This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
This work was conducted to determine the volumetric mass transfer coefficient (Ky.a) infixed bed adsorption using hexane-benzene mixture by adsorption onto a fixed bed of white silica gel. Benzene concentration was measured by gas chromatography. The effect of feed flow rate and initial concentration of benzene in hexane-benzene mixture on the volumetric mass transfer coefficient and on the adsorption capacity of silica gel was investigated.
In general, the volumetric mass transfer coefficient increases with increasing hexane flow rate, and with increasing initial concentration of benzene in the mixture. The ultimate value of (Ky.a) was at 53 ml/min of hexane flow rate with benzene initial concentration of (6.53 wt. %), and it wa
... Show MoreThe objective of the study was to predict crop coefficient (K) values for cucumber inside the greenhouse during the growing season 2014, using watermarks gypsum blocks and atmometer c apparatus during the growing stages and to compare the predicted values of the crop coefficient with different methods and approaches. The study was conducted in the greenhouses field within Al-Mahawil Township, 70 km south of Baghdad, Iraq. The watermarks soil water sensors and atmometer apparatus were used to measure crop evapotranspiration and reference evapotranspiration on daily basis, respectively. The comparison and the statistical analysis between the calculated K in this study and values obtained from greenhouse gave a good agreement. The root mean
... Show MoreThis research examines the use of time in Hebrew children's literature and how historical narratives about the biblical period and beyond formed an arena for narrative conflict between the 1960s and the mid-1980s. The research clarifies the nature of narrative time: the time of events within the story itself (the sequence of events، the rhythm، and the occasional shifts between past and present)، as well as the framing time، which is the historical period the narrator perceives as the backdrop to the narrative. It also explores the time of memory and the use of flashbacks، evocations، or temporal allusions that connect young readers to a collective past. Our research also addresses how Zionist narratives began to lose credibility afte
... Show MoreThis paper focuses on the most important element of scientific research: the research problem which is confined to the concept of concern or concern surrounding the researcher about any event or phenomenon or issue paper and need to be studied and addressed in order to find solutions for them, to influence the most scientific research steps from asking questions and formulating hypotheses, to employ suitable methods and tools to choose the research and sample community, to employ measurement and analysis tools. This problem calls for a great effort by the researcher intellectually or materially to develop solutions.
This paper introduces a relation between resultant and the Jacobian determinant
by generalizing Sakkalis theorem from two polynomials in two variables to the case of (n) polynomials in (n) variables. This leads us to study the results of the type: , and use this relation to attack the Jacobian problem. The last section shows our contribution to proving the conjecture.
Accurate computation of the roughness coefficient is important in the studies of open channel flow. To measure and identify the hydraulic characteristics of the flow system, the model simulation is necessary to study and get the results of the hydraulic properties to specify Manning coefficient of the Euphrates River. In this study, the reach is extended along the Euphrates River from Haditha Dam to Ramadi Barrage with a distance of 169km. The HEC-RAS model was implemented to simulate the flow within the study reach. The geometry of the river was represented by more than two hundred cross-sections surveyed in 2013 and 2021. The model was calibrated using some observed discharges at the Heet gage station for records of th
... Show MoreThe target of this study was to synthesize several new Ciprofloxacin drug analogs by providing a nucleophilic substitution procedure that provides new functionality at the carboxylic group location. The analogs were synthesized, designed, and characterized by 1HNMR, and FTIR. The synthetic path began from the reaction of ciprofloxacin drug with morpholine to give compound[B], ciprofloxacin derivative was linked with a variety of primary and secondary amines to give compounds[B1-B9]. The above-mentioned prepared compounds [B3 and B5] were applied to liver enzymes, and the increase in the activity of these enzymes was observed. In addition, a theoretical study was conducted to study the energies and properties of the prepared co
... Show MoreThe target of this study was to synthesize several new Ciprofloxacin drug analogs by providing a nucleophilic substitution procedure that provides new functionality at the carboxylic group location. The analogs were synthesized, designed, and characterized by 1HNMR, and FTIR. The synthetic path began from the reaction of ciprofloxacin drug with morpholine to give compound[B], ciprofloxacin derivative was linked with a variety of primary and secondary amines to give compounds[B1-B9]. The above-mentioned prepared compounds [B3 and B5] were applied to liver enzymes, and the increase in the activity of these enzymes was observed. In addition, a theoretical study was conducted to study the energies and properties of the prepared compounds.