The discussion in this paper gives several theorems and lemmas on the Sums of Squares of consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.
In this paper, the Monte-Carlo simulation method was used to compare the robust circular S estimator with the circular Least squares method in the case of no outlier data and in the case of the presence of an outlier in the data through two trends, the first is contaminant with high inflection points that represents contaminant in the circular independent variable, and the second the contaminant in the vertical variable that represents the circular dependent variable using three comparison criteria, the median standard error (Median SE), the median of the mean squares of error (Median MSE), and the median of the mean cosines of the circular residuals (Median A(k)). It was concluded that the method of least squares is better than the
... Show MoreA new Schiff base, 2-N( 4- N,N – dimethyl benzyliden )5 – (p- methoxy phenyl) – 1,3,4- thiodiazol ,and their metal complexes Cu (Π) ,Ni (Π), Fe (III) , Pd (Π) , Pt (IV) , Zn(Π) ,V(IV) and Co (Π) , were synthesized. The prepared complexes were identified and their structural geometries were suggested by using flam atomic absorption technique , FT-IR and Uv-Vis spectroscopy, in addition to magnetic susceptibility and conductivity measurements. The study of the nature of the complexes formed in ethanol solution , following the mole ratio method , gave results which were compared successfully with those obtained from the isolated solid state studied. Structur
... Show MoreSulfamethoxazole (SMX) was added to P-N,N-dimethyl amino benzaldehyde (PDAB) by condensation reaction in acidic medium to form, a yellow colored dye compound which exhibits maximum absorption (λmax) at 450.5 nm. The concentration of (SMX) was determined spectrophotometrically. The optimum reaction conditions and other analytical parameters were evaluated. In addition to classical univariate optimization, design of experiment method has been applied in optimization of the variables affecting the color producing reaction. Beer’s law obeyed in the concentration range of 0.1-10 μg.mL-1 with molar absorptivity of 5.7950×104 L.mol-1.cm-1. The limit of detection and Sandell's sensitivity value were 0.078 μ
... Show MoreA biconical antenna has been developed for ultra-wideband sensing. A wide impedance bandwidth of around 115% at bandwidth 3.73-14 GHz is achieved which shows that the proposed antenna exhibits a fairly sensitive sensor for microwave medical imaging applications. The sensor and instrumentation is used together with an improved version of delay and sum image reconstruction algorithm on both fatty and glandular breast phantoms. The relatively new imaging set-up provides robust reconstruction of complex permittivity profiles especially in glandular phantoms, producing results that are well matched to the geometries and composition of the tissues. Respectively, the signal-to-clutter and the signal-to-mean ratios of the improved method are consis
... Show MoreCoronavirus disease (COVID-19) is an acute disease that affects the respiratory system which initially appeared in Wuhan, China. In Feb 2019 the sickness began to spread swiftly throughout the entire planet, causing significant health, social, and economic problems. Time series is an important statistical method used to study and analyze a particular phenomenon, identify its pattern and factors, and use it to predict future values. The main focus of the research is to shed light on the study of SARIMA, NARNN, and hybrid models, expecting that the series comprises both linear and non-linear compounds, and that the ARIMA model can deal with the linear component and the NARNN model can deal with the non-linear component. The models
... Show MoreUse of lower squares and restricted boxes
In the estimation of the first-order self-regression parameter
AR (1) (simulation study)
Background Bilateral cleft lip deformity is much more difficult to correct than unilateral cleft lip deformity. The complexity of the deformity and the sensitive relationships between the arrangement of the muscles and the characteristics of the external lip necessitate a comprehensive preoperative plan for management. The purpose of this study was to evaluate the repair of bilateral cleft lip using the Byrd modification of the traditional Millard and Manchester methods. A key component of this repair technique is focused on reconstruction of the central tubercle.
Methods Fourteen patients with mean age of 5.7 months presented with bilateral cleft lip deformity and were operated on using a mod
... Show MoreSome transition metal ions (Cr +3, Co+2 , Ni+2,Cu+2, Zn+2,Ag + ,Cd+2 ) complexes of [(N, N- - Bis(2- hydroxy ethyl) Glycine] (Bicine) have been synthesized and characterized by FTIR ,UV-Visble spectroscopy, atomic absorption, magnetic susceptibility, conductivity measurements and study of the nature of the complexes formed in ethanolic solution following the moleratio method. From the results obtained the following general formola have been given for the prepared complexes [M m+ (Bicine)n]. XH2O
Throughout this paper we study the properties of the composition operator
C
p1 o
p2 o…o
pn induced by the composition of finite numbers of special
automorphisms of U,
pi (z) i
i
p z
1 p z
Such that pi U, i 1, 2, …, n, and discuss the relation between the product of
finite numbers of automorphic composition operators on Hardy space H2 and some
classes of operators.