An enumerative invariant theory in Algebraic Geometry, Differential or Representation Theory, is the study of invariants which 'count' $\tau$-(semi)stable objects $E$ with fixed topological $[E]=\alpha$ some geometric problem, using a virtual class $[{\cal M}_\alpha^{\rm ss}(\tau)]_{\rm virt}$ homology for moduli spaces ${\cal st}(\tau)\subseteq{\cal ss}(\tau)$ objects. Examples include Mochizu...

A log-linear modelling will take quite a long time if the data involves many variables and if we try to deal with all the variables at once. Fienberg and Kim (1999) investigated the relationship between log-linear model and its conditional, and we will show how this relationship is employed to make the log-linear modelling easier. The result of this article applies to all the hierarchical log-l...

the interactive effects of adjacent buildings on their seismic performance are not frequently considered in seismic design. the adjacent buildings, however, are interrelated through the soil during seismic ground motions. the seismic energy is redistributed in the neighboring buildings through multiple structure-soil-structure interactions (sssi). for example, in an area congested with many nea...

Abstract. A new application of the elastic no-tension material model is developed through Sequential Linear Analysis (SLA) to analyze masonry structures. The approach has been demonstrated be more robust compared incremental analysis procedures. In SLA framework, equilibrium state a masonry-like sought series linear analyses. loading process, cracking strains are simulated by sequential reducti...