Method

Dai Yan-wei

This text is through introducing the daily operation method of several kinds of operators for example: Direct method , function method , parameter differentiation method, integral transformations method , undetermined operator method , representation method.

Aidan Strathearn

Bart Vandewoestyne, Hongmei Chi, Michael Mascagni +1 more

Quasi-Monte Carlo (QMC) methods are now widely used in scientific computation, especially in estimating integrals over multidimensional domains and in many different financial computations. The use of randomized QMC methods, where randomness can be brought to bear on quasirandom sequences through scrambling and other related randomization techniques, brings more wide applications for QMC. However, the integration variance can depend strongly on the scrambling methods. Much of the work dealing with scrambling methods has been aimed at ways of linear scrambling methods. In this paper, we take a close look at the quadratic scrambling method for Faure sequences and compare with other linear scrambling methods. We will investigate the implementation and the performance of nonlinear scrambling methods for Faure sequences. The scrambling methods will focus on quadratic and inversive scrambling. We will compare those nonlinear scrambling methods with linear scrambling methods by a set of test-integral functions. Pseudorandom number generation by nonlinear methods will be expensive when their moduli are large. In our case, the modulus is relatively small. To the best of our knowledge, such a comparison has never been done before.

Adam Iaizzi

Pierre Bouillot

Farrin Payandeh, T. Mohammadpour

In this paper, pursuing a new advised method called Delta method which is basically similar to variational method, we find the ground and excited states, according to a typical quantum Hamiltonian. Moreover, applying this method, the upper bound values for the eigenenergies of the so-called ground and excited states are estimated. We will show that this new method, is as beneficial as the traditional variational method which is common in deriving eigenenergies of some of the quantum Hamiltonians. This method helps physics students to broaden their knowledge about the possible mathematical ways; they can use to obtain eigenenergies of some quantum Hamiltonians. The advantage of Delta method to variational method is in its simplicity and reduction of the calculation procedures.