Harish Parthasarathy | Category: Engineering

Book Details

ISBN: 9788193877272

YOP: 2017

Pages: 624

Order also on

This book is a research monograph covering a variety of problems in (a) statistical state and parameter estimation in nonlinear stochastic dynamical system in both the classical and quantum scenarios, propagation of electromagnetic waves in a plasma described by the Boltzmann Kinetic transporo equation, classical and quantum general relativity etc. It will be of use to Engineering undergraduate students interested in analysing the motion of robotic subject to random perturbation and also to research scientists working in quantum filtering and study problems of inhomogeneous perturbation to in a homogenous and isotropic universal leading to the formation of galaxies in an expanding universe.

1. Basic Markov chain theory

2. Basic quantum mechanics and quantum field theory

3. Solving RDRA problem with arbitrary boundary using orthogonal curvilinear co-ordinate

4. Optimal control of the average values of a set of observables in a quantum system.

5. Optimal control of observable averages in quantum mechanics.

6. Single link robot

7. Klein-garden field interacting with a robot classical and quantum cases

8. Stochastic optimal control.

9. RLS algorithm for P.D. feedback coefficient estimation in a robot system.

10. Quantum gate design using fractional delay filters

11. Non-Gaussian tremor estimation in master slake dynamics: q = T, qsT]T ∈ Rzd where the master and slave Robots are d-link systems These angles satisfy the difference equation

12. To see how the decomposition of the dynamics explicitly into the master and slave components occurs, we write down the equations of motion in continuous time

13. Consider the measurement model

14. General statistical analysis of slave Robot dynamics. The slave state q = , ] __ sT s T T n n satisfies the difference equation

15. Electromagnetic fields generated in inhomogeneous wave=guides and cavity resonators for controlling a slave Robot.

16. Generalized Sudarshan–Lindblad equation

17. Quantum image processing

18. Computation of the information transmitted by a classical source through a quantum channel defined by Schrodinger’s equation

19. Optimal control of a dynamical system using pd controllers The dynamical system has the form

20. Control of Robot with updating of parametric uncertainties based on the Lyapunov energy method.

21. Estimating the initial state of a quantum system from continuous measurements of the average value of an observable.

22. Estimating the configuration of two link Robot system using group representation theory.

23. Evans-Hudson diffusions, control using quantum pd controllers

24. Belavkin quantum filter

25. Estimating parameters in nonlinear systems driven by iid Gaussian noise. The signal model is

26. Lyapunov functions in control

27. Estimating the configuration of a two link 3-D Robot carrying current from the electromagnetic field pattern abstract

28. Tunnelling problems in quantum mechanics

29. K-variate generalization of Bernoulli filters

30. Disturbance observer and parametric uncertainty equation in Robotics

31. Performance analysis of the disturbance observer in robots.

32. Some aspects of quantum robotics

33. Consider the following problem

34. Quantum channel estimation

35. Estimation of the initial quantum state based on measurements with state collapse incorporated.

36. Statistical problems in robotic vision

37. Simulink model for filter design with em field inputs that guarantee optimum tracking of a 3-D quantum harmonic oscillator unitary evolution matrix with a given unitary evolution.

38. Cavity resonator in an inhomogeneous medium. The basic Maxwell equations at frequency w are

39. Radon transform based estimation of rotations of an object in the presence of noise.

40. Recursive least squares lattice algorithm.

41. Propagator computation for the Klein-Gordon field, electromagnetic field and Dirac field.

42. Cosmological metric (Robertson-Walker metric) and the analysis of gravitationsl wave propagation and Maxwell’s equation in this metric.

43. Filtering theory applied to robot trajectory measurement from noisy measurements of the position of an object by a camera on the robot with the image recorded on a flat curved screen.

44. Propagation of em waves in an inhomogeneous and anisotropic medium. The permittivity tensor has the form

45. MHD equations after spatial discretization

46. Problems in signal processing and control

47. Consider a nonlinear system defined by the difference equation

48. Wavelet based parameter estimation of nonlinear system

49. Large deviation methods in cosmological models

50. Nonlinear system identification using fractional delay Volterra filters.

51. Quantum gravitational search algorithm (QGSO).

52. Tele-opration for linear control systems.

53. Tele-operation for nonlinear robotic systems

54. Fluid dynamics in a pipe of non-uniform time varying cross section and nonlinear viscosity

55. Gravitational N-body problem in general relativity.

56. Let f(t, r) be random force field (input field) applied to a fluid dynamical system whose output is the velocity field v(t, r). The fluid is assumed to be incompressible and hence the equations of motion and continuity are

57. Gravitational swarm optimization for the design of quantum gates

58. Nono-robotice using quantum mechanices

59. Three dimensional quantum harmonic oscillator in an electromagnetic field. The Hamiltonian of the system is given

60. Problems in control and signal processing

61. Nonlinear filtering in discrete time, approximate algorithms

62. Problems in number theory and infinite series

63. Propagation of em waves in nonlinear media. The motion of an electron in the electrostatic field of the nucleus and in addition subject to an external electric field E(t, r) is given approximately by

64. Discrete time nonlinear filtering equations, approximations.

65. Dispersion relations for gravitational waves in the general theory of relativity

66. Ricci tensor components for the Robertson-Walker metric.

67. Image processing applied to the study of fluid dynamical perturbations and galactic evolution perturbations in cosmology

68. Compound Poisson processes and Levy process.

69. Designing an equalizer for a classical electromagnetic channel modelled by a linear frequency dependent susceptibility and a quadratically nonlinear frequency dependent susceptibility.

70. Coherent states: Let a, a* denote the annihilation and creation operators of a harmonic oscillator. Consider the operator

71. GSA (Gravitational search algorithm) for estimating the parameters of a fractional delay based linear time invariant system.

72. Parameter estimation in dynamical models involving Levy noise.

73. Classical and quantum nonlinear filtering for parameter estimation in physical models

74. Alfven waves in a plasma: The dispersion relations for magneto hydrodynamics.

75. Energy momentum tensor of the em field

76. Relativistic MHD: The total energy momentum tensor of the matter fluid and radiation field is given by

77. Compound Poisson processes: Estimating parameters in dynamical systems driven by compound Poisson processes.

78. Dirac Hamiltonian perturbed by quantum noise. The Dirac Hamiltonian for a free particle is given by

79. Brownian motion on a Riemannian manifold. Let the manifold M be imbedded in Rn as x x Fx T T _ ( ) __ __ , = H(x) where x ∈ Rp and F(x) ∈ Rn–p. The p dimensional Riemannian manifold M has x as its coordinates. Its metric is given by given by

80. Quantum stochastis processes in quantum field theory: The free Dirac wave function is

81. Approximate quantization of the gravitational field. The Lagrangian density of the free gravitational field is given by

82. Lie group-Lie algebra approach to modelling the motion of multiple 3-D robot links.

83. Group algebras with multiplicative noise

84. Teleoperation robotic fields

85. Quantization of the dynamical system

86. Ito’s formula of or quantum semi martingales

87. Quantization of the transmission line equations.

88. Quantum Lorentz transformations

89. Scalar Klein-Gordon equation in a perturbed metric

90. Optimal control of the wave function of an atomic system using eternally applied electromagnetic fields. The Hamitonian of the atom after interaction with the em field described by the potentials (A(t, r), F(t, r)) is given by

91. Stochastic version of the previous problem: The wave function satisfies a stochastic differential equation

92. Quantum stochastic Bellman-Hamilton-Jacobi equation for optimal control of a quantum stochastic differential equation

93. A more rigorous formulation of quantum stochastic optimal control: X ∈ h, L t b a ( ) ∈ h ⊗ Gs(Ht]). We assume that L t b a ( ) has the form

94. Problem on fractional delay nonlinear system design

95. Commuting non-demolition measurement processes in quantum filtering.

96. Quantum particle in a spherically symmetric box solving the Schrodinger equation

97. The general relativistic equations for a conducting fluid

98. Evolution of in homogeneities in a homogeneous and isotropic background universe as a model for galactic evolution

99. Quantization of the two link robot

100. Computation of the perturbation in the Ricci tensor around the Robertson-Walker metric.

101. Problem: Random perturbations in the feedback loop of an LTI system.

102. Consider a random variable X assuming values in Rn that has an infinitely divisible probability distribution. The levy-Khintchine formula for the characteristic function of X is

103. GSA paper of Navneet: At the point r0 in space is located a set of p infinitesimal current elements pointed along different directions. This current vector is described by

104. Generalized quantum filtering for non-demolition measurements in the sense of Belavkin

105. Ph.D thesis summary of K. Gautam.

106. Haar measure on some semisimple Lie groups

107. Invariants for functions defined on a semisimple Lie group. Let fk:G → C, k = 1, 2 be two functions. Suppose X is the character of a representation of G. Then define

108. Quantum Robotic teleoperation system analysis: Master robot dynamical equations

109. Quantum filtering and control

110. Combination of state observer and state trajectory tracking in classical probability.

111. Let the metric be expressed upto second order of smallness as

112. Stability and robustness analysis for a state observer with state error feedback

113. Quantum system perturbed by classical Levy noise: The Schrodinger evolution operator U (t) satisfies the complex stochastic differential equation

114. Pattern classification for the joint action of rotation and permutation groups

115. Design of quantum unitary gates by matching the generator

116. Estimating the parameters of the Hamiltonian and the Sudarshan Lindblad quantum noise from repeated measurement.

117. Hilbert’s Fourteen problem: Given a vector space V and the action of a group G on V (for example representation of G in V), an invariant of G is a function f V m :_C such that

118. Fractional delay system in discrete time.

119. Proposed five year research plan

120. Estimating the rotation angle of an image using the Radon transform: f (x, y) is the image field.

121. Gauge fields and field equations associated to a matrix Lie group. Let G be a matrix Lie group with ta, a = 1, 2, …,…N a basis for its Lie algebra g. The commutation relations are

122. Study topic as Transmission lines and waveguides course

123. Schrodinger, Heisenbery and Dirac’s interaction pictures of quantum dynamics

124. Generators of the homogeneous Lorentz group and its application to the construction of the curvature tensor of general relativity

125. Bloch wave functions in determining the band structure of semiconductors. The potential V(r) is periodic with periods of dx, dy, dz along the three directions i.e.,

126. Robot hitting a stretched elastic sheet, dynamics, End point of the robot at time t has coordinates

127. Estimating parameters of a quantum system when the Hamiltonian depends on unknown parameters.

128. Feynman diagrams for interaction between matter (electrons and positrons), photons and gravitons.

129. EKF for obtained for the filtered estimate of the pure state of a noisy quantum system based on noisy measurements of the average of an observable

130. Dirac’s equation in curved space-time.

131. Velocity and rotation angle estimation in two dimensional images.

132. Newtonian cosmology can reproduce all the results of general relativistic cosmology

133. Chandrasekhar limit on the size of a white dwarf

134. Dirac’s equation in curved space-time is given by

135. Post-Newtonian approximation in general relativity

136. Spherically symmetric metrics

137. Action functional for a robot moving in a gravitational field in the presence of an electromagnetic field and the electron-positron field.

138. Radial time independent metric with spherical distribution of matter and pressure.

139. ] Optimal control of electromagnetic fields within a box by control currents in another box. Let V1, V2 be two disjoint volumes in R3. We apply a current density field J(w, r) in the first box V1 and the magnetic vector potential generated in the box V2 is given by

140. ] Channel capacity for a Cq channel. A finite alphabet A is encoded into density matrices r(x) , x ∈A. For n a positive integer and a sequence u ∈ An, we define

141. Viscous and thermal effects in a special and general relativistic fluid: First consider the special relativistic case. The general relativistic case can be handled by replacing all partial derivatives by covariant derivatives the Minkowski metric hmn by the metric tensor gmn (x) of space-time. The energy momentum tensor of the fluid is

142. Interaction between spin of an atom and a quantum magnetic field. The Coulomb gauge is assumed, i.e., the magnetic vector potential A (t, r) is given by

143. Some concepts in cosmology

144. Consider

145. A survey of the work of some great Indian Scientists

146. A brief survey of estimation, filtering and control theory applied to the d-link robot system.

147. Wave propagation in a plane using Boltzmann eqn. maxwell’s Morally equation.

148. Let G be a group and m, v probability meaning on G. Then if

149. Let g ∈ G have probability dissipation m.

150. Haar measure on G.

151. Approximate nonlinear filtering eqn. in discrete time

152. Estimating the time varying delay. Teleoperation with time varying delay

153. Propagation of em waves in wave guide having non-uniform and anisotropic permittivity and permeability.

154. Entropy of zero mean Gauss-Markov processes

155. Ordinary of stochastic differential equation with delay

156. Born -Oppenheimer approximation

157. Robots with periodic inputs ∼ Fourier series analysis

158. Large deviation Theory for image point of an object taken by a camera executing random motion,

159. Feynman diagram for scattering absorption and emission.

160. For Dr. Rajveer

161. Quantum filtering with robotics application

162. Problem from Thomann Quantum General Relativity

163. Parameter estimation in non-linear models?

164. Mark Wilde Quantum Information Theory

165. Stochastic differential equation driven by jump processes

166. Nano robots noise described using the quantum Langevin equation.

167. Teleoperation of system in the presence of shot noise. Let N1(t), N2(t) be two independent Poisson presence with rates l1 and l2 repeatedly. Define

168. 1. Nano-robotics in a strong gravitational field. 2. Controlling the quantum gravitational filed for properly a nono-robot.

169. Calculate the Haar measures a SL(2, R) and SL(2, C)

170. Four vector potential of a current source:

171. Quantum filtering and control

172. gmv = qmv + nmnv (quantum gravity)

173. Nonlinear Pocklington integral equation

174. Compulation of the Haar measure for some groups

175. Some important equations in quantum gravity.

176. Symplectic invariants

177. Canonical quantum gtr.

178. Path integral approach to q.m.

179. Levy process driven classical and quantum models of a two link robot arm.

180. Evolution of inhomogeneties lives in a homogeneous and isotropic universe.Analysis is based on small perturbation of the Robertson Walker matrix

181. Hamiltonian for a single charged particle moving in curved space time in the presence of an external em field.

182. Moment generating function for quantum observables in boson Fock space.

183. Generalized quantum filtering for non-demolition measurements in the series of Balavkin.

184. Evolution of the system state for H. P equn.

185. Quantum filtering (Belavkin) State process

186. Distribution of LTa

187. Quantization of Linear Gauss-Markov processes

188. Quantization of a free robot having two link with noise.

189. Robot in a box approximation

190. Quantum relative entropy evolution in the Sudarshan-Lindblad picture. Same Hamiltonian with different noise processes. How does the relative entropy evolve.

191. Evolution of quantum relative entropy (Exercise)

192. Particle in a classical and quantum noise field.

193. Galactine evolution in gtr.

194. Group representation and robot configuration estimation.

195. For Gautom: Ion trap gate design

196. Quantum filtering in Coherent states.

197. Design of quantum gates with Levy noise.

198. Problems in electrostatics

199. Solving the wave eqn. with random boundary. Let B (q) be the region in R3 (open connection set) with boundary S (q) = _B() _. We wish to solve

200. Lectures on Electromagnetics

201. Ppt. for Nanorobotics.

202. The dynamics of an extended nano robot body a fluid environment studied using joint fluid dynamics and particle mechanics.

203. The effect of the nano-robot on the fluid motion within the body msut also be studied.

204. Quantum effects.

205. Quantum stochastic filtering control

206. Quantum gravity metric

207. rt is a density matrix. Then

208. Study projects

209. Quantum teleportation

210. A quantum atomic receiver is excited by a quantum e-mfield. The Hamiltonian of the field is

211. Fluid dynamics in the Schwarzschild metrics in state variable form.

212. Introducing quantum Stochastic process in quantum field theory.

213. Left invariant measures on a general real Lie group

214. Let B t n ( ) _R be n-dimensional Brownian motion and FYY pn p () , __×RR, i.e.

215. Path integral approach to Dirac relativistic wave equation

216. Quantum fidelity.

217. Estimating the random rotation and translation applied to an object (3-D) using the Maximum A posteriori algorithm

218. Quantum Stochastic filtering

219. Proof of convergence of CRLB for Gaussian White noise

220. Cosmology with stochastic perturbation.

221. Quantum Boltzmann Equation

222. Design of unitary gates by perturbing the free Dirac equation.

223. Waves in a plasma

224. Calculate using perturbation theory the statistics of a charged particle moving in a random electromagnetic field of the form

225. Quantisation of a stochastic differential equation using the method of Evan Hudson flows

226. Filtering for independent increment measurement noise

227. Hamiltonian formulation of geodesic motion

228. Hamiltonian formulation of geodesic motion

This book is a research monograph covering a variety of problems in (a) statistical state and parameter estimation in nonlinear stochastic dynamical system in both the classical and quantum scenarios, propagation of electromagnetic waves in a plasma described by the Boltzmann Kinetic transporo equation, classical and quantum general relativity etc. It will be of use to Engineering undergraduate students interested in analysing the motion of robotic subject to random perturbation and also to research scientists working in quantum filtering and study problems of inhomogeneous perturbation to in a homogenous and isotropic universal leading to the formation of galaxies in an expanding universe.

1. Basic Markov chain theory

2. Basic quantum mechanics and quantum field theory

3. Solving RDRA problem with arbitrary boundary using orthogonal curvilinear co-ordinate

4. Optimal control of the average values of a set of observables in a quantum system.

5. Optimal control of observable averages in quantum mechanics.

6. Single link robot

7. Klein-garden field interacting with a robot classical and quantum cases

8. Stochastic optimal control.

9. RLS algorithm for P.D. feedback coefficient estimation in a robot system.

10. Quantum gate design using fractional delay filters

11. Non-Gaussian tremor estimation in master slake dynamics: q = T, qsT]T ∈ Rzd where the master and slave Robots are d-link systems These angles satisfy the difference equation

12. To see how the decomposition of the dynamics explicitly into the master and slave components occurs, we write down the equations of motion in continuous time

13. Consider the measurement model

14. General statistical analysis of slave Robot dynamics. The slave state q = , ] __ sT s T T n n satisfies the difference equation

15. Electromagnetic fields generated in inhomogeneous wave=guides and cavity resonators for controlling a slave Robot.

16. Generalized Sudarshan–Lindblad equation

17. Quantum image processing

18. Computation of the information transmitted by a classical source through a quantum channel defined by Schrodinger’s equation

19. Optimal control of a dynamical system using pd controllers The dynamical system has the form

20. Control of Robot with updating of parametric uncertainties based on the Lyapunov energy method.

21. Estimating the initial state of a quantum system from continuous measurements of the average value of an observable.

22. Estimating the configuration of two link Robot system using group representation theory.

23. Evans-Hudson diffusions, control using quantum pd controllers

24. Belavkin quantum filter

25. Estimating parameters in nonlinear systems driven by iid Gaussian noise. The signal model is

26. Lyapunov functions in control

27. Estimating the configuration of a two link 3-D Robot carrying current from the electromagnetic field pattern abstract

28. Tunnelling problems in quantum mechanics

29. K-variate generalization of Bernoulli filters

30. Disturbance observer and parametric uncertainty equation in Robotics

31. Performance analysis of the disturbance observer in robots.

32. Some aspects of quantum robotics

33. Consider the following problem

34. Quantum channel estimation

35. Estimation of the initial quantum state based on measurements with state collapse incorporated.

36. Statistical problems in robotic vision

37. Simulink model for filter design with em field inputs that guarantee optimum tracking of a 3-D quantum harmonic oscillator unitary evolution matrix with a given unitary evolution.

38. Cavity resonator in an inhomogeneous medium. The basic Maxwell equations at frequency w are

39. Radon transform based estimation of rotations of an object in the presence of noise.

40. Recursive least squares lattice algorithm.

41. Propagator computation for the Klein-Gordon field, electromagnetic field and Dirac field.

42. Cosmological metric (Robertson-Walker metric) and the analysis of gravitationsl wave propagation and Maxwell’s equation in this metric.

43. Filtering theory applied to robot trajectory measurement from noisy measurements of the position of an object by a camera on the robot with the image recorded on a flat curved screen.

44. Propagation of em waves in an inhomogeneous and anisotropic medium. The permittivity tensor has the form

45. MHD equations after spatial discretization

46. Problems in signal processing and control

47. Consider a nonlinear system defined by the difference equation

48. Wavelet based parameter estimation of nonlinear system

49. Large deviation methods in cosmological models

50. Nonlinear system identification using fractional delay Volterra filters.

51. Quantum gravitational search algorithm (QGSO).

52. Tele-opration for linear control systems.

53. Tele-operation for nonlinear robotic systems

54. Fluid dynamics in a pipe of non-uniform time varying cross section and nonlinear viscosity

55. Gravitational N-body problem in general relativity.

56. Let f(t, r) be random force field (input field) applied to a fluid dynamical system whose output is the velocity field v(t, r). The fluid is assumed to be incompressible and hence the equations of motion and continuity are

57. Gravitational swarm optimization for the design of quantum gates

58. Nono-robotice using quantum mechanices

59. Three dimensional quantum harmonic oscillator in an electromagnetic field. The Hamiltonian of the system is given

60. Problems in control and signal processing

61. Nonlinear filtering in discrete time, approximate algorithms

62. Problems in number theory and infinite series

63. Propagation of em waves in nonlinear media. The motion of an electron in the electrostatic field of the nucleus and in addition subject to an external electric field E(t, r) is given approximately by

64. Discrete time nonlinear filtering equations, approximations.

65. Dispersion relations for gravitational waves in the general theory of relativity

66. Ricci tensor components for the Robertson-Walker metric.

67. Image processing applied to the study of fluid dynamical perturbations and galactic evolution perturbations in cosmology

68. Compound Poisson processes and Levy process.

69. Designing an equalizer for a classical electromagnetic channel modelled by a linear frequency dependent susceptibility and a quadratically nonlinear frequency dependent susceptibility.

70. Coherent states: Let a, a* denote the annihilation and creation operators of a harmonic oscillator. Consider the operator

71. GSA (Gravitational search algorithm) for estimating the parameters of a fractional delay based linear time invariant system.

72. Parameter estimation in dynamical models involving Levy noise.

73. Classical and quantum nonlinear filtering for parameter estimation in physical models

74. Alfven waves in a plasma: The dispersion relations for magneto hydrodynamics.

75. Energy momentum tensor of the em field

76. Relativistic MHD: The total energy momentum tensor of the matter fluid and radiation field is given by

77. Compound Poisson processes: Estimating parameters in dynamical systems driven by compound Poisson processes.

78. Dirac Hamiltonian perturbed by quantum noise. The Dirac Hamiltonian for a free particle is given by

79. Brownian motion on a Riemannian manifold. Let the manifold M be imbedded in Rn as x x Fx T T _ ( ) __ __ , = H(x) where x ∈ Rp and F(x) ∈ Rn–p. The p dimensional Riemannian manifold M has x as its coordinates. Its metric is given by given by

80. Quantum stochastis processes in quantum field theory: The free Dirac wave function is

81. Approximate quantization of the gravitational field. The Lagrangian density of the free gravitational field is given by

82. Lie group-Lie algebra approach to modelling the motion of multiple 3-D robot links.

83. Group algebras with multiplicative noise

84. Teleoperation robotic fields

85. Quantization of the dynamical system

86. Ito’s formula of or quantum semi martingales

87. Quantization of the transmission line equations.

88. Quantum Lorentz transformations

89. Scalar Klein-Gordon equation in a perturbed metric

90. Optimal control of the wave function of an atomic system using eternally applied electromagnetic fields. The Hamitonian of the atom after interaction with the em field described by the potentials (A(t, r), F(t, r)) is given by

91. Stochastic version of the previous problem: The wave function satisfies a stochastic differential equation

92. Quantum stochastic Bellman-Hamilton-Jacobi equation for optimal control of a quantum stochastic differential equation

93. A more rigorous formulation of quantum stochastic optimal control: X ∈ h, L t b a ( ) ∈ h ⊗ Gs(Ht]). We assume that L t b a ( ) has the form

94. Problem on fractional delay nonlinear system design

95. Commuting non-demolition measurement processes in quantum filtering.

96. Quantum particle in a spherically symmetric box solving the Schrodinger equation

97. The general relativistic equations for a conducting fluid

98. Evolution of in homogeneities in a homogeneous and isotropic background universe as a model for galactic evolution

99. Quantization of the two link robot

100. Computation of the perturbation in the Ricci tensor around the Robertson-Walker metric.

101. Problem: Random perturbations in the feedback loop of an LTI system.

102. Consider a random variable X assuming values in Rn that has an infinitely divisible probability distribution. The levy-Khintchine formula for the characteristic function of X is

103. GSA paper of Navneet: At the point r0 in space is located a set of p infinitesimal current elements pointed along different directions. This current vector is described by

104. Generalized quantum filtering for non-demolition measurements in the sense of Belavkin

105. Ph.D thesis summary of K. Gautam.

106. Haar measure on some semisimple Lie groups

107. Invariants for functions defined on a semisimple Lie group. Let fk:G → C, k = 1, 2 be two functions. Suppose X is the character of a representation of G. Then define

108. Quantum Robotic teleoperation system analysis: Master robot dynamical equations

109. Quantum filtering and control

110. Combination of state observer and state trajectory tracking in classical probability.

111. Let the metric be expressed upto second order of smallness as

112. Stability and robustness analysis for a state observer with state error feedback

113. Quantum system perturbed by classical Levy noise: The Schrodinger evolution operator U (t) satisfies the complex stochastic differential equation

114. Pattern classification for the joint action of rotation and permutation groups

115. Design of quantum unitary gates by matching the generator

116. Estimating the parameters of the Hamiltonian and the Sudarshan Lindblad quantum noise from repeated measurement.

117. Hilbert’s Fourteen problem: Given a vector space V and the action of a group G on V (for example representation of G in V), an invariant of G is a function f V m :_C such that

118. Fractional delay system in discrete time.

119. Proposed five year research plan

120. Estimating the rotation angle of an image using the Radon transform: f (x, y) is the image field.

121. Gauge fields and field equations associated to a matrix Lie group. Let G be a matrix Lie group with ta, a = 1, 2, …,…N a basis for its Lie algebra g. The commutation relations are

122. Study topic as Transmission lines and waveguides course

123. Schrodinger, Heisenbery and Dirac’s interaction pictures of quantum dynamics

124. Generators of the homogeneous Lorentz group and its application to the construction of the curvature tensor of general relativity

125. Bloch wave functions in determining the band structure of semiconductors. The potential V(r) is periodic with periods of dx, dy, dz along the three directions i.e.,

126. Robot hitting a stretched elastic sheet, dynamics, End point of the robot at time t has coordinates

127. Estimating parameters of a quantum system when the Hamiltonian depends on unknown parameters.

128. Feynman diagrams for interaction between matter (electrons and positrons), photons and gravitons.

129. EKF for obtained for the filtered estimate of the pure state of a noisy quantum system based on noisy measurements of the average of an observable

130. Dirac’s equation in curved space-time.

131. Velocity and rotation angle estimation in two dimensional images.

132. Newtonian cosmology can reproduce all the results of general relativistic cosmology

133. Chandrasekhar limit on the size of a white dwarf

134. Dirac’s equation in curved space-time is given by

135. Post-Newtonian approximation in general relativity

136. Spherically symmetric metrics

137. Action functional for a robot moving in a gravitational field in the presence of an electromagnetic field and the electron-positron field.

138. Radial time independent metric with spherical distribution of matter and pressure.

139. ] Optimal control of electromagnetic fields within a box by control currents in another box. Let V1, V2 be two disjoint volumes in R3. We apply a current density field J(w, r) in the first box V1 and the magnetic vector potential generated in the box V2 is given by

140. ] Channel capacity for a Cq channel. A finite alphabet A is encoded into density matrices r(x) , x ∈A. For n a positive integer and a sequence u ∈ An, we define

141. Viscous and thermal effects in a special and general relativistic fluid: First consider the special relativistic case. The general relativistic case can be handled by replacing all partial derivatives by covariant derivatives the Minkowski metric hmn by the metric tensor gmn (x) of space-time. The energy momentum tensor of the fluid is

142. Interaction between spin of an atom and a quantum magnetic field. The Coulomb gauge is assumed, i.e., the magnetic vector potential A (t, r) is given by

143. Some concepts in cosmology

144. Consider

145. A survey of the work of some great Indian Scientists

146. A brief survey of estimation, filtering and control theory applied to the d-link robot system.

147. Wave propagation in a plane using Boltzmann eqn. maxwell’s Morally equation.

148. Let G be a group and m, v probability meaning on G. Then if

149. Let g ∈ G have probability dissipation m.

150. Haar measure on G.

151. Approximate nonlinear filtering eqn. in discrete time

152. Estimating the time varying delay. Teleoperation with time varying delay

153. Propagation of em waves in wave guide having non-uniform and anisotropic permittivity and permeability.

154. Entropy of zero mean Gauss-Markov processes

155. Ordinary of stochastic differential equation with delay

156. Born -Oppenheimer approximation

157. Robots with periodic inputs ∼ Fourier series analysis

158. Large deviation Theory for image point of an object taken by a camera executing random motion,

159. Feynman diagram for scattering absorption and emission.

160. For Dr. Rajveer

161. Quantum filtering with robotics application

162. Problem from Thomann Quantum General Relativity

163. Parameter estimation in non-linear models?

164. Mark Wilde Quantum Information Theory

165. Stochastic differential equation driven by jump processes

166. Nano robots noise described using the quantum Langevin equation.

167. Teleoperation of system in the presence of shot noise. Let N1(t), N2(t) be two independent Poisson presence with rates l1 and l2 repeatedly. Define

168. 1. Nano-robotics in a strong gravitational field. 2. Controlling the quantum gravitational filed for properly a nono-robot.

169. Calculate the Haar measures a SL(2, R) and SL(2, C)

170. Four vector potential of a current source:

171. Quantum filtering and control

172. gmv = qmv + nmnv (quantum gravity)

173. Nonlinear Pocklington integral equation

174. Compulation of the Haar measure for some groups

175. Some important equations in quantum gravity.

176. Symplectic invariants

177. Canonical quantum gtr.

178. Path integral approach to q.m.

179. Levy process driven classical and quantum models of a two link robot arm.

180. Evolution of inhomogeneties lives in a homogeneous and isotropic universe.Analysis is based on small perturbation of the Robertson Walker matrix

181. Hamiltonian for a single charged particle moving in curved space time in the presence of an external em field.

182. Moment generating function for quantum observables in boson Fock space.

183. Generalized quantum filtering for non-demolition measurements in the series of Balavkin.

184. Evolution of the system state for H. P equn.

185. Quantum filtering (Belavkin) State process

186. Distribution of LTa

187. Quantization of Linear Gauss-Markov processes

188. Quantization of a free robot having two link with noise.

189. Robot in a box approximation

190. Quantum relative entropy evolution in the Sudarshan-Lindblad picture. Same Hamiltonian with different noise processes. How does the relative entropy evolve.

191. Evolution of quantum relative entropy (Exercise)

192. Particle in a classical and quantum noise field.

193. Galactine evolution in gtr.

194. Group representation and robot configuration estimation.

195. For Gautom: Ion trap gate design

196. Quantum filtering in Coherent states.

197. Design of quantum gates with Levy noise.

198. Problems in electrostatics

199. Solving the wave eqn. with random boundary. Let B (q) be the region in R3 (open connection set) with boundary S (q) = _B() _. We wish to solve

200. Lectures on Electromagnetics

201. Ppt. for Nanorobotics.

202. The dynamics of an extended nano robot body a fluid environment studied using joint fluid dynamics and particle mechanics.

203. The effect of the nano-robot on the fluid motion within the body msut also be studied.

204. Quantum effects.

205. Quantum stochastic filtering control

206. Quantum gravity metric

207. rt is a density matrix. Then

208. Study projects

209. Quantum teleportation

210. A quantum atomic receiver is excited by a quantum e-mfield. The Hamiltonian of the field is

211. Fluid dynamics in the Schwarzschild metrics in state variable form.

212. Introducing quantum Stochastic process in quantum field theory.

213. Left invariant measures on a general real Lie group

214. Let B t n ( ) _R be n-dimensional Brownian motion and FYY pn p () , __×RR, i.e.

215. Path integral approach to Dirac relativistic wave equation

216. Quantum fidelity.

217. Estimating the random rotation and translation applied to an object (3-D) using the Maximum A posteriori algorithm

218. Quantum Stochastic filtering

219. Proof of convergence of CRLB for Gaussian White noise

220. Cosmology with stochastic perturbation.

221. Quantum Boltzmann Equation

222. Design of unitary gates by perturbing the free Dirac equation.

223. Waves in a plasma

224. Calculate using perturbation theory the statistics of a charged particle moving in a random electromagnetic field of the form

225. Quantisation of a stochastic differential equation using the method of Evan Hudson flows

226. Filtering for independent increment measurement noise

227. Hamiltonian formulation of geodesic motion

228. Hamiltonian formulation of geodesic motion

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