In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).

    The current study presents the cellar spiders genus Nita Huber & El-Hennawy, 2007 (Araneae, Pholcidae) as the first record for Iraq spider fauna, this genus represented by the species Nita elsaff Huber & El-Hennawy, 2007 were identified based on morphological characteristics and DNA sequence data. A short morphological description is also presented for cellar spiders listed in Iraq; including this species in addition to Artema Atlanta Walckenaer, 1837.

In this work the radioactive wastes in the Old Russian
Cemetery Al -Tuwaitha site were classified according to risks for
workers who are involved in the retrieval process. The exposure
assessment results expressed as estimates of radionuclide intakes by
inhalation and ingestion, exposure rates and duration for external
exposure pathways, and committed effective dose equivalents to
individuals from all relevant radionuclides and pathways. Results
showed the presence of natural radionuclides Ra-226, Th-234 and K-
40, as well as the produced radionuclide Cs-137 and Eu-152 in the
cemetery wells. The absorbed doses from the waste were classified to
two categories; exempt waste and low level waste according to

The temperature control process of electric heating furnace (EHF) systems is a quite difficult and changeable task owing to non-linearity, time delay, time-varying parameters, and the harsh environment of the furnace. In this paper, a robust temperature control scheme for an EHF system is developed using an adaptive active disturbance rejection control (AADRC) technique with a continuous sliding-mode based component. First, a comprehensive dynamic model is established by using convection laws, in which the EHF systems can be characterized as an uncertain second order system. Second, an adaptive extended state observer (AESO) is utilized to estimate the states of the EHF system and total disturbances, in which the observer gains are updated

      In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

Background: For decades, the use of naturally accessible materials in treating human disease has been widespread. The goal of this study was to determine the anti-fungal effectiveness /of the lemongrass essential oil (LGEO) versus Candida albicans (C. albicans) adhesion to polymethylmethacrylate (PMMA) materials. Material and methods: LGEO's anti-fungal activity was tested against C. albicans adhesion using the following concentration of LGEO in PMMA monomer (2.5 vol. %, 5 vol. % LGEO) selected from the pilot study as the best two effective concentrations. A total of 40 specimens were fabricated for the candida adherence test and were subdivided into four equal groups: negative control 0 vol. % addition, experimental with 2.5 vol. % and

Biologically active natural compounds are molecules produced by plants or plant-related microbes, such as endophytes. Many of these metabolites have a wide range of antimicrobial activities and other pharmaceutical properties. This study aimed to evaluate (in vitro) the antifungal activities of the secondary metabolites obtained from Paecilomyces sp. against the pathogenic fungus Rhizoctonia solani. The endophytic fungus Paecilomyces was isolated from Moringa oleifera leaves and cultured on potato dextrose broth for the production of the fungal metabolites. The activity of Paecilomyces filtrate against the radial growth of Rhizoctonia solani was tested by mixing the filtrate with potato dextrose agar medium at concentrations of 15%,