In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.

      Long memory analysis is one of the most active areas in econometrics and time series where various methods have been introduced to identify and estimate the long memory parameter in partially integrated time series. One of the most common models used to represent time series that have a long memory is the ARFIMA (Auto Regressive Fractional Integration Moving Average Model) which diffs are a fractional number called the fractional parameter. To analyze and determine the ARFIMA model, the fractal parameter must be estimated. There are many methods for fractional parameter estimation. In this research, the estimation methods were divided into indirect methods, where the Hurst parameter is estimated fir

This paper deals with the mathematical method for extracting the Exponential Rayleighh  distribution based on mixed between the cumulative distribution function of Exponential distribution and  the cumulative distribution function of Rayleigh distribution using an application (maximum), as well as derived different statistical properties for  distribution, and present a structure of a new distribution based on a modified weighted version of Azzalini’s (1985) named Modified Weighted Exponential Rayleigh  distribution such that this new distribution is generalization of the  distribution and provide some special models of the  distribution, as well as derived different statistical properties for  distribution

         Continuous functions are novel concepts in topology. Many topologists contributed to the theory of continuous functions in topology. The present authors continued the study on continuous functions by utilizing the concept of gpα-closed sets in topology and introduced the concepts of weakly, subweakly and almost continuous functions. Further, the properties of these functions are established.

The purpose of this paper is to study the properties of the
partial level density ( ) l g and the total level density g ( ),
numerically obtained as a l sum of ( ) l g up to 34 max l  , for
a Harmonic – Oscillator potential well. This method applied the
quantum – mechanical phase shift technique and concentrated
on the continuum region. Also a discussion of peculiarities of
quantal calculation for single particle level density of energy –
dependent potential

The textbook is the primary means of creativity and thinking, which has a major role in the development of the readership and mental abilities of the student. It is the basic tool in education in Iraq for the teacher and the student, which cannot be dispensed in any educational program. The current study aimed at the book of the biology of the sixth grade of science in Iraq (comparative study). It was compared to the book of biology for the twelve grade in the Kingdom of Jordan to identify the ratio of similarity and differences between them, in addition, to identify the weaknesses in the Iraq curriculum and developing appropriate solutions and suggestions to address them. The sample was represented with books of biology (six-science cla

The synthesis, characterization and mesomorphic properties of two new series of triazine-core based liquid crystals have been investigated. The amino triazine derivatives were characterized by elemental analysis, Fourier transforms infrared (FTIR), 1HNMR and mass spectroscopy. The liquid crystalline properties of these compounds were examined by differential scanning calorimetry (DSC) and polarizing optical microscopy (POM). DSC and POM confirmed nematic (N) and columnar mesophase textures of the materials. The formation of mesomorphic properties was found to be dependent on the number of methylene unit in alkoxy side chains.