The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see [10, 11]), and studdied for example in [5] and [12]. In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this concept to covariant derivation on tangent BUNDLEs and vector BUNDLEs, and find natural relations between them and other familiar concepts. Also in SPINOR BUNDLEs, we introduce a covariant derivation along multivector fields and call it the Clifford covariant derivation of that SPINOR BUNDLE, which is related to its structure and has a natural relation to its Dirac operator.

The Elko SPINOR field is a spin 1/2 fermionic quantum field with a mass dimension introduced as a candidate of dark matter. In this work, we study the localization of Elko fields on a de Sitter thick brane constructed by a canonical or phantom scalar field. By presenting the mass-independent potentials of Kaluza-Klein (KK) modes in the corresponding Schrö dinger equations, it is shown that the Elko SPINOR field with a five-dimensional mass term can be localized on de Sitter branes. Also, by using a Yukawa type coupling term, we find that the Elko SPINOR field can be localized on this brane with a particular coupling constant. Furthermore, it is shown that the zero mode of the Elko field is localized on the de Sitter brane through a Yukawa geometrical coupling term.

Background: Anterior cruciate ligament (ACL) tear is a common injury in sports. Different techniques for reconstruction of this ligament have been suggested. This paper compares the knee kinematics between "single BUNDLE" and "double BUNDLE" ACL reconstruction with hamstring tendon in a computerized knee model.Methods: A computer-knee modle was constructed. Then "single BUNDLE" and "double BUNDLE" ACL reconstruction was performed. The knee stability and ligament tension were tested in 3 different settings: 1) At 30o knee flexion under isolated posteroanterior load, valgus and rotational torque was applied, 2) In weight-bearing flexion range (from extension to 70o of flexion) an anterior load of 134 Newton was applied, 3) Knee model was loaded by a non-contact pivot farce to produce ACL rupture.Results: The results showed no significant difference between "single BUNDLE" and "double BUNDLE" under isolated loading. The second and third model, however, showed 4 times greater tension on the ligament in "single BUNDLE". The "single BUNDLE" in the second technique of testing (weight bearing) showed at most 7 mm more displacement compared with "double BUNDLE". In the third testing technique "double BUNDLE" was stronger than "single BUNDLE" in valgus torque resistance. The internal rotation stability was also more in "double BUNDLE".Conclusion: Functional stability of knee model of ACL reconstruction with a "double BUNDLE" graft is superior to a "single BUNDLE" graft.

One of the many important decisions organizations must make is project selection. Every project includes an initial plan to run, but not every plan can be implemented as a project. In situations where they lack resources or funds, all different plans must first be able to assess profitability in an accurate way, leading to the selection of a combination of proposals to carry out as projects. This paper provides a method to select the most effective set of proposals while considering the maximum use of available resources. Assessing efficiency is considered by a data envelopment analysis (DEA) model.Note that it is assumed that a vector of limited sources is at hand. This vector of resources can be contained human resource, budget, equipment, and facilities. Here, while reviewing some of the models in the selection project field, a common set of weight approach performance evaluation model for assessing the efficiency of the selected proposals is proposed. In this article it has tried to resolve the problems of former models.