The aim of this paper is to prove a theorem on the Riesz means of expansions with respect to Riesz bases, which extends the previous results of [1] and [2] on the Schrödinger operator and the ordinary differential operator of 4-th order to the operator of order 2m by using the eigen functions of the ordinary differential operator. Some Symbols that used in the paper:     the uniform norm. <,>   the inner product in L2. G   the set of all boundary elements of G. ˆ u   the dual function of u.

The groundwater recharge from rainfall for the main shallow aquifer in the northeastern Missan governorate south of Iraq is investigated via classical and refined chloride mass balance techniques. Application of both techniques reveals that the mean annual groundwater recharge is 0.82 mm/y. The annual recharge received by the aquifer approximately reaches to three million cubic meters after multiply this figure by the area of the study area (about 1856 km2). This figure represents a renewable storage from which a sustainable management of the groundwater reserve could be implemented. The techniques applied are robust, costly-effective, and could be used with other methods such as groundwater table fluctuation method to give a more realis

Background: The mechanical properties of 3D-printed denture base resins are crucial factors for determining the quality and performance of dentures inside a patient’s mouth. Tensile strength and diametral compressive strength are two properties that could play significant roles in assessing the suitability of a material. Although they measure different aspects of material behavior, a conceptual link exists between them in terms of overall material strength and resilience. Aim: This study aims to investigate the correlation between tensile strength and diametral compressive strength after incorporating 2% ZrO2 nanoparticles (NPs) by weight into 3D-printed denture base resin. Methods: A total of 40 specimens (20 dumbbell-shaped and

Accurate description of thermodynamic, structural, and electronic properties for bulk and surfaces of ceria (CeO₂) necessitates the inclusion of the Hubbard parameter (U) in the density functional theory (DFT) calculations to precisely account for the strongly correlated 4f electrons. Such treatment is a daunting task when attempting to draw a potential energy surface for CeO₂-catalyzed reaction. This is due to the inconsistent change in thermo-kinetics parameters of the reaction in reference to the variation in the U values. As an illustrative example, we investigate herein the discrepancy in activation and reaction energies for steps underlying the partial and full hydrogenation of acetyl

The study aims to design an electronic puppet educational theater by Camtasia studio and identify the effectiveness in learning some of the artistic gymnastics skills for first grade, the research curriculum is experimental by designing two equal groups, and the research sample first grade students are distributed among 4 grade, and by the pumpkin determines two divisions (15 from each) representing the experimental group and control group, the main experiment conducted for 8 weeks by two educational units per week after which the post-tests were conducted, SPSS was used to process the results, and it was found that the electronic puppet educational theater contributed by making the learning process enjoyable and interesting and meeting the

In The Name of Allah Most Gracious Most Merciful

The fundamentals of jurisprudence have a great role in facilitating the ways to know the Shari’a rulings for everything that takes place between people in terms of relationships, and the actions that are issued by them, because without it, the sources from which the rulings were taken are not known, and the methods used by the imams of ijtihad in taking these rulings from those sources are not understood. The foundations on which they followed in the interpretation of texts and its rules, and Muslim scholars in different eras celebrated this science and gave it great care: with what they wrote in it from the works of different directions, but of course the complexity printed many

The concentrations of naturally radioactive made occurring and technically enhanced radioisotopes of fly ash samples, collected from Al-Dura thermal power Plant- south of Baghdad, have been investigated using the NaI(Tl) gamma-ray spectroscopy. The average Activity concentrations of the radio elements 238 U, 232Th and 40K in Fly ash samples are measured accurately and found to be 33.860, 32.6 and 644.64Bq/kg respectively. On the whole the radionuclide's concentrations are still below the global average of 50 Bq/kg for 238U and 232Th, but are much higher in 40K, relative to the global average, about 500 Bq/kg. The absorbed gamma doses in air, due to naturally occurring radionuclides in fly ash samples, are measured and found within the ra