A general method for obtaining minimal interatomic distance in molecule conformation problems is introduced. The method can be applied to a wide family of potential energy functions having reasonable properties. Using this method new lower bounds for the minimal inter-particle distance for the optimal Lennard-Jones and Morse potential functions are derived which are independent from the number ...

In this paper, the numerical solution methods of one- particale, one – dimensional time- independentSchrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function V(x). These methods included the FEM(Finite Element Method), Cooly, Numerov and others. Here we considered the Numerov method inmore details...

Scientific data is becoming increasingly complex, and sophisticated techniques are required for its effective analysis and visualization. The Morse-Smale complex is an efficient data structure that represents the complete gradient flow behavior of a scalar function, and can be used to identify, order, and selectively remove features. This dissertation presents two algorithms for constructing Mo...

Morse decompositions have been proposed to compute and represent the topological structure of steady vector fields. Compared to the conventional differential topology, Morse decomposition and the resulting Morse Connection Graph (MCG) is numerically stable. However, the granularity of the original Morse decomposition is constrained by the resolution of the underlying spatial discretization, whi...

Morse decompositions have been proposed to compute and represent the topological structure of steady vector fields. Compared to the conventional differential topology, Morse decomposition and the resulting Morse Connection Graph (MCG) is numerically stable. However, the granularity of the original Morse decomposition is constrained by the resolution of the underlying spatial discretization, whi...

The Morse code is an international communication language that is simple, speedy, and low cost. The automatic recognition of Morse code is difficult because maintaining a stable typing rate is not easy. In this paper, a suitable adaptive automatic recognition method, the variable degree variable step size Least-Mean-Square algorithm, is provided and its procedure is divided into three modules: ...

The Nikiforov-Uvarov method is employed to calculate the Schrödinger equation with a rotation Morse potential. The bound state energy eigenvalues and the corresponding eigenfunction are obtained. All of these calculations present an effective and clear method under a Pekeris approximation to solve a rotation Morse model. Meanwhile the results got here are in a good agreement with ones before. P...

Ikegami and Saeki have proved that the cobordism group of Morse functions on oriented surfaces is an infinite cyclic group. Their method is applicable with a little modification to the computation of the cobordism group of Morse functions on unoriented surfaces. We prove that this group is isomorphic to the direct sum of the infinite cyclic group and the finite group of order two.

in this paper, the numerical solution methods of one- particale, one – dimensional time- independentschrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function v(x). these methods included the fem(finite element method), cooly, numerov and others. here we considered the numerov method inmore details...