In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

Extension of bandwidth for high reflectance zone for the spectral region (8-14pm) was studied adapting the concept of contiguous and overlapping high reflectance stacks. Computations was carried out using the modified characteristic matrix theory restricted to near-normal incidence of light on dielectric , homogenous and isotropic symmetrical stack. Certain precautions must be taken in the choice of stacks to avoid deep —reflectance minima from developing within the extended high reflectance region. Results illustrate that the techniques of extending the high reflectance regions are applicable not only to mirrors , but also to short-and long-edge filter and to narrow band pass filters.

The presented research investigated the pollen morphology of endemic Iraqi Hypericum species. The study revealed phenotypic features of pollen grains in the polar and equatorial views and their quantitative and qualitative characteristics. The results showed that the pollen grains of the genus Hypericum were radially symmetrical and isopolar, and their apertures were simple and tricolporate, except the species H. davisii, distinguished as tetracolprate. Dividing the studied species based on pollen grain sizes comprised two groups. Small pollen grains with an average length of the equatorial view ranged between 10–16 μm in H. lysimachioides and H. vermiculare. Medium-sized pollen grains with an average extent between 17–26 μm e

     In this paper, the class of meromorphic multivalent functions of the form by using fractional differ-integral operators is introduced. We get Coefficients estimates, radii of convexity and star likeness. Also closure theorems and distortion theorem for the class ,  is calculaed.

Background: Age progression is regarded as a critical risk factor in morbidity and mortality because of a weakened immune system. Although various studies have dealt with electrolyte imbalance in COVID-19 patients, the outcomes of these studies were partially understood. Objective: The current study aims to determine some biochemical parameters in old Iraqi COVID-19 patients and highlight the outcomes according to the aging role in the development of COVID-19 by suggesting new mechanisms. Materials and methods: forty COVID-19 patients were enrolled in the current study and divided into two groups: Gm includes (20) men, and Gf includes  (20) women. The parameters (Na+, K+, Cl-, LDH, and Hb ) were determined in sera of patients and c

This paper presents an analytical study on the serviceability of reinforced concrete gable roof beams with openings of different sizes, based on an experimental study which includes 13 concrete gable roof beams with openings under static loading. For deflection and crack widths under static loading at service stage, a developed unified calculation procedure has been submitted, which includes prismatic beams with one opening subjected to flexure concentrated force. The deflection has been calculated with two methods: the first method calculated deflections via relevant equations and the second was Direct Stiffness Method in which the beam is treated as a structural member with several segments constituting the portions with solid sec