Hamilton-Jacobi quantization of singular Lagrangians with linear velocities

In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton-Jacobi method. We shall consider the integrablity conditions on the equations of motion and the action function as well in order to obtain the path integral quantization of singular Lagrangians with linear velocities.Comment: late

The Influence of the Application of Learning Strategies Model Elaboration Results Learn Aqeedah Akhlaq in MTs Mu\u27allimat College Cukir Jombang

Learning models of elaboration is to start learning the contents of the presentation on the general level of moving to a detailed level (elaborative sequence). By learning from the general to the particular pattern, giving students a simple description contained in the content frame (epitome) then develop into sub-sub material in more detail. Besides that, there are two stages of elaboration stimulate students\u27 memory where the second elaboration stage as the consolidation of the student\u27s abilities in the first stage of elaboration. Also students are encouraged to develop a sense of high social learning designed to implement cooperatively, it Allows students who are less intelligent can ask more intelligent students in the group (peer learning) .The purpose of this research are: 1) Describe the learning strategy elaboration on the models of morality in subjects aqeedah; 2) Describe the learning outcomes of subjects aqeedah morality; 3) Describe the effect of the application of learning strategies elaboration models of the learning outcomes of aqeedah morality in MTs-PM Cukir Jombang. This research is a quantitative research approach ex post facto. Conclusion: 1. Learning models of elaboration is to start learning the contents of the presentation on the general level of moving to a detailed level (elaborative sequence), giving students a simple description contained in the content frame (epitome) then develop into sub- sub material in more detail.2. The learning result is Obtained behavioral changes after studying the material learners demonstrated creed Akhlaq results.3 through the final test. There is a positive and significant influence between the Implementation of Learning Strategy Elaboration Of Learning Outcomes creed Akhlaq College Students at MTs Cukir Mu\u27alimat Jombang

Fractional Hamiltonian analysis of higher order derivatives systems

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives.Comment: 13 page

Gauge independent Hamiltonian reduction of constrained systems

A gauge independent method of obtaining the reduced space constrained dynamics is discussed in a purely Hamiltonian formalism. Three examples are studied

Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.Comment: 10 page

Fractional Hamilton formalism within Caputo's derivative

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange formulations lead to the same set of equations.Comment: 8 page

Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.Comment: 9 page

A Scaling Method and its Applications to Problems in Fractional Dimensional Space

A scaling method is proposed to find (1) the volume and the surface area of a generalized hypersphere in a fractional dimensional space and (2) the solid angle at a point for the same space. It is demonstrated that the total dimension of the fractional space can be obtained by summing the dimension of the fractional line element along each axis. The regularization condition is defined for functions depending on more than one variable. This condition is applied (1) to find a closed form expression for the fractional Gaussian integral, (2) to establish a relationship between a fractional dimensional space and a fractional integral, (3) to develop the Bochner theorem, and (4) to obtain an expression for the fractional integral of the Mittag–Leffler function. Some possible extensions of this work are also discussed

Solutions of a particle with fractional δ\delta-potential in a fractional dimensional space

A Fourier transformation in a fractional dimensional space of order \la (0<\la\leq 1) is defined to solve the Schr\"odinger equation with Riesz fractional derivatives of order \a. This new method is applied for a particle in a fractional $\delta$-potential well defined by V(x) =- \gamma\delta^{\la}(x), where $\gamma>0$ and \delta^{\la}(x) is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if 0< \la<\a. The results for \la= 1 and \a=2 are in exact agreement with those presented in the standard quantum mechanics