The smoothed particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) are well-known and efficient mesh-less numerical methods widely used to investigate a wide range of complicated practical engineering problems. Recently, two modified Laplacian models [1, 2] have been proposed by using different efficient mathematical techniques, and the analogy between SPH and MPS methods. These two models exhibit significantly superior precision in comparison with several existing modified schemes [3-9] but still suffer from lower accuracy near calculation domain boundaries as they work with the conventional weight or interpolation functions. In this paper, the models were reformulated and further improved by replacing the weight functions with well-known moving least squares (MLS) shape functions without requiring dummy calculation nodes beyond boundaries. The proposed Laplacian models in this study could achieve very accurate results compared with the existing models [1, 2] for the solution of four different two-dimensional Poisson equations on irregular node distributions.

Many structural models such as grids, barrel vaults, trusses and frames with repetitive units, known as regular structures, have structural matrices in the form of M = F(B; A; BT ). In this paper, a simple and efficient method is presented for calculating the eigenvalues of the adjacency and Laplacian matrices of regular structures. These eigenvalues can be used in studying the combinatorial properties of these structures. Examples are included to show the accuracy of the presented approach.

The modelling of strategies for buying and selling in Stock Market Investment have been the object of numerous advances and uses in economic studies, both theoretically and empirically. One of the popular models in economic studies is applying the Semi-parametric Markov Switching models for forecasting the time series observations based on stock prices. The Semi-parametric Markov Switching models for these models are a class of popular methods that have been used extensively by researchers to increase the accuracy of fitting processes. The main part of these models is based on kernel and core functions. Despite of existence of many kernel and core functions that are capable in applications for forecasting the stock prices, there is a widely use of Gaussian kernel and exponential core function in these models. But there is a question if other types of kernel and core functions can be used in these models. This paper tries to introduce the other kernel and core functions can be offered for good fitting of the financial data. We first test three popular kernel and four core functions to find the best one and then offer the new strategy of buying and selling stocks by the best selection on these functions for real data.

The process in which response of soil influences the motion of foundation and vice-versa, is known as Soil-Foundation Interaction (SFI). This paper deals with the different types of soil-foundation interaction models useful for structural as well as geotechnical engineers and researchers for safe and economical raft design. The study offers a gist of all the models in literature and their applications. Several approaches for analysis which include analytical methods and numerical methods have been described here. Analytical models based on Winklerian and Continuum approach have been discussed. Moreover, modified forms of such approaches have also been discussed. In general, all the models make use of a parameter known as Modulus of Subgrade Reaction to model soil interaction. This parameter can be calculated either through experiments or empirical formulas. Different numerical methods have also been presented along with a few literatures. Further, some of the studies on raft foundation are also included.

The emphasis of this paper is the role of volatility indices on improvement Artificial Neural Networks (ANNs) forecasting models for the daily USD/EUR and USD/GBP exchange rates Two volatility indices are used. First; the realized volatility, which is based on intra-daily data, and second the GARCH volatility. They are applied into the model in two ways. Firstly, the lagged volatility index is added to the model. Secondly, some levels for the volatility are defined and the time series are partitioned according to the level of volatility, and then different models of exchange rate forecasting are built for each level of volatility. The forecasting results demonstrate that the models with low and middle volatility are not preferred to the model without volatility index. However, in case of high volatility, the level models improve forecasting power. This means that high volatility provides new information for foreign exchange market.

Let S(G) be the Seidel matrix of a graph G of order n and let DS(G) = diag(n 􀀀 1 􀀀 2d1; n 􀀀 1 􀀀 2d2; : : :; n 􀀀 1 􀀀 2dn) be the diagonal matrix with di denoting the degree of a vertex vi in G. The Seidel Laplacian matrix of G is defined as SL(G) = DS(G) 􀀀 S(G) and the Seidel signless Laplacian matrix as SL+(G) = DS(G) + S(G). The Seidel signless Laplacian energy ESL+(G) is defined as the sum of the absolute deviations of the eigenvalues of SL+(G) from their mean. In this paper, we establish the main properties of the eigenvalues of SL+(G) and of ESL+(G).