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.
Application of SVM on satellite images to detect hotspots in Jharia coal field region of India
The present paper deals with the application of Support Vector Machine (SVM) and image analysis techniques on NOAA/AVHRR satellite image to detect hotspots on the Jharia coal field region of India. One of the major advantages of using these satellite data is that the data are free with very good temporal resolution; while, one drawback is that these have low spatial resolution (i.e., approximately 1.1 km at nadir). Therefore, it is important to do research by applying some efficient optimization techniques along with the image analysis techniques to rectify these drawbacks and use satellite images for efficient hotspot detection and monitoring. For this purpose, SVM and multi-threshold techniques are explored for hotspot detection. The multi-threshold algorithm is developed to remove the cloud coverage from the land coverage. This algorithm also highlights the hotspots or fire spots in the suspected regions. SVM has the advantage over multi-thresholding technique that it can learn patterns from the examples and therefore is used to optimize the performance by removing the false points which are highlighted in the threshold technique. Both approaches can be used separately or in combination depending on the size of the image. The RBF (Radial Basis Function) kernel is used in training of three sets of inputs: brightness temperature of channel 3, Normalized Difference Vegetation Index (NDVI) and Global Environment Monitoring Index (GEMI), respectively. This makes a classified image in the output that highlights the hotspot and non-hotspot pixels. The performance of the SVM is also compared with the performance obtained from the neural networks and SVM appears to detect hotspots more accurately (greater than 91% classification accuracy) with lesser false alarm rate. The results obtained are found to be in good agreement with the ground based observations of the hotspots. This type of work will be quite helpful in the near future to develop a hotspots monitoring system using these operational satellites data.