The aim of this paper is prove a theorem on the Riesz mean of expansions with respect to Riesz bases, which extends the previous results of Loi and Tahir on the Schrodinger operator to the operator of 4-th order.

  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 thin films of cadmium oxide (CdO) were deposited using the SILAR (Successive ionic layer absorption and reaction) method at various deposition cycles. CdO thin films were made on glass substrates at a temperature of  95°C, using a cadmium acetate source material and an ammonium hydroxide solution. One of the main criteria that impact the quality of thin films is the number of deposition cycles. The size of the crystals decreases with the increase in the number of cycles from 33.7 nm at the immersion cycle 10 to 22.7 nm at the immersion cycle 20, as shown by the X-ray diffraction results. The optical band gap energy of the films reduces as the number of deposition cycles increases, while the transmittance of the Cadmium oxide film i

Radiotherapy is medical use of ionizing radiation, and commonly applied to the cancerous tumor because of its ability to control cell growth. The amount of radiation used in photon radiation therapy called dose (measured in grey unit), which depend on the type and stage of cancer being treated. In our work, we studied the dose distribution given to the tumor at different depths (zero-20 cm) treated with different field size (4×4- 23×23 cm). Results show that the deeper treated area has less dose rate at the same beam quality and quantity. Also it has been noted increasing in the field increasing in the depth dose at the same depth even if the radiation energy is constant. Increasing in radiation dose attributed to the scattere

Zygapophyseal joints (or facet joints), are a plane synovial joint which located between the articular facet processes of the vertebral arch which is freely guided movable joints. Ten dried vertebrae were used for the lumbar region and taking (L₄) as a sample to reveal stress pathways across the joints by using ANSYS program under different loading conditions which used Finite Elements Analysis model. Results obtained from the ANSYS program are important in understanding the boundary conditions for load analysis and the points of stress concentration which explained from the anatomical point of view and linked to muscle and ligament attachments. This model used as a computational tool to joint biomechanics and to prosthetic im

Background: White-spot lesion is one of the problems associated with the fixed orthodontic treatment. The aims of this in-vitro study were to investigate enamel damage depth on adhesive removal when the adhesive were surrounded by sound, demineralized or demineralized enamel that had been re-mineralized prior to adhesive removal using 10% Nano-Hydroxy apatite and to determine the effect of three different adhesive removal techniques. Materials and methods: Composite resin adhesive (3M Unitek) was bonded to 60 human upper premolars teeth which were randomly divided in to three groups each containing ten sound teeth and ten teeth with demineralized and re-mineralized lesions adjacent to the adhesive. A window of 2 mm was prepared on the bucca

The present study develops an artificial neural network (ANN) to model an analysis and a simulation of the correlation between the average corrosion rate carbon steel and the effective parameter Reynolds number (Re), water concentration (Wc) % temperature (T o) with constant of PH 7 . The water, produced fom oil in Kirkuk oil field in Iraq from well no. k184-Depth2200ft., has been used as a corrosive media and specimen area (400 mm2) for the materials that were used as low carbon steel pipe. The pipes are supplied by Doura Refinery . The used flow system is all made of Q.V.F glass, and the circulation of the two –phase (liquid – liquid ) is affected using a Q.V.F pump .The input parameters of the model consists of Reynolds number , w

In this study, active knife and fixed knife of single-row disc silage machine has three different clearance C1, C2 and C3 (1, 3 and 5 mm) and it is tried in three different working speed V1, V2 and V3 (1.8, 2.5 and 3.7 km / h) and PTO speed (540 min-1) and machine's fuel consumption (l/h), average power consumption (kW), field energy consumption (kW/da), product energy consumption (kW/t), field working capacity (da/h), product working capacity (t/h) and Chopping size distribution characteristics of the fragmented material were determined. It has been found that knife-counter knife clearances smaller than 3 mm (1 mm) and larger (5 mm) have a negative effect on machine performance in general. In terms of fuel and power consumptions, the m

This paper proposes and studies an ecotoxicant system with Lotka-Volterra functional response for predation including prey protective region. The equilibrium points and the stability of this model have been investigated analytically both locally and globally. Finally, numerical simulations and graphical representations have been utilized to support our analytical findings

Bending effects on the transmission of optical signal are investigated on a single mode
optical fiber (SMOF) of 10 m length, core radius of 5 μm and optical refractive index difference
0.003. The bending radii (R) were between 0.08 and 0.0015 m. A great decrease in the amplitude is
shown for radii below 0.01 m. Sudden break down occurs for radii less than 0.0015 m. Birefringence
(B) is difficult to measure for long fibers. Meanwhile, B was found by comparing with calibrated
fiber of the same properties but of length of 0.075 m. The results show an increase in propagation
constant (Δβ) and the decrease in beat length (Lb), and show that bending decreases the critical radius
of curvature (Rc) related to B. The chang