Linearly Induced Mappings between Cones of Quadratic Forms
This paper deals with mappings between cones of positive quadratic forms which are induced by linear mappings between the underling vector spaces, i.e., the spaces which are the domains of the forms. Three fundamental results are proved, two of which were previously announced by the second author. The first result states that there is an inclusion-reversing one-to-one correspondence between the lattice of subspaces of a given space and the lattice of faces of the cone of quadratic forms on that space. The second result states that all cone-isomorphisms between cones of quadratic forms are induced by linear isomorphisms between the underlying spaces. The third result states that a given cone-linear mapping F between cones of quadratic forms is induced by some linear mapping between the underlying spaces if and only if both F and its transpose preserve faces.
Scientific Life and Works of Walter Noll
Walter Noll (1925–2017) was an American mathematician of German birth who made lasting contributions to the foundations of continuum physics and the classical non-linear field theory. This essay is an attempt to put in a broader perspective Noll’s methods and achievements in the hope that young generations of researchers may find their inspiration in the talent and depth of the old. By no means should this be considered as a historical account on the development of continuum mechanics through the second half of the twentieth century. We are content to illuminate Noll’s precious legacy.
Texture Feature Extraction of RGB, HSV, YIQ and Dithered Images using GLCM, Wavelet Decomposition Techniques
When changing the format of an image from simple RGB to HSV, YIQ and Dithered image, the characteristics of image also change. In this paper, the similar images in the above formats are retrieved using statistical and structural retrieving techniques i.e. GLCM (Gray Level Co-occurrence Matrix) and Wavelet Decomposition techniques. The best results are coming for dithered, HSV images by using GLCM technique for feature extraction and by using Wavelet decomposition; HSV images are giving the best results. While other formats also give the correct retrieval but from the accuracy point of view, HSV images are retrieved with better accuracy using both techniques.