The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

This research aims to present a proposed model for disclosure and documentation when performing the audit according to the joint audit method by using the questions and principles of the collective intelligence system, which leads to improving and enhancing the efficiency of the joint audit, and thus enhancing the confidence of the parties concerned in the outputs of the audit process. As the research problem can be formulated through the following question: “Does the proposed model for disclosure of the role of the collective intelligence system contribute to improving joint auditing?”   

The proposed model is designed for the disclosure of joint auditing and the role

In recent years, the Global Navigation Satellite Services (GNSS) technology has been frequently employed for monitoring the Earth crust deformation and movement. Such applications necessitate high positional accuracy that can be achieved through processing GPS/GNSS data with scientific software such as BERENSE, GAMIT, and GIPSY-OSIS. Nevertheless, these scientific softwares are sophisticated and have not been published as free open source software. Therefore, this study has been conducted to evaluate an alternative solution, GNSS online processing services, which may obtain this privilege freely. In this study, eight years of GNSS raw data for TEHN station, which located in Iran, have been downloaded from UNAVCO website

The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition for a membership function to find near interior, near boundary and near exterior vertices. Moreover, proved results, examples and counter examples are provided. The Gm-closure structure which suggested in this paper opens up the way for applying rich amount of topological facts and methods in the process of granular computing.

In this work, a joint quadrature for numerical solution of the double integral is presented. This method is based on combining two rules of the same precision level to form a higher level of precision. Numerical results of the present method with a lower level of precision are presented and compared with those performed by the existing high-precision Gauss-Legendre five-point rule in two variables, which has the same functional evaluation. The efficiency of the proposed method is justified with numerical examples. From an application point of view, the determination of the center of gravity is a special consideration for the present scheme. Convergence analysis is demonstrated to validate the current method.

     The concept of separation axioms constitutes a key role in general topology and all generalized forms of topologies. The present authors continued the study of gpα-closed sets by utilizing this concept, new separation axioms, namely gpα-regular and gpα-normal spaces are studied and established their characterizations. Also, new spaces namely gpα-T_k  for k = 0, 1, 2 are studied.

Modeling the microclimate of a greenhouse located in Baghdad under its weather conditions to calculate the heating and cooling loads by computer simulation. Solar collectors with a V-corrugated absorber plate and an auxiliary heat source were used as a heating system. A rotary silica gel desiccant dehumidifier, a sensible heat exchanger, and an evaporative cooler were added to the collectors to form an open-cycle solar assisted desiccant cooling system. A dynamic model was adopted to predict the inside air and the soil surface temperatures of the greenhouse. These temperatures are used to predict the greenhouse heating and cooling loads through an energy balance method which takes into account the soil heat gain. This is not included in

     In this paper we prove that the planar self-assembling micelle system

 has no Liouvillian, polynomial and Darboux first integrals. Moreover, we show that the system

has only one irreducible Darboux polynomial  with the cofactor being   if and only if  via  the weight homogeneous polynomials and  only two irreducible exponential factors  and  with  cofactors    and   respectively with be the unique Darbox invariant of system.