On Some Infinite Convex Invariants

The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions

Data Security in Fault Tolerant Hard Real Time Systems- Use of Time Dependant Multiple Random Cipher Code

The present research problem is to study the existing encryption methods and to develop a new technique which is performance wise superior to other existing techniques and at the same time can be very well incorporated in the communication channels of Fault Tolerant Hard Real time systems along with existing Error Checking / Error Correcting codes, so that the intention of eaves dropping can be defeated. There are many encryption methods available now. Each method has got it's own merits and demerits. Similarly, many crypt analysis techniques which adversaries use are also available.

Permutation entropy based real-time chatter detection using audio signal in turning process

Machine tool chatter is an unfavorable phenomenon during metal cutting, which results in heavy vibration of cutting tool. With increase in depth of cut, the cutting regime changes from chatter-free cutting to one with chatter. In this paper, we propose the use of permutation entropy (PE), a conceptually simple and computationally fast measurement to detect the onset of chatter from the time series using sound signal recorded with a unidirectional microphone. PE can efficiently distinguish the regular and complex nature of any signal and extract information about the dynamics of the process by indicating sudden change in its value. Under situations where the data sets are huge and there is no time for preprocessing and fine-tuning, PE can effectively detect dynamical changes of the system. This makes PE an ideal choice for online detection of chatter, which is not possible with other conventional nonlinear methods. In the present study, the variation of PE under two cutting conditions is analyzed. Abrupt variation in the value of PE with increase in depth of cut indicates the onset of chatter vibrations. The results are verified using frequency spectra of the signals and the nonlinear measure, normalized coarse-grained information rate (NCIR).

Real Time Raga Detection and Analysis Using Computer

Department of Computer Applications, Cochin University of Science and Technology

Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

Evaluation Of A Novel Method Of Real Time Computer Assisted Spine Surgery

In this paper the effectiveness of a novel method of computer assisted pedicle screw insertion was studied using testing of hypothesis procedure with a sample size of 48. Pattern recognition based on geometric features of markers on the drill has been performed on real time optical video obtained from orthogonally placed CCD cameras. The study reveals the exactness of the calculated position of the drill using navigation based on CT image of the vertebra and real time optical video of the drill. The significance value is 0.424 at 95% confidence level which indicates good precision with a standard mean error of only 0.00724. The virtual vision method is less hazardous to both patient and the surgeon

Real Estate Development In India And The Behavior of Investors to Invest In The Real Estate Market: An Empirical Investigation

This study examines the behavioral factors that influence the Indian Investors to invest in the Real Estate Market. Among the various factors that affect the tendency of investors to invest in the real market, certain factors are greatly influenced the investors at greatest extend while others at least level. From this study it is revealed that motivation from the real estate developers and brokers (mean value- 3.46) is most influencing factor and happening of uncertain events (mean value- 1.75) is the least factor that influences the investors’ investment behavior. In this study, the behavioral factor like over confidence and the hypotheses regarding education, religion were analyzed and found that religious factor influences the Indian investors to invest in the real estate