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-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.
In this paper, a fusion of K models of full-rank weighted nonnegative tensor factor two-dimensional deconvolution (K-wNTF2D) is proposed to separate the acoustic sources that have been mixed in an underdetermined reverberant environment. The model is adapted in an unsupervised manner under the hybrid framework of the generalized expectation maximization and multiplicative update algorithms. The derivation of the algorithm and the development of proposed full-rank K-wNTF2D will be shown. The algorithm also encodes a set of variable sparsity parameters derived from Gibbs distribution into the K-wNTF2D model. This optimizes each sub-model in K-wNTF2D with the required sparsity to model the time-varying variances of the sources in the s
... Show MoreIn this work, the nano particles of Na-A zeolite were synthesized by sol –gel method. The samples were characterized by X-ray diffraction (XRD), X-ray luorescence (XRF), Surface area and pore volume, Atomic Force Microscope (AFM) and Fourier Transform Infrared Spectroscopy (FTIR). Results show that the nano A zeolite is with average crystal size is 74.77 nm., Si/Al ratio 1.03, BET surface area was 581.211m2/g and the pore volume for NaA was found equal to 0.355cm3/g.
The purpose of research is highlighting the role of tax expenses in promoting direct foreign investment in Iraq, The main objective of the increase in the field of tax expenses is to manage the competition in the production of goods and services locally, in addition to the various qualities of the economical. As the search contributes to the idea of the role of the policy of the tax expenses in the promotion of foreign companies operating in Iraq. The analytical and transparent transparency used by adoption of cases of the relevant body of the tax body. For each image or form of tax expenses have been reliably related to the promotion of direct foreign investment, the taxpayers highlighted the annual controls, tax cuts as the sample was
... Show MoreThe present investigation is concerned for the purification of impure zinc oxide (80-85 wt %) by using petroleum coke
(carbon content is 76 wt %) as reducing agent for the impure zinc oxide to provide pure zinc vapor, which will be
oxidized later by air to the pure zinc oxide.
The operating conditions of the reaction were studied in detail which are, reaction time within the range (10 to 30 min),
reaction temperature (900 to 1100 oC), air flow rate (0.2 to 1 l/min) and weight percentage of the reducing agent
(petroleum coke) in the feed (14 to 30 wt %).
The best operating conditions were (30 min) for the reaction time, (1100 oC) for the reaction temperature, (1 l/min) for
the air flow rate, and (30 wt %) of reducing
In this work, laboratory experiments were carried out to verify direct contact membrane distillation system’s performance in highly saline water desalination. The study included the investigation of various operating conditions, like feed flow rate, temperature and concentration of NaCl solution and their impact on the permeation flux were discussed. 16 cm2 of a flat sheet membrane module with commercial poly-tetra-fluoroethylene (PTFE) membrane, which has 0.22 μm pore size, 96 µm thickness and 78% average porosity, was used. A high salt rejection factor was obtained greater than 99.9%, and the permeation flux up to 17.27 kg/m2.h was achieved at 65°C for hot feed side and 20°C for cold side stream.
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 MoreThis paper presents a novel inverse kinematics solution for robotic arm based on artificial neural network (ANN) architecture. The motion of robotic arm is controlled by the kinematics of ANN. A new artificial neural network approach for inverse kinematics is proposed. The novelty of the proposed ANN is the inclusion of the feedback of current joint angles configuration of robotic arm as well as the desired position and orientation in the input pattern of neural network, while the traditional ANN has only the desired position and orientation of the end effector in the input pattern of neural network. In this paper, a six DOF Denso robotic arm with a gripper is controlled by ANN. The comprehensive experimental results proved the appl
... Show MoreSummary First: The importance of the study and the need for it: The society is composed of an integrated unit of groups and institutions that seek to achieve a specific goal within a system of salary, and the family remains the most influential institutions on the individual and the unity of society, with the roles and responsibilities of the individual and society, and through the continuation and strength of other social organizations derive their ability On the other hand, any break-up in the institution of the family is reflected negatively on the cohesion of society and its interdependence, and the causes of this disintegration vary from society to another, but family problems remain the main factor in obtaining it. Second: Study Ob
... Show More