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.

The new ligand [N1,N4-bis((1H-benzo[d]Glyoxalin-2-yl)carbamothioyl)Butanedi amide] (NCB) derived from Butanedioyl diisothiocyanate with 2-aminobenz imidazole was used to prepare a chain of new metal complexes of Cr(III), Mn(II), Co(II), Ni(II), Cu(II), Pd(II), Ag(I), Cd(II) by general formula [M(NCB)]Xn ,Where M= Cr(III), n=3, X=Cl; Mn(II), Co(II), Ni(II), Cu(II), Pd(II), Cd(II) ,n=2 , X=Cl; Ag(I), n=1, X=NO3. Characterized compounds on the basis of 1H, 13CNMR (for (NCB), FT-IR and U.V spectrum, melting point, molar conduct, %C, %H, %N and %S, the percentage of the metal in complexes %M, Magnetic susceptibility, thermal studies (TGA),while its corrosion inhibition for mild steel in Ca(OH)2 solution is studied by weight loss. These measureme

Finance is an essential element when developing any housing policy because of its role in providing funds to institutions concerned with housing lending. Therefore, the research aims to evaluate the financial aid provided by the Central Bank of Iraq in solving the housing crisis through the adoption of the Central Bank of Iraq initiatives to support the financing of the housing sector, and here The importance of the research is highlighted to determine the role of the initiative by drawing an effective strategy aimed at providing the housing sector with the necessary funding. By providing financing to financial institutions directed towards providing real estate credit, and that the percentage of the contribution of the implement

Mechanical and thermal properties of composites, consisted of unsaturated polyester resin, reinforced by different kinds of natural materials (Orange peels and Date seeds) and industrial materials (carbon and silica) with particle size 98 µm were studied. Various weight ratios, 5, 10, and 15 wt. % of natural and industrial materials have been infused into polyester. Tensile, three-point bending and thermal conductivity tests were conducted for the unfilled polyester, natural and industrial composite to identify the weight ratio effect on the properties of materials. The results indicated that when the weight ratio for polyester with date seeds increased from 10% to 15%, the maximum Young’s modulus decreased by 54%. When the weight rat

   The aim of this study is to investigate the kinetics of copper removal from aqueous solutions using an electromembrane extraction (EME) system. To achieve this, a unique electrochemical cell design was adopted comprising two glass chambers, a supported liquid membrane (SLM), a graphite anode, and a stainless-steel cathode. The SLM consisted of a polypropylene flat membrane infused with 1-octanol as a solvent and bis(2-ethylhexyl) phosphate (DEHP) as a carrier. The impact of various factors on the kinetics constant rate was outlined, including the applied voltage, initial pH of the donor phase solution, and initial copper concentration. The results demonstrated a significant influence of the applied voltage on enhancing the rate of c

This paper studied the behaviour of reinforced reactive powder concrete (RPC) two-way slabs under static load. The experimental program included testing three simply supported slabs of 1000 mm length, 1000 mm width, and 70 mm thickness. Tested specimens were of identical properties except their steel fibers volume ratio (0.5 %, 1 %, and 1.5 %). Static test results revealed that, increasing steel fibers volume ratio from 0.5% to 1% and from 1% to 1.5%, led to an increase in: first crack load by (32.2 % and 52.3 %), ultimate load by (36.1 % and 17.0 %), ultimate deflection by (33.6 % and 3.4 %), absorbed energy by (128 % and 20.2 %), and the ultimate strain by (1.1 % and 6.73 %). The stiffness and ductility of the specimens also increased. A

In this paper, Nordhaus-Gaddum type relations on open support independence number of some derived graphs of path related graphs under addition and multiplication are studied.

This paper aims to study the effects of the long term solar activity on the critical frequencies of ionospheric F1 layer over Baghdad city, during the solar cycle 22, within (1988- 1995). It is found that the critical frequency of this layer is closely related to the sunspots number during the years of the solar cycle 22, at a middle latitude region of the world. The study discussed the effect of sunspot numbers and solar events on the electron densities of F1 layer, which is the most important ionospheric parameter.