The study presents the modification of the Broyden-Flecher-Goldfarb-Shanno (BFGS) update (H-Version) based on the determinant property of inverse of Hessian matrix (second derivative of the objective function), via updating of the vector s ( the difference between the next solution and the current solution), such that the determinant of the next inverse of Hessian matrix is equal to the determinant of the current inverse of Hessian matrix at every iteration. Moreover, the sequence of inverse of Hessian matrix generated by the method would never approach a near-singular matrix, such that the program would never break before the minimum value of the objective function is obtained. Moreover, the new modification of BFGS update (H-version) preserves the symmetric property and the positive definite property without any condition.
Each school of Islamic jurisprudence has principles and rules upon which the diligent work in these schools is based. This is due to the view of sanctification of these rulings, as they are divine rulings. Therefore, the goal is to reach a ruling that represents the intent of the legislator as much as possible.
Hence, these schools of thought established rules for issuing fatwas with the intention of restricting the performance of a fatwa to the hands of those who are qualified for it and have met its conditions, so they gave priority to the most knowledgeable person over others to perform the fatwa. In the Hanafi school of thought, for example, the saying of Imam Abu Hanifa (may God have mercy on him) is given precedence over others,
Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-pose
In this work, some mechanical properties of the polymer coating were improved by preparing a hybrid system containing Graphene (GR) of different weight percentages (0.25, 0.5, 1, and 2wt%) with 5wt% carbon fibres (CF) and added to a polymer coating by using casting method. The properties were improved as GR was added with further improvement on adding 5wt% of CF. The impact strength of acrylic polymer with GR increases with increasing weight ratio of GR; maximum value was obtained when the polymer coating was incorporated with 1wt% GR and 5wt% CF. The impact strength of acrylic polymer with GR and GR/CF composites incorporated with GR at 1wt% and CF at 5wt%. Hardness increase with increasing weight ratio of Gr and a significant imp
... Show MoreThis research deals with increasing the hardening and insulating the petroleum pipes against the conditions and erosion of different environments. So, basic material of epoxy has been mixed with Ceramic Nano Zirconia reinforcement material 35 nm with the percentages (0,1,2,3,4,5) %, whereas the paint basis of broken petroleum pipes was used to paint on it, then it was cut into dimensions (2 cm. × 2 cm.) and 0.3cm high. After the paint and percentages are completed, the samples were immersed into the paint. Then, the micro-hardness was checked according to Vickers method and thermal inspection of paint, which contained (Thermal conduction, thermal flux and Thermal diffusivity), the density of the painted samples was calculate
... Show MoreSteganography is a mean of hiding information within a more obvious form of
communication. It exploits the use of host data to hide a piece of information in such a way
that it is imperceptible to human observer. The major goals of effective Steganography are
High Embedding Capacity, Imperceptibility and Robustness. This paper introduces a scheme
for hiding secret images that could be as much as 25% of the host image data. The proposed
algorithm uses orthogonal discrete cosine transform for host image. A scaling factor (a) in
frequency domain controls the quality of the stego images. Experimented results of secret
image recovery after applying JPEG coding to the stego-images are included.
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-
... Show MoreThe present study discusses the problem based learning in Iraqi classroom. This method aims to involve all learners in collaborative activities and it is learner-centered method. To fulfill the aims and verify the hypothesis which reads as follow” It is hypothesized that there is no statistically significant differences between the achievements of Experimental group and control group”. Thirty learners are selected to be the sample of present study.Mann-Whitney Test for two independent samples is used to analysis the results. The analysis shows that experimental group’s members who are taught according to problem based learning gets higher scores than the control group’s members who are taught according to traditional method. This
... Show MoreThe present study discusses the problem based learning in Iraqi classroom. This method aims to involve all learners in collaborative activities and it is learner-centered method. To fulfill the aims and verify the hypothesis which reads as follow” It is hypothesized that there is no statistically significant differences between the achievements of Experimental group and control group”. Thirty learners are selected to be the sample of present study.Mann-Whitney Test for two independent samples is used to analysis the results. The analysis shows that experimental group’s members who are taught according to problem based learning gets higher scores than the control group’s members who are taught according to traditional method. This
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