During the last years nonlinear eigenvalue problems of the type T (λ)x = 0 became more and more important in many applications with the rapid development of computing performance. In parallel the minmax theory for symmetric nonlinear eigenvalue problems was developed which reveals a strong connection to corresponding linear problems. We want to review the current theory for symmetric nonlinear ...

This paper proposes a nonlinear oscillator network model for gray-level image segmentation suitable for massively parallel VLSI implementation. The model performs image segmentation in parallel using nonlinear analog dynamics. Because of the limited calculation precision in VLSI implementation, it is important to estimate the calculation precision required for proper operation. By numerical sim...

A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernelbased orthogonal multiplicative update rules to solve the subspace clustering problem. In nonlin...

This paper generalizes Elkies’ construction of error-correcting nonlinear codes found in [N. Elkies, Excellent nonlinear codes from modular curves, in: Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing, STOC’01, Hersonissos, Crete, Greece, 2001, pp. 200–208]. The generalization produces a precise average code size over codes in the new construction. The result is a larger ...

We elaborate an unified geometric approach to classical mechanics, Riemann–Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N–connection) structure. There are investigated the conditions when the fundamental geometric objects like the anchor, metric and linear connection, almost sympletic and related almost complex structures may be canonically defined b...

The unanticipated brittle fracture of connection of the steel moment resisting frame (SMRF) occurred in 1994 the Northridge earthquake. Since then, the researches for the vulnerability of connection of the existing SMRF and for rehabilitation of those buildings were conducted. This paper suggests performance-based optimal seismic retrofit technique using connection upgrade. For optimal design, ...

We investigate bi–Hamiltonian structures and mKdV hierarchies of solitonic equations generated by (semi) Riemannian metrics and curve flows of non–stretching curves. There are applied methods of the geometry of nonholonomic manifolds enabled with metric–induced nonlinear connection (N–connection) structure. On spacetime manifolds, we consider a nonholonomic splitting of dimensions and define a ...

Residual drifts after severe earthquakes interrupt serviceability of buildings. Retrofitting of such buildings is in many cases very difficult and consumes lots of time and money. Recently, there are some attempts to develop the seismic design procedures to not only satisfy life safety criteria but also lead to more economical buildings. One of these modern methods of improving seismic performa...

Grey-box’ models take advantage of physical insight about the dynamical system in question. This reduces uncertainty and facilitates the remaining system identification process. Here a grey-box system identification (GBSI) method for nonlinear dynamical systems is presented, which first establishes a linear model (the ‘white box’) using a priori knowledge and conventional tools, and then adds a...

The column-tree constructional schemes allows for a reliable and convenient erection of moment resisting steel frames. Strengthening of column-tree connection with a haunch part can significantly improve seismic behavior of whole system. In the current study behavior of column-tree connections with haunched beams and end plate splices have been investigated. Special attention was paid for evalu...