Staircase System Research Articles

Staircase Matrices and Systems

Difference equations, spline approximations and multiperiod linear programs all give rise to linear equation systems that have a characteristic staircase structure. A staircase system’s variables can be partitioned, into a natural sequence of periods, in such a way that every equation involves at most the variables of two adjacent periods.This paper surveys the numerous properties of staircase systems and of the staircase matrices that comprise their coefficients. Particular attention is given to reduced and sparse staircase forms and to the varieties of Gaussian elimination for solving staircase systems.

Theoretical models for investigation of sound transmission through isolation layers in staircase systems

The behaviour patterns of staircase dynamic response to structure-borne sound are given through analysis of two-dimensional models. Typical models of this kind include angular discontinuities which represent the intersection line between the horizontal slabs and the stair's slope. Numerical examples illustrate the effect of elastic isolation layers on the solid-borne transmission loss between the stairs and the other parts of the building, the strong coupling between the stairs and the building caused by substitution of the elastic isolation layers by rigid sound bridges, the dependence of the dynamic response of the staircase on frequency, and the coupling between the longitudinal and flexural waves due to the aforementioned angular discontinuities of the staircase system.

Analysis and optimization of a class of non-linear staircase systems for random processes

Analysis and optimization of a class of non-linear staircase systems for random processes