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.
The aim of the work is synthesis and characterization of bidentate ligand [3-(3-acetylphenylamino)-5,5-dimethylcyclohex-3-enone][HL], from the reaction of dimedone with 3-amino acetophenone to produce the ligand [HL], the reaction was carried out in dry benzene as a solvent under reflux. The prepared ligand [HL] was characterized by FT-IR, UV-Vis spectroscopy, 'H, 8C-NMR spectra, Mass spectra, (C.H.N) and melting point. The mixed ligand complexes were prepared from ligand [HL] was used as a primary ligand while 8-hydroxy quinoline [HQ] was used as a secondary ligand with metal ion M(IT).Where M(IT) = (Mn ,Co ,Ni ,Cu ,Zn ,Cd and Pd) at reflux ,using ethanol as a solvent, KOH as a
... Show MoreThis mini review provides an overview of methods for manufacturing expanded graphite (EGT) and the use of its composites with metal oxides in the field of photodegradation of dyes. Dyes from textile manufacturing represent a significant environmental pollution problem in waterways worldwide, highlighting the need for environmentally friendly and efficient technologies to remove dyes from industrial and local wastewater. Photodegradation technologies offer a low-cost, sustainable solution with minimal secondary pollution. Carbon-based materials, such as expanded graphite, are advantageous in enhancing catalytic activity. Accordingly, this review will explore the different fabrication techniques of expanded graphite and summarize the recent d
... Show MoreChalcogenide glasses SeTe have been prepared from the high purity constituent elements .Thin films of SeTe compound have been deposited by thermal evaporation onto glass substrates for different values of film thickness . The effect of varying thickness on the value of the optical gap is reported . The resultant films were in amorphous nature . The transmittance spectra was measured for that films in the wavelength range (400-1100) nm . The energy gap for such films was determined .
This paper studies the adaptive coded modulation for coded OFDM system using punctured convolutional code, channel estimation, equalization and SNR estimation. The channel estimation based on block type pilot arrangement is performed by sending pilots at every sub carrier and using this estimation for a specific number of following symbols. Signal to noise ratio is estimated at receiver and then transmitted to the transmitter through feedback channel ,the transmitter according to the estimated SNR select appropriate modulation scheme and coding rate which maintain constant bit error rate
lower than the requested BER. Simulation results show that better performance is confirmed for target bit error rate (BER) of (10-3) as compared to c
The aim of this work is to develop an axi-symmetric two dimensional model based on a coupled simplified computational fluid dynamics (CFD) and Lagrangian method to predict the air flow patterns and drying of particles. Then using this predictive tool to design more efficient spray dryers. The approach to this is to model what particles experience in the drying chamber with respect to air temperature and humidity. These histories can be obtained by combining the particles trajectories with the air temperature/humidity pattern in the spray dryer. Results are presented and discussed in terms of the air velocity, temperature, and humidity profiles within the chambers and compared for drying of a 42.5% solids solution in a spray chamber
... Show MoreDifferent ANN architectures of MLP have been trained by BP and used to analyze Landsat TM images. Two different approaches have been applied for training: an ordinary approach (for one hidden layer M-H1-L & two hidden layers M-H1-H2-L) and one-against-all strategy (for one hidden layer (M-H1-1)xL, & two hidden layers (M-H1-H2-1)xL). Classification accuracy up to 90% has been achieved using one-against-all strategy with two hidden layers architecture. The performance of one-against-all approach is slightly better than the ordinary approach
A new approach for baud time (or baud rate) estimation of a random binary signal is presented. This approach utilizes the spectrum of the signal after nonlinear processing in a way that the estimation error can be reduced by simply increasing the number of the processed samples instead of increasing the sampling rate. The spectrum of the new signal is shown to give an accurate estimate about the baud time when there is no apriory information or any restricting preassumptions. The performance of the estimator for random binary square waves perturbed by white Gaussian noise and ISI is evaluated and compared with that of the conventional estimator of the zero crossing detector.