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 proved.
This paper is concerned with finding the approximation solution (APPS) of a certain type of nonlinear hyperbolic boundary value problem (NOLHYBVP). The given BVP is written in its discrete (DI) weak form (WEF), and is proved that it has a unique APPS, which is obtained via the mixed Galerkin finite element method (GFE) with implicit method (MGFEIM) that reduces the problem to solve the Galerkin nonlinear algebraic system (GNAS). In this part, the predictor and the corrector technique (PT and CT) are proved convergent and are used to transform the obtained GNAS to linear (GLAS ), then the GLAS is solved using the Cholesky method (ChMe). The stability and the convergence of the method are studied. The results
... Show MoreThis paper presents the design, construction and investigates an experimental study of a parabolic Trough Solar Collector (PTSC). It is constructed of multi – piece glass mirror to form the parabolic reflector (1.8 m ? 2.8 m) its form were checked with help of a laser and carbon steel rectangular as receiver. Sun tracker has been developed (using two – axis) to track solar PTSC according to the direction of beam propagation of solar radiation. Using synthetic oil as a heat transfer its capability to heat transfer and load high temperature (?400 oc). The storage tank is fabricated with stainless steel of size 50 L. The experimental tests have been carried out in Baghdad climatic conditions (33.3o N, 44.4o E) during selective days of the
... Show MoreThis paper aims to investigate the flexural behavior of reinforced concrete beams considering fire resistance by adding Lightweight Expanded Clay Aggregates (LECA) to the concrete mix as partial coarse aggregate replacement. LECA is a type of porous clay with a uniform pore structure with fine, closed cells and hard, tightly sintered skin. The experimental work comprised four reinforced self-compacted concrete beams. All the specimens were identical in their geometrical layout of 1600×240×200 mm, reinforcement details, and support condition (simply supported). For all the beams, the main reinforcement was provided by two bars, each having a diameter of 12 mm, while a bar of 6 mm diameter was employed for the top and shear reinforc
... Show MoreA total of (25) stool samples were collected from children and adults (2- 4) years old suffering from diarrhea to isolate E. coli strains that produce heat-stable enterotoxin a (STa), and after performing microscopic examination, cultural characterization and biochemical identification only (11) isolates showed positive E. coli. STa activity was estimated by using suckling mouse assay (SMA) and from these (11) isolates only (5) showed STa activity and the one with the highest STa activity was selected for large scale production of STa, which was followed by partial purification using ion-exchange chromatography (normal phase) using DEAE sephadex A-50 column. After purification and determination of protein concentration by using the standard
... Show MoreIn this paper, we have been used the Hermite interpolation method to solve second order regular boundary value problems for singular ordinary differential equations. The suggest method applied after divided the domain into many subdomains then used Hermite interpolation on each subdomain, the solution of the equation is equal to summation of the solution in each subdomain. Finally, we gave many examples to illustrate the suggested method and its efficiency.
We wrote this paper to proffer new types of the perfectly supra continuous functions. We also introduced new types of supra continuous, supra open and supra closed functions.
In bilateral contracts, if one of the contracting parties does not fully perform his obligation the other contracting party may ask the court to rescission the contract in full, but the failure to perform may be limited to part of his obligation, then the following question arises: Can the contract be partially rescission ? It is noted that there is a great jurisprudential and judicial disagreement on this subject, And we ended up saying that it is not permissible for a court to order on partial rescission without the approval of the creditor, because the judgment of partial rescission requires to compel the creditor to accept partial payment, which is rejected under Article (392) of the Iraqi Civil law.