Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The rec...

We show that, for vector spaces in which distance measurement is performed using a gauge, the existence of best coapproximations 1-codimensional closed linear subspaces implies dimensions ≥2 that gauge norm, and ≥3 even Hilbert space norm. also coproximinality all fixed dimension lower finite dimensions.

For a matrix polynomial P (λ) and a given complex number μ, we introduce a (spectral norm) distance from P (λ) to the matrix polynomials that have μ as an eigenvalue of geometric multiplicity at least κ, and a distance from P (λ) to the matrix polynomials that have μ as a multiple eigenvalue. Then we compute the first distance and obtain bounds for the second one, constructing associated pertur...

In this paper we consider the following problem: viewing both a nonlinear system model and its linearization as mappings from input-tostate, we define the error between the state of the original nonlinear system and that of the linearization and find the region of the state space where this error is norm-bounded, in the integral-square (or L2-norm) sense. Using the Hamilton–Jacobi inequality we...

My research in graph theory focuses on asymptotic maximal bounds for Cartesian powers of finite graphs. This line of inquiry was opened up by [4], in which the authors proved that the maximal spherical averaging operator on the N -dimensional hypercube K 2 satisfies a bound in the L 2 norm independent of the dimension N . That is, if Sk(x) := {y : d(x, y) = k} in the graph distance metric on K ...

In this article we describe how to find the parameters of subfield subcodes of extended Norm–Trace codes. With a Gröbner basis of the ideal of the Fqr rational points of the Norm–Trace curve one can determine the dimension of the subfield subcodes or the dimension of the trace code. We also find a BCH–like bound from the minimum distance of the original supercode. AMS Subject Classification: Pr...

Lipschitz condition is a natural notion of function regularity in this context, and the norm dual to the mixed Lipschitz space is a natural distance between measures. In this paper, we consider the tensor product of spaces equipped with tree metrics and give effective formulas for the mixed Lipschitz norm and its dual. We also show that these norms behave well when approximating an arbitrary me...

We introduce compactness classes of Hilbert space operators by grouping together all for which the associated singular values decay at a certain speed and establish upper bounds norm resolvent belonging to particular class. As consequence we obtain explicitly computable Hausdorff distance spectra two same class in terms operator norm.

Background. The integer distance graph G(Z, D) with distance set D = {d1, d2, . . .} has the set of integers Z as the vertex set and two vertices x, y ∈ Z are adjacent if and only if |x − y| ∈ D. The integer distance graphs (under Euclidean norm) were first systematically studied by Eggleton–Erdős–Skilton in 1985 [12, 13], and have been investigated in many ways [50, 56, 57, 61]. One of main go...