Some Paranormed Difference Sequence Spaces of Order mm Derived by Generalized Means and Compact Operators

We have introduced a new sequence space $l(r, s, t, p ;\Delta^{(m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{(m)})$ is complete under some suitable paranorm and it has Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of this space is computed and also obtained necessary and sufficient conditions for some matrix transformations from $l(r, s, t, p; \Delta^{(m)})$ to $l_{\infty}, l_1$. Finally, we obtained some identities or estimates for the operator norms and the Hausdorff measure of noncompactness of some matrix operators on the BK space $l_{p}(r, s, t ;\Delta^{(m)})$ by applying the Hausdorff measure of noncompactness.Comment: Please withdraw this paper as there are some logical gap in some results. 20 pages. arXiv admin note: substantial text overlap with arXiv:1307.5883, arXiv:1307.5817, arXiv:1307.588

Interplay between Negation of a Probability Distribution and Jensen Inequality

Yager[5] proposed a transformation for opposing(negating) the occurence of an event that is not certain using the idea that one can oppose the occurence of any uncertain event by allocating its probability among the other outcomes in the sample space without preference to any particular outcome \textit{i.e.} the probability of every event in the sample space is redistributed equally among the other outcomes in the sample space. However this redistribution increases the uncertainty associated with the occurence of events. In the present work, we have established bounds on the uncertainty associated with negation of a probability distribution using well known Jensen inequality. The obtained results are validated with the help of various numerical examples. Finally a dissimilarity function between a probability distribution and its negation has been developed

Shape Memory Alloy Actuators and Sensors for Applications in Minimally Invasive Interventions

Reduced access size in minimally invasive surgery and therapy (MIST) poses several restriction on the design of the dexterous robotic instruments. The instruments should be developed that are slender enough to pass through the small sized incisions and able to effectively operate in a compact workspace. Most existing robotic instruments are operated by big actuators, located outside the patient’s body, that transfer forces to the end effector via cables or magnetically controlled actuation mechanism. These instruments are certainly far from optimal in terms of their cost and the space they require in operating room. The lack of adequate sensing technologies make it very challenging to measure bending of the flexible instruments, and to measure tool-tissue contact forces of the both flexible and rigid instruments during MIST. Therefore, it requires the development of the cost effective miniature actuators and strain/force sensors. Having several unique features such as bio-compatibility, low cost, light weight, large actuation forces and electrical resistivity variations, the shape memory alloys (SMAs) show promising applications both as the actuators and strain sensors in MIST. However, highly nonlinear hysteretic behavior of the SMAs hinders their use as actuators. To overcome this problem, an adaptive artificial neural network (ANN) based Preisach model and a model predictive controller have been developed in this thesis to precisely control the output of the SMA actuators. A novel ultra thin strain sensor is also designed using a superelastic SMA wire, which can be used to measure strain and forces for many surgical and intervention instruments. A da Vinci surgical instrument is sensorized with these sensors in order to validate their force sensing capability