This paper studies impulsive dynamic Sturm-Liouville boundary value problems. The existence of a countably infinite set of eigenvalues and Eigenfunctions is proved and a uniformly convergent expansion formula in the Eigenfunctions is established.

An axisymmetric cup-cored coil placed above a layered conductive half-space is analyzed by using the truncated region Eigenfunction expansion method. Closed-form expressions are presented for the coil impedance as well as the induced eddy current density. The results are in very good agreement with results from 2D-FEM and with experimental ones.

Radial basis functions (RBFs) are a powerful method for obtaining the numerical solution of high-dimensional problems. They are often referred to as a meshfree method and the spectrally accurate can be achieved by them. In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the Eigenfunction expansion. We develop our approach in two-dimensional spaces for solving Helmholtz equations. In this paper, the Eigenfunction expansions are rebuilt based on Chebyshev polynomials which are more suitable in numerical computations. Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed method for solving two-dimensional Helmholtz equations.

Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ principal component analysis, allowing finite dimensional analysis of the problem. The authors gave stochastic expansions of estimators eigenvalues and Eigenfunctions, providing not only a new understanding of the effects of truncating to a finite number of principal components, but also pointing to new methodology, such as simultaneous and individual bootstrap confidence statements for eigenvalues and Eigenfunctions. The expansions explicitly include terms of sizes n-1/2, n-1, and a remainder of order n-3/2, where n denotes sample size. The terms of size n-1/2 are related to limit theory. Because for many situations, the exact statistical properties of the eigenvalues and Eigenfunctions estimators are not directly obtainable, the way by which we can approximate their distributions is of interest in practice. In this paper, we discuss asymptotic results for eigenvalues and Eigenfunctions. The work shows that eigenvalue spacings have only a second-order effect on properties of eigenvalue estimators, but a first-order effect on properties of Eigenfunction estimators.

Purpose: The aim of this research was to study the effects of different doses of LIF on GVBD and MII development rate and cumulus expansion.Materials and Methods: Immature mice superovulated with HMG and GV oocytes obtained from ovary 48 hours later. The GV oocytes were cultured in TCM199 with 100, 500 and 1000 IU /ml LIF. Cumulus expansions were evaluated with two examiners and numbers of MII oocytes were recorded. For denuding the oocytes hyaloronidase was used.Results: Our results showed that the rate of GVBD and MII development increased in groups with LIF compared with control group. Rate of MII development with 1000 IU/ml LIF was significantly higherthan that of control group (P<0.05). Cumulus expansion in group with 1000 IU/ml LIF improved significantly compared with control group (p<0.05).Conclusion: Our results showed that LIF could improve IVM rate in dose dependant. Also cumulus expansion improved in group with LIF and increased oocyte quality.

The significance of multiple porous structures with finite spacing upon elevated seabed in the presence and absence of the leeward wall is examined under oblique wave impinging. Fluid propagation is assumed over the impermeable elevated bottom, and the fluid realm is separated into open water and porous structure regions. Continuity of the dynamic pressure and mass fluxes at the interfaces of the porous structure and the open water regions are adopted. The resistance and reactance due to the presence of the porous structure are taken into account using the porous structure dispersion relation. The numerical model is developed based on the Eigenfunction expansion method along with matched velocity potentials at the interfaces of open water and the porous block regions. The wave reflection and transmission characteristics, energy damping and wave force impact on the leeward wall is analysed. The significance of the porosity, structural width, angle of incidence, width between the two structures and water chamber length is studied considering multiple porous blocks with finite spacing under oblique wave impinging in the presence and absence of leeward wall. The numerical results obtained in the present study agrees well with the theoretical and experimental results available in the literature. The present study illustrates that, with the increase in the number of porous blocks and gap between the porous blocks, the resonating trend is observed in the wave transformation and the influence of the elevated step height is revealed for the wave trapping.

In this study, the dynamic response of a Timoshenko beam under moving mass is investigated. To this end, vectorial form orthogonality property of the Timoshenko beam free vibration modes is applied to the EEM (Eigenfunction expansion Method). The implication of the vectorial form series and an appropriate inner product of mode shapes in combination are focused for a beam with arbitrary boundary conditions. Consequently, significant simplifications and efficacy in the utilization of the EEM in eliminating the spatial domain is achieved. In order to comprise validation, the present study is compared with the DET (Discrete Element Technique) and the RKPM (Reproducing Kernel Particle Method).

Dynamic analysis of cracked thin rectangular plates subjected to a moving mass first is investigated in this paper. To this end, the Eigenfunction expansion method is utilized to solve the governing equation. For the first time, the intact plate orthogonal polynomials in combination with admissible crack functions as a composition, are employed in the Eigenfunction expansion method formulation, required professional computer programming to solve the equation. The proposed approach guarantees upper bound of the true solution, which is the property of an appropriate numerical solution. Parametric investigation is performed to determine the effect of the moving mass weight, the moving mass velocity, the crack length, and the crack angular orientation as well as the plate’s aspect ratio, on the dynamic response of cracked plates. The results confirm, that the moving mass has a greater impact than the moving load on the dynamic responses of cracked plates. Furthermore, there is nonlinear relation among enhancing the dynamic responses of the cracked plates with various boundary conditions, and magnifying the moving mass weights, elevating the moving mass velocities, lengthening the crack length, raising the inclined crack angels as well as augmenting the plates aspect ratios.

Purpose: Treatment of patients with class III malocclusion is one of the most challenging problems in orthodontic practice. This problem which causes functional and esthetic problems can result from prognathism of mandible or deficiency of nasomaxillary complex or a combination of both. It has been estimated that the incidence of this type of malocclusion in Iranian population is between 7.22- 19.5 percent. The importance of early identification and treatment of this malocclusion is significant. The aim of this study was to determine the cephalometric changes following combined use of rapid maxillary expansion and facemask therapy in class III malocclusion.Methods & Materials: In this quasi experimental prospective clinical trial, 15 Iranian patients (6 males and 9 females with a mean age of 8.6 years) were selected. They were first treated with rapid maxillary expansion for 14 days prior to facemask delivery. Then facemask therapy was initiated untill normal canines and molars relationship and a normal overjet were achieved. Cephalometric means (consist of 11 angular and 8 linear measure) before and after treatment was calculated and compared with paired t-test to determine significant differences.Results: Cephalometric analysis showed following changes:SNA=1.3±1.6, SNB=-0.5±1.6, ANB=1.7±2.3, Gonial Angle=-1.4±4.1, Articular Angle=-6±27.5, SNPog=-0.7±1.7, Inclination Angle=2.3±7.3, Y axis Angle=1.5±3.4, Mandibular Plan Angle=2.3±3.3, Occlusal Plan to SN=1±5.4, NSAr=0.8±2.3, PFH/AFH=0.8±1.9,N┴LFH to A=1.1mm±1.9, N┴LFH to Pog=1mm±4.6, Maxilla length=2.3mm±2.9, Mandible length=0.4mm±0.8, Overjet=3.8±2.7, Overbite=-0.8mm±1.5, Wit's appraisal=2.4±2.5.Conclusion: This result indicate that facemask and rapid maxillary expansion improve class III malocclusion by increase in maxillary growth in anterioposterior dimension and a slight limitation of mandibular growth.