<Para ID="Par1">In this paper, we investigate the optimal control problems governed by elliptic equations with integral constraint for state variable in one dimension by Legendre–Galerkin spectral methods. We deduce optimal conditions of the optimal control problems. Meanwhile, we obtain an a priori error...</para>

We present the Phillips curve in Australia in the frequency domain and document an evolving pattern in its slope at low frequencies under different monetary policy regimes and labor market regulations. The RBA adopted monetary targeting in 1976 and inflation targeting in 1993. There were...

In this paper, we are concerned with centered Markov Additive Processes {(Xt,Yt)}t∈T where the driving Markov process {Xt}t∈T has a finite state space. Under suitable conditions, we provide a local limit theorem for the density of the absolutely continuous part of the probability...

The Kadomtsev–Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two-dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and classified. Those soliton solutions are localized along...

The nature of the dynamics of opinion formation or zero-temperature Ising models modeled as a decision-by-majority process in complex networks is investigated using eigenmode analysis. The Hamiltonian of the system is defined and estimated by eigenvectors of the adjacency matrix constructed from...

We develop a Fourier–Galerkin spectral technique for computing the stationary solutions of 2D generalized wave equations. To this end a special complete orthonormal system of functions in L2(−∞,∞) is used for which product formula is available. The exponential rate of convergence is...

Functional integrals constitute a powerful tool in the investigation of financial models. In the recent econophysics literature, this technique was successfully used for the pricing of a number of derivative securities. In the present contribution, we introduce this approach to the field of...