Qualitative analysis for solutions of a class of nonlinear ordinary differential equations
The boundary value problem (BVP) for a class of nonlinear ordinary differential equations is examined. It can be used to describe the eversion problem for a spherical shell composed of a class of transversely isotropic incompressible Mooney-Rivlin materials. The solutions of the nonlinear equation describing the relation among deformed thickness, initial thickness and material parameters of the spherical shell are obtained. The effects of structure parameter and material parameters on the thickness of the everted spherical shell are discussed by numerical examples.
Inversion of a perfectly elastic spherical shell
The problem of inversion of a spherical shell which is made of an incompressible, perfectly elastic material is solved in full generality. It is shown that, if the strain energy is of the form assumed in the Mooney-Rivlin theory for rubber, then the surfaces of the deformed shell may be left free of surface tractions. 
 
 
 
Das Problem der Umkehrung (Umstulpung) einer spharischen Hulle, die aus einem nicht zusammendruckbaren, vollkommen elastischen Material hergestellt ist, wird in volliger Allgemeinheit gelost. Es wird gezeigt, das, wenn die Spannungsenergie von der in der Mooney-Rivlin-Theorie fur Gummi angenommenen Form ist, dann die Oberflachen der deformierten Hulle von Oberflachenspannungen freibleiben.
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.