The aim of this paper is to derive a posteriori error estimates for semilinear parabolic interface problems. More specifically, optimal order a posteriori error analysis in the - norm for semidiscrete semilinear parabolic interface problems is derived by using elliptic reconstruction technique introduced by Makridakis and Nochetto in (2003). A key idea for this technique is the use of error estimators derived for elliptic interface problems to obtain parabolic estimators that are of optimal order in space and time.

The aim of this study is to evaluate oxidative stress in diabetes mellitus (DM) Type1 by the measurement of Glucose-6-phosphate Dehydrogenase (G-6-PD), an enzyme expressed in human RBCs, is important in the generation of reduced glutathione which is the key product in oxidative stress controls. The Study was carried on 80 samples of blood and serum of National Diabetes Center (NDC). The study groups under fasting conditions and they divided as:20 samples of diabetes mellitus patients without complications and 20 samples of diabetes mellitus with cardiovascular (CV) complications and 20 samples of diabetes mellitus with Nephropathy (Neph) complications compared with 20 control group with average age (13-67) years.. The results sh

This article introduces a novel procedure to detect an approximate solution to Fredholm fractional integro-differential equations with linear type (LFFIDE) defined using Caputo fractional derivative. The new procedure approximates the solution using three types of polynomials: Laguerre polynomials, Hermite polynomials, and Legendre polynomials, thereafter transforming the problem into a linear programming problem. The approximate solutions are compared using testing examples to examine the efficiency of the suggested approach. Also, a comparison with the other methods using the same polynomials illustrates The effectiveness and consistency of the proposed technique. Finally, the error analysis of the proposed technique and convergent are di

This paper presents the Extended State Observer (ESO) based repetitive control (RC) for piezoelectric actuator (PEA) based nano-positioning systems. The system stability is proved using Linear Matrix Inequalities (LMIs), which guarantees the asymptotic stability of the system. The ESObased RC used in this paper has the ability to eliminate periodic disturbances, aperiodic disturbances and model uncertainties. Moreover, ESO can be tuned using only two parameters and the model free approach of ESO-based RC, makes it an ideal solution to overcome the challenges of nano-positioning system control. Different types of periodic and aperiodic disturbances are used in simulation to demonstrate the effectiveness of the algorithm. The comparison studi

This paper deals with founding an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to the convex polynomials by means of weighted moduli of smoothness of fractional order  , ( , ) p f t . In addition we prove some properties of weighted moduli of smoothness of fractional order.

Ration power plants, to generate power, have become common worldwide. One such one is the steam power plant. In such plants, various moving parts of heavy machines generate a lot of noise. Operators are subjected to high levels of noise. High noise level exposure leads to psychological as well physiological problems; different kinds of ill effects. It results in deteriorated work efficiency, although the exact nature of work performance is still unknown. To predict work efficiency deterioration, neuro-fuzzy tools are being used in research. It has been established that a neuro-fuzzy computing system helps in identification and analysis of fuzzy models. The last decade has seen substantial growth in development of various neuro-fuzzy systems

This study addresses the selection of the optimal site for establishing a waste landfill within the study area by utilizing Geographic Information Systems (GIS) techniques integrated with the Analytic Hierarchy Process (AHP) methodology and the Weighted Overlay tool for multi-criteria spatial analysis. Six key criteria influencing site suitability were identified, including distance from urban areas, agricultural lands, irrigation canals, roads, villages, and barren (uncultivated and uninhabited) areas, with a focus on potential environmental and health impacts. The results indicate that ideal landfill sites are located at distances exceeding 800 to 1000 meters from agricultural and urban areas, providing effective protection to soil and gr