Goran S. Djordjevic

p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY

We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle–Hawking proposal does not work in models with matter fields. p-adic and adelic minisuperspace quantum cosmology is well defined as an ordinary application of p-adic and adelic quantum mechanics. It is illustrated by a few cosmological models in one, two and three minisuperspace dimensions. As a result of p-adic quantum effects and the adelic approach, these models exhibit some discreteness of the minisuperspace and cosmological constant. In particular, discreteness of the de Sitter space and its cosmological constant is emphasized.

Adelic Path Integrals for Quadratic Lagrangians

Feynmans path integral in adelic quantum mechanics is considered. The propagator for one-dimensional adelic systems with quadratic Lagrangians is analytically evaluated. Obtained exact general formula has the form which is invariant under interchange of the number fields ℝ and ℚp.

p-Adic Path Integrals for Quadratic Actions

The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude for one-dimensional systems with quadratic actions is calculated in an exact form, which is the same as that in ordinary quantum mechanics.

p-Adic and adelic harmonic oscillator with a time-dependent frequency

The classical and quantum formalism for a p-adic and adelic harmonic oscillator with a time-dependent frequency is developed, and general formulas are obtained for the main theoretical quantities. In particular, the p-adic propagator is calculated, and the existence of a simple vacuum state as well as adelic quantum dynamics is shown. A spatial discreteness and a p-adic quantum mechanical phase are noted.

p-ADIC AND ADELIC FREE RELATIVISTIC PARTICLE

We consider spectral problem for a free relativistic particle in p-adic and adelic quantum mechanics. In particular, we found p-adic and adelic eigenfunctions. Within adelic approach there exist quantum states that exhibit discrete structure of space–time at the Planck scale.

Variable structure systems for control of redundant robot

Abstract A combination of one class of kinematic control of redundant robot and Variable Structure Systems (VSS) in manipulating tasks that require large accelerations or decelerations is the main issue of this paper. The inverse kinematic problem will, on a tactical control level, be solved through Distributed Positioning (DP) concept, while the solution of the executive control level will be solved by using a combination of two common VS control algorithms with PI controller. A complete synthesis of VS local regulators for the redundancy, along with stability analysis, will be given. Comparison of VS with PD controller tracking characteristics will be studied on a suitable SCARA robot with redundancy performing one typical pick-and-place movement.

Tachyon inflation in an AdS braneworld with backreaction

We analyze the inflationary scenario based on the tachyon field coupled with the radion of the second Randall–Sundrum model (RSII). The tachyon Lagrangian is derived from the dynamics of a 3-brane moving in the five-dimensional bulk. The AdS5 geometry of the bulk is extended to include the radion. Using the Hamiltonian formalism we find four nonlinear field equations supplemented by the modified Friedmann equations of the RSII braneworld cosmology. After a suitable rescaling we reduce the parameters of our model to only one free parameter related to the brane tension and the AdS5 curvature. We solve the equations numerically assuming a reasonably wide range of initial conditions determined by physical considerations. Varying the free parameter and initial conditions we confront our results with the Planck 2015 data.

Kinematic Redundancy and Sensor Redundancy for Enhancement of Robot Tracking Performance

Imprecision of robots internal sensors and its influence on trajectory tracking tasks along with high dynamic requirements are the main issues in this paper. The solution proposes redundancy introduction (in the shape of small mechanism at the top of the robot) for resolving both problems. The inverse kinematics of the redundant robot has been solved at the tactical level of control via the Distributed Positioning (DP) concept. The redundancy applied reduces the tracking error caused by dynamic requirements and partly by imprecision of internal sensors. However, additional solutions with external position sensor could be used in order to reduce sensor imprecision influence. All solutions are very conservative considering changes in basic (non-redundant) robot. Simulation results provide clear insight in the validity of proposed solutions.

Tachyon with an inverse power-law potential in a braneworld cosmology

We study a tachyon cosmological model based on the dynamics of a 3-brane in the bulk of the second Randall-Sundrum model extended to more general warp functions. A well known prototype of such a generalization is the bulk with a selfinteracting scalar field. As a consequence of a generalized bulk geometry the cosmology on the observer brane is modified by the scale dependent four-dimensional gravitational constant. In particular we study a power law warp factor which generates an inverse power-law potential

Signature change in p-adic and noncommutative FRW cosmology

V\propto \varphi^{-n}