In this paper, the homotopy perturbation method is applied to solve inverse problem of finding an unknown source term in a parabolic equation. In this method, the solution is found in the form of a convergent series. The terms of the series can be computed easily. To illustrate the method, three examples are presented. The results show the simplicity and efficiency of the method.

This paper demonstrates the effect of independent noise in principal components of k normally distributed random variables defined by a population covariance matrix. We prove that the principal components determined by a joint distribution of the original sample affected by noise can be essentially different in comparison with those determined from the original sample. However when the differences between the eigenvalues of the population covariance matrix are sufficiently large compared to the level of the noise, the effect of noise in principal components proved to be negligible. We support the theoretical results by using simulation study and examples. We also compare the results about the eigenvalues and eigenvectors in the two dimensional case with other models examined before. This theory can be applied in any field for the decomposition of the time series in multivariate analysis.

The aim of the present paper is to establish a fixed point theorem in Quasi Semi 2- Metric Spaces introducing Ф - contraction.

In this paper, we study the flow shop scheduling problem with increasing and decreasing linear deterioration on weighted dominant machines and also deal with some special case of general, no-wait permutation flow shop scheduling problem, respectively. Special cases mean that the machines form an increasing series of dominant machines, and decreasing series of dominant machines. The objectives are to minimize one of the two regular performance criteria, namely, makespan, total completion time and weighted completion time. This objective is considered under following dominant machine constraint: idm and ddm are considered. Numerical examples of the solution approaches are provided.

This paper is focused on the application of Linear Programming (LP) in combination with a Geographic Information System (GIS) in planning agricultural land-use strategies. A recent study described the advantages that could be achieved by combining LP models with geographical information systems (GIS) in the context of land-use planning. The integration of these two technologies follows approach: (1) a GIS is utilized to assemble data for the aggregate land-use alternatives; (2) the data are used as input to an LP model which determines the optimal land-use pattern as measured by the selected objective function and subject to all requisite constraints.