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.

Chaotic systems have been proved to be useful and effective for cryptography. Through this work, a new Feistel cipher depend upon chaos systems and Feistel network structure with dynamic secret key size according to the message size have been proposed. Compared with the classical traditional ciphers like Feistel-based structure ciphers, Data Encryption Standards (DES), is the common example of Feistel-based ciphers, the process of confusion and diffusion, will contains the dynamical permutation choice boxes, dynamical substitution choice boxes, which will be generated once and hence, considered static,

            While using chaotic maps, in the suggested system, called

This study was designed to investing the drug prescribing pattern which is the important point in the rational or irrational use of drugs among patients dispensing their prescriptions from the private pharmacies in Maysan governorate, Iraq for a period of 1 month. The data collected from prescriptions were calculated and analyzed according to the WHO prescribing guidelines. The data showed that the mean of drugs included in single prescription was 3.4, and 12% of prescribed drugs were written as generic names; moreover, the percentage of antibiotics, corticosteroids and anxiolytics were 33.3%, 11.4% and 23.8% respectively. Those results indicate the irrational use of drugs when compared with the world health organization standard values

Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope

In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

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.

Background: Langerhans' cell histiocytosis (LCH) is a group of conditions affecting the reticuloendothelial system. It includes Letterer-Siwe disease, Hand-Schuller-Christian disease and eosinophilic granuloma and most often presents in childhood. Materials and methods: Twenty-five cases of LCH were diagnosed histologically and confirmed by CD1a antibody and assessed immunohistochemically using anti-RANKL and anti-RANK antibodies to evaluate osteoclastogenic mechanism. Results: Regarding jaw cases, there was a significant correlation between CD1a and RANK (P=0.016). While in the skull, highly significant correlation existed between RANK and RANKL (p=0.001). Among the sites, there was no statistically significant difference found for each

Scams remain among top cybercrime incidents happening around the world. Individuals with high susceptibility to persuasion are considered as risk-takers and prone to be scam victims. Unfortunately, limited number of research is done to investigate the relationship between appeal techniques and individuals' personality thus hindering a proper and effective campaigns that could help to raise awareness against scam. In this study, the impact of fear and rational appeal were examined as well as to identify suitable approach for individuals with high susceptibility to persuasion. To evaluate the approach, pretest and posttest surveys with 3 separate controlled laboratory experiments were conducted. This study found that rational appeal treatm