Solution of the Bosonic and Algebraic Hamiltonians by using AIM

We apply the notion of asymptotic iteration method (AIM) to determine eigenvalues of the bosonic Hamiltonians that include a wide class of quantum optical models. We consider solutions of the Hamiltonians, which are even polynomials of the fourth order with the respect to Boson operators. We also demonstrate applicability of the method for obtaining eigenvalues of the simple Lie algebraic structures. Eigenvalues of the multi-boson Hamiltonians have been obtained by transforming in the form of the single boson Hamiltonian in the framework of AIM

Structure theory of central simple ℤd-graded algebras

This paper investigates the structure theory of ℤd- central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are motivating examples of ℤd-central simple graded algebras. © TÜBİTAK

Adsorption of Nitrogen Dioxide (NO2) for Different Gas Concentrations, Temperatures and Relative Humidities by using Activated Carbon Filter: An Experimental Study

Noxious gases can be reduced through activated carbon; nevertheless, this process is very complex due to the changing parameters. Nitrogen dioxides take place in the so-called reactive gases. The nitrogen dioxide concentration existing in the environment can be harmful, in particular for asthmatics and it also has the potential to bring about other serious diseases. For instance, interior diseases are often caused by nitrogen oxide gases. Through this study, we have observed the nitrogen dioxide adsorption on the active carbon for varying air temperatures, gas concentrations and air relative humidities. In this context, it has been examined the effect of all three parameters. While conducting this project, we have used parameters between 1ppm and 30ppm (for NO2 concentration), 23°C and 33°C (for air temperature), 30% and 90% (for air relative humidity). In order to understand this process, breakthrough curves of NO2evaluated from experiments have been used in the present study. Results show that the humidity has not a remarkable effect on the adsorption of NO2; however, increasing relative humidity causes to a decrease in the capacity of the activated carbon for NO2 adsorption. Additionally, NO2 adsorption is exothermic, therefore it increases the air temperature

Analysis of Heat Transfer in the Material during Pulsed Laser-Metal Interaction by Using Kinetic Theory

Nowadays technological developments, the use of lasers in production is increasing and plays an important role due to low cost and high accuracy. The heat transfer, over the course of laser-metal interplay, has a great importance in metal forming. In this study, different types of materials were investigated in order to designate the temperature distributions inside material and on the material surface versus the thermodynamic properties of the material used and then the temperature distributions obtained from the analysis were compared each other. In addition, the heat transfer is occurring during the interaction of the laser power of 1.1010 W/m2 and 5.1010 W/m2 with laser power intensity in two main groups using different materials these are steel, nickel, tantalum and titanium, and numerical results are obtained using the finite-difference method. In the first step, a solution is obtained by electron kinetic theory according to the basic heat transfer. In the second step, since heat convection is formed after material has reached the melting point. Using electron kinetic theory model for convection solutions have been obtained. Moreover, the temperature distribution that occurs during the laser metal interaction was studied by variation of the time chart and the material depth. As a result of the study, material's surface at the correct temperature of liquid phase change material and increased depth in the direction perpendicular to the electro-kinetic theory approach is further demonstrated by the decrease in the first manner and then remains constant in exponential phase change temperature. In addition to this the analysis results, the substrate temperature increases, the change in phase in the material becomes smaller and smaller

Exactly solvable effective mass D-dimensional Schrodinger equation for pseudoharmonic and modified Kratzer problems

We employ the point canonical transformation (PCT) to solve the D-dimensional Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In mapping the transformed exactly solvable D-dimensional ($D\geq 2$) Schr\"{o}dinger equation with constant mass into the effective mass equation by employing a proper transformation, the exact bound state solutions including the energy eigenvalues and corresponding wave functions are derived. The well-known pseudoharmonic and modified Kratzer exact eigenstates of various dimensionality is manifested.Comment: 13 page

Jointly learning trajectory generation and hitting point prediction in robot table tennis

This paper proposes a combined learning framework for a table tennis robot. In a typical robot table tennis setup, a single striking point is predicted for the robot on the basis of the ball's initial state. Subsequently, the desired Cartesian racket state and the desired joint states at the striking time are determined. Finally, robot joint trajectories are generated. Instead of predicting a single striking point, we propose to construct a ball trajectory prediction map, which predicts the ball's entire rebound trajectory using the ball's initial state. We construct as well a robot trajectory generation map, which predicts the robot joint movement pattern and the movement duration using the Cartesian racket trajectories without the need of inverse kinematics, where a correlation function is used to adapt these joint movement parameters according to the ball flight trajectory. With joint movement parameters, we can directly generate joint trajectories. Additionally, we introduce a reinforcement learning approach to modify robot joint trajectories such that the robot can return balls well. We validate this new framework in both the simulated and the real robotic systems and illustrate that a seven degree-of-freedom Barrett WAM robot performs well

Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass

Known shape-invariant potentials for the constant-mass Schrodinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance condition turns out to be deformed. Its solvability imposes the form of both the deformed superpotential and the PDEM. A lot of new exactly solvable potentials associated with a PDEM background are generated in this way. A novel and important condition restricting the existence of bound states whenever the PDEM vanishes at an end point of the interval is identified. In some cases, the bound-state spectrum results from a smooth deformation of that of the conventional shape-invariant potential used in the construction. In others, one observes a generation or suppression of bound states, depending on the mass-parameter values. The corresponding wavefunctions are given in terms of some deformed classical orthogonal polynomials.Comment: 26 pages, no figure, reduced secs. 4 and 5, final version to appear in JP

Deformed algebras, position-dependent effective masses and curved spaces: An exactly solvable Coulomb problem

We show that there exist some intimate connections between three unconventional Schr\"odinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective mass or of a curved space, respectively. This occurs whenever a specific relation between the deforming function, the position-dependent mass and the (diagonal) metric tensor holds true. We illustrate these three equivalent approaches by considering a new Coulomb problem and solving it by means of supersymmetric quantum mechanical and shape invariance techniques. We show that in contrast with the conventional Coulomb problem, the new one gives rise to only a finite number of bound states.Comment: 22 pages, no figure. Archive version is already official. Published by JPA at http://stacks.iop.org/0305-4470/37/426