This paper proposes a system that detects and recognizes speed-limit signs automatically. The system detects potential speed-limit sign regions by detecting maximally stable extremal regions (MSERs). The recognition is achieved by using a Support Vector Machine (SVM) classifier. The proposed system provides robustness and high accuracy in detecting and recognizing speed-limit signs when input i...

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.

This paper presents a computational framework that allows for a robust extraction of the extremal structure of scalar and vector fields on 2D manifolds embedded in 3D. This structure consists of critical points, separatrices, and periodic orbits. The framework is based on Forman’s discrete Morse theory, which guarantees the topological consistency of the computed extremal structure. Using a gra...

We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions, for which a dual extremal function exists in terms of the existence of a maximizing vector of the corresponding Hankel operator and in terms of certain spec...

Analogs of well-known problems and theorems on convex bodies are considered for the case where the convex bodies are replaced by continuous fields of convex bodies in vector bundles.

The disc multiplier may be seen as a vector valued operator when we consider its projections in terms of the spherical harmonics. In this form, it represents a vector valued Hankel transform. We know that, for radial functions, it is bounded on the spaces Lplq (r n−1 dr) when 2n n+1 < p, q < 2n n−1 . Here we prove that there exist weak-type estimates for this operator for the extremal exponents...

In this paper, we investigate some properties of the Perron vector of connected graphs. These results are used to characterize all extremal connected graphs which attain the minimum value among the spectral radii of all connected graphs with order n = kα and the independence number α. Moreover, all extremal graphs which attain the maximum value among the spectral radii of clique trees with orde...

We say that a set system F ⊆ 2 shatters a given set S ⊆ [n] if 2 = {F ∩ S : F ∈ F}. The Sauer-Shelah lemma states that in general, a set system F shatters at least |F| sets. A set system is called shattering-extremal if it shatters exactly |F| sets. In [9] and [13] an algebraic characterization of shattering-extremal set systems was given, which offered the possibility to generalize the notion ...

We prove that every J-holomorphic variational vector field can be realized as derivation $$\frac{d}{dt}_{|t=0}f_t$$ where $$(f_t)$$ is a one parametric family of discs. Furthermore, we discuss properness an extremal disc in bounded pseudoconvex domain.

In this paper, we show a method for finding all extremal rays of polyhedral convex cones with some complementarity conditions. The polyhedral convex cone is defined as the intersection of half-spaces expressed by linear inequalities. By a complementarity extremal ray, we mean an extremal ray vector that satisfies some complementarity conditions among its elen~nts. Our method is iterative in the...