In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov

This paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.

This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint

A group of acceptance sampling to testing the products was designed when the life time of an item follows a log-logistics distribution. The minimum number of groups (k) required for a given group size and acceptance number is determined when various values of Consumer’s Risk and test termination time are specified. All the results about these sampling plan and probability of acceptance were explained with tables.

Drip irrigation is one of the conservative irrigation techniques since it implies supplying water directly on the soil through the emitter; it can supply water and fertilizer directly into the root zone. An equation to estimate the wetted area in unsaturated soil is taking into calculating the water absorption by roots is simulated numerically using HYDRUS (2D/3D) software. In this paper, HYDRUS comprises analytical types of the estimate of different soil hydraulic properties. Used one soil type, sandy loam, with three types of crops; (corn, tomato, and sweet sorghum), different drip discharge, different initial soil moisture content was assumed, and different time durations. The relative error for the different hydrauli

This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

Simulation  of  the  Linguistic  Fuzzy Trust  Model  (LFTM)  over  oscillating  Wireless  Sensor Networks (WSNs) where the goodness of the servers belonging to them could change along the time is presented in this paper, and the comparison between the outcomes achieved with LFTM model over oscillating WSNs with the outcomes obtained by applying the model over static WSNs where the servers maintaining always the same goodness, in terms of the selection percentage of trustworthy servers (the accuracy of the model) and the average path length are also presented here. Also in this paper the comparison between the LFTM and the Bio-inspired Trust and Reputation Model for Wireless Sensor Network

Theoretical calculation of the electronic current at N 3 contact with TiO 2 solar cell devices ARTICLES YOU MAY BE INTERESTED IN Theoretical studies of electronic transition characteristics of senstizer molecule dye N3-SnO 2 semiconductor interface AIP Conference. Available from: https://www.researchgate.net/publication/362813854_Theoretical_calculation_of_the_electronic_current_at_N_3_contact_with_TiO_2_solar_cell_devices_ARTICLES_YOU_MAY_BE_INTERESTED_IN_Theoretical_studies_of_electronic_transition_characteristics_of_senstiz [accessed May 01 2023].

      In this article, we introduce a new type of soft spaces namely, soft  spaces as   a generalization of soft paces. Also, we study the weak forms of soft  spaces, namely, soft  spaces, soft  spaces, soft  space, and soft  spaces. The characterizations and fundamental properties related to these types of soft spaces and the relationships among them are also discussed.