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.

To assesse the iron and silicon effects on the yield and physiological characteristics of green pea, Wando cultivar by ASGrow Corporation was used in three levels of iron chelate (0.05, 0.1 and 0.3 gr per l-1) and silicon (0, 14 and 28 mg per l-1), as a factorial experimental in completely randomized design with three replications. In this experiment, characterisics such as fresh and dry weight of grain, the number of grain per pod, concentration of Fe, Cu, Mn, Zn and Si in leaf and grain were measured. Results showed that the INTERACTION of Fe and Si was significant at p<0.01 on grain fresh and dry wigeht, concentratin of leaf and grain Fe, leaf Mn, leaf and grain Zn and leaf Si and the application of Fe and Si was significant separately, on other traits such as number of grain per pod, concentration of leaf and grain Cu, Mn and Si in grain.  The Mean squares showed that the application of Fe and Si significantly increased fresh and dry grain weight and Si laef concetration and decreased the concentratin of leaf and grain Fe and Mn as well as grain Mn.  The enhancement of Fe and Si application separately decreased the concentration of Mn, Cu and zinc leaf and grains, but the Si concentration of leaf and grain were increased by Si application. The concentration of Fe, Mn, Cu and Zn were decreased in leaf and grain because of antagonistic effects. It can be concluded that Si reduces the harmfull effects of high levels of iron toxicity and the application of 0.1 g/l and 25 mg/l can be recommended as the best treatments.

In this research paper, we introduce a new transform belonging to the class of Laplace transforms, called the Yasser-Jassim Transform (YJ Transform). We explore its properties and compare it to the classical Laplace transform. Furthermore, we provide proofs for the key properties associated with this transform and demonstrate its application in solving differential and INTEGRAL equations. By employing this new transform, we can reduce the original problem to an algebraic equation that can be solved directly, followed by applying the inverse transform to obtain the solution to the original problem.

This article investigates the problem of simultaneous attitude and vibration control of a flexible spacecraft to perform high precision attitude maneuvers and reduce vibrations caused by the flexible panel excitations in the presence of external disturbances, system uncertainties, and actuator faults. Adaptive INTEGRAL sliding mode control is used in conjunction with an attitude actuator fault iterative learning observer (based on sliding mode) to develop an active fault tolerant algorithm considering rigid-flexible body dynamic INTERACTIONs. The discontinuous structure of fault-tolerant control led to discontinuous commands in the control signal, resulting in chattering. This issue was resolved by introducing an adaptive rule for the sliding surface. Furthermore, the utilization of the sign function in the iterative learning observer for estimating actuator faults has not only enhanced its robustness to external disturbances through a straightforward design, but has also led to a decrease in computing workload. The strain rate feedback control algorithm has been employed with the use of piezoelectric sensor/actuator patches to minimize residual vibrations caused by rigid-flexible body dynamic INTERACTIONs and the effect of attitude actuator faults. Lyapunov's law ensures finite-time overall system stability even with fully coupled rigid-flexible nonlinear dynamics. Numerical simulations demonstrate the performance and advantages of the proposed system compared to other conventional approaches.

Weighted INTEGRAL inequalities for general INTEGRAL operators on monotone positive functions with parameters $p$ and $q$ are established in [4]. The aim of this work is to extend the results to different cases of these parameters, in particular for negative $p$ and $q$. We give some new lemmas which will be frequently used in the proofs of the main theorems.