In this paper,the orthonormality in 2-normed spaces is discussed and Bessel s inequality in 2-normed spaces is deduced.

Based on the analysis of conventional phase difference detection method,a new algorithm of phase difference detection is presented according to Fourier series decomposition method and the characteristic that inner product of two orthogonal vectors in a linear space is zero.

The main methods include:1) Invariant local feature regions are generated using locally most stable feature points of images;2) An approach is proposed to rapidly find the best image regular geometric flow in these local feature regions;and 3) An orthogonal vector is designed to extract the watermark blindly.

This paper presents a new perceptual digital watermarking scheme based on human vision system,discrete wavelet transform and orthogonal vector.

A found method of the standard vector group in a finite generating fuzzy vector subspace is given in this paper.

On the foundation of the conception of orthonormal basis in finite dimensional Euclidean space,this paper provides the theory of completely orthonormal system in infinite dimensional Euclidean space.

Consider the state linear system ∑(A,B,C),If the orthonormal basis _n,n∈N exist in the state space Z,it is proved that the solution of the differential Riccati equation is of general form,i.

In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.