This paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica^®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving

The topological indices are functions on the graph that do not depend on the labeling of their vertices. They are used by chemists for studying the properties of chemical compounds.  Let  be a simple connected graph. The Hyper-Zagreb index of the graph ,  is defined as  ,where  and  are the degrees of vertex  and , respectively. In this paper, we study the Hyper-Zagreb index and give upper and lower bounds for .

The study examined the assessment of raw water and drinking water projects of  Diyala Governorate for the year 2017, amounting to (24) projects, The average per capita supply of potable water (0.396 m3 / day/person), which is less than the global standard for the average per capita of drinking water, and constitute water rumors within the network of water transport in the province (3%), and the water of raw and drinking value within the limits allowed to be used by Iraq and the global indicators of {Total acidity, alkaline, acidic function, chlorides, magnesium, Electrical conductivity, total soluble salts, sodium, potassium, sulfates, turbidity other than (raw water)}. While the index of calcium only a value higher than the limits

In the current study, haemoglobin analytes dissolved in a special buffer (KH₂PO₄(1M), K₂HPO₄(1M)) with pH of 7.4 were used to record absorption spectra measurements with a range of concentrations from (10^-8 to 10^-9) M and an absorption peak of 440nm using Broadband Cavity Enhanced Absorption Spectroscopy (BBCEAS) which is considered a simple, low cost, and robust setup. The principle work of this technique depends on the multiple reflections between the light source, which is represented by the Light Emitting Diode 3 W, and the detector, which is represented by the Avantes spectrophotomer. The optical cavity includes two high reflectivity  ≥99%  dielectric mirrors (dia

This study aimed to show the relationship between mental health and shyness for university students in Baghdad and Al – Mustansiria university which its subject was (200) students  ,          ( 100) males and  ( 100) females , Mental Health scale which is constructed by (Al – Janabi 1991) and developed by (Hassan 2006) was used for this aim  ,The scale of shyness was built according to a questioner to the students and according to previous publications and studies .

Multiple regulation analysis step - wise was used for data analysis in order to identify the possibility to find single or couple indications for the independent variable (mental

Moment invariants have wide applications in image recognition since they were proposed.

Construction and operation of (2 m) parabolic solar dish for hot water application were illustrated. The heater was designed to supply hot water up to 100 oC using the clean solar thermal energy. The system includes the design and construction of solar tracking unit in order to increase system performance. Experimental test results, which obtained from clear and sunny day, refer to highly energy-conversion efficiency and promising a well-performed water heating system.