For a given class F of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation |〈fk, fl〉| among all frames {fk}k∈I ∈ F . We first analyze finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These ...

The theory of relativity links space and time to account for observed events in four-dimensional space. In this article we describe an alternative static state causal discrete modeling system using omniscient viewpoint dynamical systems that can express object relations the moment(s) they are observed. To do this, three key components required, including introduction independent object-relative...

It is usual to assume that a displacement caused at any point in structure linearly dependent on the magnitude of loads applied. This paper focuses linear analysis 2-D frames with flexural connected beam-column members considering shear displacements. A computer program was written MATLAB for this purpose. To achieve above purpose, first, element stiffness matrix springs its ends has been obtai...

One of the important issues in the study of steel frames is to find a suitable formulation for semi-rigid connections. In this paper, the explicit stiffness matrix for a two-dimensional beam-column element having end-flexibilities is derived. The effects of the lateral uniformly distributed load on the deflection are considered. Both tensile and compressive axial loads are also taken into accou...