Since 1970s, Lie algebras have played more important and extensive roles in nonlinear partial differential equations and theoretical physics than they did before. One of the most interesting examples is the birth of the theory of Hamiltonian operators in middle 1970s, which was a work of Gel’fand, Dikii and Dorfman (cf. [GDi1-2], [GDo]). The existence of certain Hamiltonian operators associated...

Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations (the system model is in a differential-algebraic equation form)....

Compatible Hamiltonian pairs play a crucial role in the structure theory of integrable systems. In this paper we consider the question of how much of the structure given by compatibility is bound to the situation of hamiltonian dynamic systems and how much of that can be transferred to a complete abstract situation where the algebraic structures under consideration are given by bilinear maps on...

We give a spinorial set of Hamiltonian variables for General Relativity in any dimension greater than 2. This approach involves a study of the algebraic properties of spinors in higher dimension, and of the elimination of second-class constraints from the Hamiltonian theory. In four dimensions, when restricted to the positive spin-bundle, these variables reduce to the standard Ashtekar variable...

We present a formal development of the tensorial rotational Hamiltonian using symbolic calculations. Algebraic manipulations thanks to open-source Maxima software allow us get expressions use for various molecular spectroscopy problems. first some simple applications so-called semi-classical approach that allows study level structures in energy spectrum. Then, we perform comparisons between and...

We give a spinorial set of Hamiltonian variables for General Relativity in any dimension greater than 2. This approach involves a study of the algebraic properties of spinors in higher dimension, and of the elimination of second-class constraints from the Hamiltonian theory. In four dimensions, when restricted to the positive spin-bundle, these variables reduce to the standard Ashtekar variable...

in this research we work with the effective hamiltonian and the quark model. we investigate the decay rates of matter-antimatter of quark. we describe the effective hamiltonian theory and apply this theory to the calculation of current-current ( ), qcd penguin ( ), magnetic dipole ( ) and electroweak penguin ( ) decay rates. the gluonic penguin structure of hadronic decays is studied through th...

The algebraic and the canonical approaches to the quantization of a class of classical symplectic dynamical systems on the two-torus are presented in a simple unified framework. This allows for ready comparison between the two very different approaches and is well adapted to the study of the semi-classical behaviour of the resulting models. Ergodic translations and skew translations, as well as...

Using the U(2) Lie algebraic approach, it is determined that vibrational energies of aluminumdihydride (AlH2) molecule up to fifth overtone and reported combinational bands third harmonic.In this parameters operators are used represent Hamiltonian operator calculate energies.

We consider linear Hamiltonian equations in R2n of the following typedγdt(t)=J2nA(t)γ(t),γ(0)∈Sp(2n,R), where J=J2n=def[0Idn−Idn0] and A:t↦A(t) is a C1 curve space 2n×2n real matrices which are symmetric. Then, t↦γ(t) C2 (real) symplectic matrices. obtain second order asymptotics for eigenvalues bifurcated from non-real Krein indefinite with algebraic multiplicity two geometric one. As corollar...