In this paper, the scattering of a plane monochromatic electromagnetic wave from a nanowire with circular cross-section in the transverse electric (TE) mode is simulated using the well-known Stratton-Chu surface INTEGRAL equations. For an ordinary dielectric nanowire the refraction phenomenon is nicely simulated. In the case of a plasmonic nanowire no sign of surface plasmon excitation and propagation is seen. Transition from electrostatic regime to the geometrical shadow through diffraction regime by decreasing the light wavelength is also observable.

A method is presented to reduce the singular Lippmann-Schwinger INTEGRAL equation to a simple matrix equation. This method is applied to calculate the matrix elements of the reaction and transition operators, respectively, on the real axis and on the complex plane. The phase shifts and the differential scattering amplitudes are computable as well as the differential cross sections if the R- and/or T-matrix elements on the energy-shell are known. The method is applicable by using the Gaussian quadratures based on the Legenre, Laguer Chebyshev and shifted Chebyshev polynomials. Choosing the nodal points and weight functions depends on the aspects of the problem.

To investigate, understanding and predicting dynamic fracture behavior of a cracked body, dynamic stress intensity factors (DSIFs) are important parameters. In the present work INTERACTION INTEGRAL method is presented to compute static and dynamic stress intensity factors for three-dimensional cracks contained in the functionally graded materials (FGMs), and is implemented in conjunction with the finite element method (FEM). By a suitable definition of the auxiliary fields, the INTERACTION INTEGRAL method which is not related to derivatives of material properties can be obtained. For the sake of comparison, center, edge and elliptical cracks in homogeneous and functionally graded materials under static and dynamic loading are considered. Then material gradation is introduced in an exponential form in the two directions in and normal to the crack plane. Then the influence of the graded modulus of elasticity on static and dynamic stress intensity factors is investigated. It has been shown that, material gradation has considerable reduce influence on DSIFs of functionally graded material in comparison with homogenous material. While, static stress intensity factors can decrease or increase, depend on the direction of gradation material property.

The matching polynomial of a graph has coefficients that give the number of matchings in the graph. In this paper, we determine all connected graphs on eight vertices whose matching polynomials have only integer zeros. A graph is matching INTEGRAL if the zeros of its matching polynomial are all integers. We show that there are exactly two matching INTEGRAL graphs on eight vertices.

In this paper we specify the class of INTEGRAL circulant graphs ICG(n; D), which can be characterized by their order n and the set D of positive divisors of n in such a way that they have the vertex set Zn and the edge set (Formola). This group of graphs is called BMM graphs because of the form of its set of edges. A bipartite G graph is a graph whose vertex set can be divided into two subsets X, and Y such that no two vertices in X and no two vertices in Y are adjacent. The duplicate graph is called complete if each vertex in X is connected to all vertices in Y. This graph is represented by K_ (m, n), if | X | = m and | Y | = n. Multipartite graphs are also defined as bipartite graphs.

It is about 30 years that Helicopter electromagnetic (HEM) surveys are being used for rapid mineral and ground water exploration, environmental investigations and also geological mapping in extensive areas. Despite this, one of the most important problems in using obtained data from the surveys is accurate interpretation of the data. Otherwise, there will be no beneficial results while spending high costs. Thus the interpretation of the data is as old as the surveys. Several experts have tried to improve the interpretation of HEM data and they have achieved great successes. Almost the results of all these surveys are presented as resistivity (or conductivity)-depth sections. To reach this target, the first step is to solve the electromagnetic induction INTEGRAL equation. As solving this INTEGRAL is not possible using analytical methods, several numerical methods such as Laplace transformation, Hankel transformation and Jacobi-Matrix methods have been suggested for the solution of the INTEGRAL, and different approaches have been presented with each method by various authorities. One of the most important solution methods is fast Hankel transformation. In this paper, it is attempted to use this method for finally obtaining resistivity-depth sections. For solving the induction equation by this method, we need the kernel function of the INTEGRAL and weighting coefficients that replace the Bessel function in the INTEGRAL. For this, first we use the Guptasarma-Singh method. Then results of this method are corrected and evaluated. Then, these results will be analyzed and tested with two synthetic models in addition to presenting the results of inverse modeling. Finally, by adding new parameter named a0 to induction equation, we will clearly see an improvement in the results of inverse modeling. Meanwhile, the problem of singularity that occurs at high frequencies is almost removed.

In the paper we consider a generalized join operation, that is, the H-join on graphs where H is an arbitrary graph. In terms of Seidel matrix of graphs we determine the Seidel spectrum of the graphs obtained by this operation on regular graphs. Some additional consequences regarding S-INTEGRAL complete split graphs are also obtained, which allows to exhibit many infinite families of Seidel INTEGRAL complete split graphs.

We study a fuzzy type INTEGRAL for measurable multifunctions with respect to a fuzzy measure. Some classical properties and convergence theorems are presented.