We investigate the one-parametric set G of projective subspaces that is generated by a set of rational curves in projective relation. The main theorem connects the algebraic degree δ of G, the number of degenerate subspaces inG and the dimension of the variety of all rational curves that can be used to generateG. It generalizes classical results and is related to recent investigations on projec...

The invariant subspace method is used to classify a class of systems of nonlinear dispersive evolution equations and determine their invariant subspaces and exact solutions. A crucial step is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that systems of evolution equations admit. A few examples of presenting exact solutions with generalized sepa...

This paper presents the recognition method of fractal images. The approach is considered based on using support subspaces. Support subspaces are constructed with vectors of source data using a conjunction index. The proposed new computing algorithm for the conjugation index reduces requirements for computing capacities and memory. It is shown that the proposed method of construction, supporting...

In this paper, we comment on the complexity of the invariant subspaces (under the bilateral Dirichlet shift f → ζf ) of the harmonic Dirichlet space D. Using the sampling theory of Seip and some work on invariant subspaces of Bergman spaces, we will give examples of invariant subspaces F ⊂ D with dim(F /ζF ) = n, n ∈ N ∪ {∞}. We will also generalize this to the Dirichlet classes Dα, 0 < α < ∞, ...

for a bounded linear operator on hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎we study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎also we show that any quasinilpotent operator $t$ has an hypernoncyclic vector‎, ‎and so $t$ has a nontrivial hyperinvariant subspace‎.