry buildings is presented in this paper. The verification is performed using a calculation model calibrated with the results from ambient vibration measurements. The calibrated model serves as an input for a deformation-based verification procedure based on the Capacity Spectrum Method (CSM). The bearing capacity of the building is calculated from experimental capacity curves of the individual walls idealized with bilinear elastic-perfectly plastic curves. The experimental capacity curves were obtained from in-plane cyclic loading tests on unreinforced and strengthened masonry walls with reinforced concrete jackets. The seismic action is compared with the load-bearing capacity of the building considering non-linear material behavior with its post-peak capacity. The application of the CSM to masonry buildings and the influence of a traditional strengthening method are demonstrated on the example of a public school building in Skopje, Macedonia.