In this paper, the packing problem for complete (  4)-arcs in  is partially solved. The minimum and the maximum sizes of complete (  4)-arcs in  are obtained. The idea that has been used to do this classification is based on using the algorithm introduced in Section 3 in this paper. Also, this paper establishes the connection between the projective geometry in terms of a complete ( , 4)-arc in  and the algebraic characteristics of a plane quartic curve over the field  represented by the number of its rational points and inflexion points. In addition, some sizes of complete (  6)-arcs in the projective plane of order thirteen are established, namely for  = 53, 54, 55, 56.

Introduction and Aim: Diabetes mellitus patients almost always struggle with a metabolic condition known as chronic hyperglycemia. According to the World Health Organization, osteoporosis is a progressive systemic skeletal disorder that is characterized by decreasing bone mass and microstructural breakdown of bone tissue that increases susceptibility to fracture and increased risk of breaking a bone. Here, we aimed to compare the levels of CatK and total oxidative state in patients with diabetes and osteoporosis among the female Iraqi population and study the possible relationship between them. Materials and Methods: This study included 40 females with diabetes (Group G1), 40 with diabetes and osteoporosis (Group G2) and 40 normal healthy f

This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied.

This article studied some linear and nonlinear optical characteristics of different pH solutions from anthocyanin dye extract at 180 oC from red cabbage. First, the linear spectral characteristics, including absorption and transmittance in the range 400-800 nm for anthocyanin solution 5% v/v with different pHs, were achieved utilizing a UV/VIS spectrophotometer. The experimental results reveal a shift in the absorption toward the longer wavelength direction as pH values increment. Then, the nonlinear features were measured using the Z-scan technique with a CW 532 nm laser to measure the nonlinear absorption coefficient through an open aperture. A close aperture (diameter 2 mm) calculates the nonlinear refractive index. The open Z-scan sh

            This paper is interested in certain  subclasses of univalent and bi-univalent functions concerning  to shell- like curves connected with k-Fibonacci numbers involving modified Sigmoid activation function θ(t)=2/(1+e^(-t) ) ,t ≥0 in unit disk |z|<1 . For estimating of the initial coefficients |c_2 | , |c_3 |, Fekete-Szego ̈ inequality and the  second Hankel determinant have been investigated for the functions in our classes. 

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

In the present work, the surface properties of mixed binary surfactants containing sodium dodecylbenzene sulfate (SDBS) and Tween 80 (TW80) surfactants in aqueous solutions were studied at temperature 293 K using surface tension measurements. The critical micelle concentration (cmc) magnitude for both individual surfactants and their mixtures were established the obtained results revealed  that the magnitude of cmc of the mixtures are less than the magnitude of individual surfactants and decrease with the increase in Tween 80 percent in solution which indicate the nonideal  mixing of the two surfactants. The values of molecular interaction parameters  and the mole fraction of surfactants in the micelle (X1) were calculated

   The inhibition of mild steel corrosion in 1.0M HCl by 1-propanol and the synergistic effect of potassium iodide (KI) was investigated using weight loss and polarization techniques in the temperature range (30 ‒ 50) ̊ C. A matrix of Doelhert to three factors was used as the experimental design, adopting weight loss results as it permits the use of the response surface methodology which exploited in determination of the synergistic effect as inhibition on the mild steel. The results were confirmed using electrochemical polarization measurements. Experimental results showed that the inhibition efficiency (IE%) increases with increase in concentration of inhibitor and with increasing of temperature. The addition iodide ions t

The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.

HCl is separated from HCl –H₂SO₄  solution by membrane distillation process(MD). The flat –sheet membranes made from polyvinylidene fluoride (PVDF) and polypropylene (pp.). Plate and frame these types of membrane where used in the process. The feed is a mixture of HCl and H₂SO₄ acids compositions depended on metals treated object.HCl concentration increased in the permeate during the process but sulfuric acid increased gradually in the feed .During the concentration of solution acids concentrations in the feed at the beginning were 50 g/dm³ of sulfuric acid and 50 g/dm³ of hydrochloric acid at 333K feed temperature the permeate flux was 71 dm