The dual boundary element method is formulated for the analysis of linear elastic cracked plates. The dual boundary integral equations of the method are the displacement and the traction equations. When these equations are simultaneously applied along the crack boundaries, general crack problems can be solved in a single-region formulation, with both crack boundaries discretized with discontinuous boundary elements. The stress intensity factors evaluation is carried out by the J-integral decomposition method which is applied on a circular path, defined around each crack tip. Examples of geometries with edge, and embedded cracks are analyzed. The accuracy and efficiency of the dual boundary element method and the J-integral make the present formulation ideal for the study of cracked plates.

Several numerical methods have been emerged to analyze the engineering problems. Boundary Element Method (BEM) is an important method for solving the partial differential equation in engineering problems. The Poison equation is an applicable equation in various engineering problems. General solution of this equation is obtained based on BEM by definition of the two integrals on the domain boundaries, and one integral in the internal domain which is a drawback for this method. To remove this disadvantage, Dual Reciprocity Method (DRM) is suggested. For example, in analysis of the welding heat transfer problems in transient zone where not homogeneous part is involved time dependent terms, is solved by this method. The calculation of the welding zone temperature history is a significant step for the thermal loading and residual stress analysis of the process.In this work, welding temperature history is obtained using the DRM. The Method and its theory are explained. Then, the code validation is carried out by common heat transfer problems. The welding temperature history is studied for a specific case by the created code. Because of the method simplicity and low time and error in computation process, the application of DRM is recommended.

In the present work, the dual reciprocity boundary element method along with sequential function specification method is used for solution of inverse heat conduction problems involving time and space varying heat flux estimation. A new version of the sequential specification method based on using polynomial fit is presented, which shows reduction in sensitivity of the solution to thermocouple locations. The results demonstrate that the method is accurate enough in cases which the amplitude of the errors is up to 2% of the maximum measured temperature. This study illustrate that, the optimum number of future time steps depends on error amplitude.

In this paper, we study the categorical and algebraic properties, such as limits and colimits of the category Pos-S with respect to order dense embeddings. Injectivity with respect to this class of monomorphisms has been studied by the author and used to obtain information about injectivity relative to regular monomorphisms. Then, we study three di erent kinds of essentiality, usually used in literature, with respect to the class of all order dense embed-dings of S-posets, and investigate their relations to order dense injectivity. We will see, among other things, that although all of these essential extensions are not necessarily equivalent, they behave equivalently with respect to order dense injectivity. More precisely, it is proved that order dense injectivity well behaves regarding these essentialities. Finally, a characterization of these essentialities over pogroups is given.

In this article, we present the concept of an N −ideal within the structure of an Almost Distributive Lattice (ADL). We demonstrate that the collection of N −ideals constitutes a distributive lattice, which is distinct from and not a sublattice of the lattice of ideals in an ADL. Additionally, we define N −lets in ADLs. We derive the necessary and sufficient conditions for an ideal to be classified as an N −ideal using N −lets. Finally, we establish the conditions required for an ADL to achieve the property of being soft relatively complemented.

In this study, a new numerical method based on Dual Reciprocity Boundary Element Method (DRBEM) is presented to interpolate scattered data. For this purpose, water samples were taken from 120 wells in Nuq region, Rafsanjan, for salinity measurements. The proposed estimator was compared with respect to its precision with the conventional ones, i.e., ordinary kriging and inverse distance weighting (IDW) while the spatial mapping of ground water salinity was performed in the study area. Besides, a more revealing measure of performance was obtained by computing the mean rank of each interpolation method. Results revealed the superiority of DRBEM over the kriging and IDW methods due to its lower root mean square error (RMSE) and relative root mean square error (RMSE%) as well as its higher goodness of prediction index (G). It was also found that DRBEM is the most accurate one when the mean rank and standard deviations of the ranks are used to avoid the outlier effects in assessing the prediction performance of the three methods. Nevertheless, further research is required before DRBEM could be properly combined with ancillary variables to improve the interpolation performance and to develop a user-friendly algorithm that can be implemented in a GIS package.

Background: Laser Interstitial Thermo Therapy (LITT) is a minimally invasive surgical method to treat tumors in liver. Modeling laser effects on tissue in LITT has many advantages over other heat monitoring methods such as studying light and heat transfer in tissue, changing the effective parameters of the laser and lower cost. Among different numerical methods, Dual Reciprocity Boundary Element Method (DRBEM) is the newest method used by researchers to solve problems of heat transfer in tissue.Material and Methods: In this study the temperature increase in liver tissue is analyzed with DRBEM. Monte Carlo method with variable step size and implicit capture technique is used for light transport in tissue. The result of the DRBEM is also compared with Finite Element Method (FEM) results.Results: The results showed that both methods converge to similar results and the differences in temperatures are less than 1oC. Due to one dimension decrease of the problem in DRBEM, the solving time increases comparing with other numerical methods like FEM.Conclusion: DRBEM is an accurate and fast method to study heat transfer in biological tissue in laser-tissue interaction.

Let M and P be right R-modules. A submodule K of an R-module M is called P-dense if for each m Î M; (K: m) is a P-faithful right ideal of R: PR is nonsingular if and only if, for each R-module M; every essential submodule of M is a P-dense submodule. For any R-module M, we obtain P-rational extention of M and equivalent condition in order that M is equal with its P-rational extention is found. An R-module P is called right Kasch if every simple R-module can be embedded in P: Finally, we given some equivalent conditions for an R-module P to be right Kasch.

The submodules with the property of the title (a submodule N of an R -module M is called strongly dense in M, denoted by N£sd M, if for any index set I, ΠIN£d ΠIM) are introduced and fully investigated. It is shown that for each submoduleN of M there exists the smallest subsetD′ ÍM such that N+D′ is a strongly dense submodule of M and D′ ∩ N=0. We also introduce a class of modules in which the two concepts of strong essentiality and strong density coincide. It is also shown that for any module M, dense submodules in M are strongly dense if and only if M £sd ~E (M), where ~E (M) is the rational hull of M. It is proved that R has no strongly dense left ideal if and only if no nonzeroelement of every cyclic R -module M has a strongly dense annihilator in R. Finally, some properties and new concepts related to strong density are studied.