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.

In solar-thermal adsorption/desorption processes, it is not always possible to preserve equal operating times for the adsorption/desorption modes due to the fluctuating supply nature of the source which largely affects the system’s operating conditions. This paper seeks to examine the impact of adopting unequal adsorption/desorption times on the entire cooling performance of solar adsorption systems. A cooling system with silica gel–water as adsorbent-adsorbate pair has been built and tested under the climatic condition of Iraq. A mathematical model has been established to predict the system performance, and the results are successfully validated via the experimental findings. The results show that, the system can be operational

Iraqi bentonite is used as main material for preparing ceramic samples with the additions of alumina and magnesia. X-ray diffractions analyses were carried out for the raw material at room temperature. The sequence of mineral phase's transformations of the bentonite for temperatures 1000 ,1100 ,1200 and 1250 ºC reflects that it finally transformed in to mullite 39.18% and cristobalite 62.82%. Samples of different weight constituent were prepared. The effect of its constitutional change reveals through its heat treatments at 1000,1100,1200,1250and 1300ºC .The samples of additions less than 15% of alumina and magnesia could not stand up to 1300ºC while the samples of addition more than 15% are stable .That is shown by analy

The problem with research lies in hiding the Hanbali approach in building long and short travel provisions, as well as hiding some provisions relating to short travel that are not provided for by the jurists of Hanbali (in their books).

The research aims to demonstrate the approach and standards on which they based the long and short travel provisions, as well as to reflect the provisions of some of the issues that are silent on long and short travel, with evidence and significance.

The research included a preface and two researches, the researcher in the preface talked about the reality of long and short travel, in the first research on the approach of ha

In order to study the effect of inoculation with mycorrhiza and fertilization with plant residues on the growth of plants, we used two factors: the first two levels of mycorrhiza inoculation, Glumus mossea (0 and 10 g.pot^-1) and the second factor, four levels of plant residues (10 g.pot^-1) celery plant residues, 10 g pot^-1 mint residues, and 10 g pot^-1 black bean seed residues. Mychorrizal treatment (10 g pot^-1) increased the number of mycorrhiza spores and the infection percentage of mycorrhizal by 917.44% and 13088.23%, respectively; celery treatment (10 g.pot^-1) increased the chlorophyll index in the leaves and height of the chard plant by 31.34% and 94.04%, re

The synthesis and characterisation of new macrocyclic binuclear metal(II) complexes derived from dithiocarbamate (DTC) ligand are reported. The reaction of a bis-secondary amine, CS2 and KOH resulted in the formation of the free ligand. Two approaches were implemented to synthesis the macrocyclic bis(dithiocarbamate) complexes; (i) from the reaction of the free ligand with a metal ion, and (ii) via a one-pot reaction. In the free ligand approach, complexes were obtained by the reaction of dithiocarbamate salt with the metal ions; CoII, ZnII and CdII. However, the one-pot reaction is based on the mixing of the bissecondary amine, CS2, KOH and metal(II) chloride. Physico-chemical analyses were implemented to characterise the ligand and its

The new polydentate Schiff-base oxime  (1E,1`E)-2hydroxy-3-((E)-(2-((E)-2hydrxy3-((E)-(hydroxyimino)methyl)-5-methylbenzyldeneamino)ethylimino)methyl)-5methylbenzaldehyde oxime H4L and its binuclear metal complexes with Mn(II), Fe(II), Co(II) and Cu(II) are reported. The reaction of 2,6 diformyl–4–methyl phenol with hydroxyl amine hydrochloride in mole ratios of 1:1 gave the precursor (E)-2-hydroxy-3((hydroxyimino)methyl)-5-methylbenzaldehyde. Condensation reaction of precursor with ethylenediamine in mole ratios of 2:1 gave the new N4O2 Schiff-base oxime ligand H4L. Upon complex formation, the ligand behaves as a tribasic hexadantate species.  The mode of bonding and overall geometry of the complexes were determi

The presented work shows a preliminary analytic method for estimation of load and pressure distributions on low speed wings with flow separation and wake rollup phenomena’s. A higher order vortex panel method is coupled with the numerical lifting line theory by means of iterative procedure including models of separation and wake rollup. The computer programs are written in FORTRAN which are stable and efficient.

      The capability of the present method is investigated through a number of test cases with different types of wing sections (NACA 0012 and GA(W)-1) for different aspect ratios and angles of attack, the results include the lift and drag curves, lift and pressure distributions along the wing s