In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an examp...

Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space. Furthermore, we show that none of the conditions can be weakened. However, if the eigenvalues (co...

The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback is studied. Firstly, two auxiliary operators are introduced, and the Riesz basis property of their eigenvector systems is proved. This property is used to show that the generalized eigenvector system of a Timoshenko beam with some linear boundary feedback forms a Riesz basis in the corresp...

In this letter, the two wavelet families, biorthogonal and Riesz bases are introduced. Biorthogonality for two possible decompositions in these bases, The Riesz stability implies that there exist such that Biorthogonal wavelet bases are related to multiresolution approximations. The direct consequence of the above derivation is tradeoff made between the support size of a wavelet and its number ...

This paper systematically studies finite rank dimension groups, as well as finite dimensional ordered real vector spaces with Riesz interpolation. We provide an explicit description and classification of finite rank dimension groups, in the following sense. We show that for each n, there are (up to isomorphism) finitely many ordered real vector spaces of dimension n that have Riesz interpolatio...

Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Space fractional diffusion equations with a nonlinear reaction term have been presented and used to model many problems of practical interest. In this paper, a two-dimensional Riesz space fractional diffusion equation with a nonlinear reaction term (2D-RSFDE-NR...

We develop a texture analysis framework to assist radiologists in interpreting high-resolution computed tomography (HRCT) images of the lungs of patients affected with interstitial lung diseases (ILD). Novel texture descriptors based on the Riesz transform are proposed to analyze lung texture without any assumption on prevailing scales and orientations. A global classification accuracy of 78.3%...

Texture-based computerized analysis of high-resolution computed tomography images from patients with interstitial lung diseases is introduced to assist radiologists in image interpretation. The cornerstone of our approach is to learn lung texture signatures using a linear combination of N-th order Riesz templates at multiple scales. The weights of the linear combination are derived from one-ver...