Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an ef

In Iraqi patients with acromegaly the present investigation included 40 control group and 70 patients with acromegaly divided 35 patients with Diabetic while another 35 patients without Diabetic, with ages between (29-72) years for the identification of GST activity polymorphisms by present and absent GSTM1, GSTT1, and PCR-RFLP, enzymatic digestions were carried out using BsmAI (Biolabs. England, UK) for GSTP1b and AciI (Biolabs, England, UK) for GSTP1c.the association GSTActivity with GST genotype were investigated in a cohort of Iraq acromegaly patients comparing with the healthy control group. The results show a non-significant change in GSTP1b gene in both groups, while show high significantly in GSTP1c in diabetic and non-diabetic acro

In this study, the spreading of the pandemic coronavirus disease (COVID-19) is formulated mathematically. The objective of this study is to stop or slow the spread of COVID-19. In fact, to stop the spread of COVID-19, the vaccine of the disease is needed. However, in the absence of the vaccine, people must have to obey curfew and social distancing and follow the media alert coverage rule. In order to maintain these alternative factors, we must obey the modeling rule. Therefore, the impact of curfew, media alert coverage, and social distance between the individuals on the outbreak of disease is considered. Five ordinary differential equations of the first-order are used to represent the model. The solution properties of the system ar

Background: Thermocycling simulates the temperature dynamics in the oral environment. This in vitro study done to measure and compare the effect of thermocycling on the shear bond strength of stainless steel and sapphire brackets bonded to human enamel teeth using light cured orthodontic adhesive and debonded at various time, and to measure adhesive remnant index after debonding. Materials and Methods: one-hundred-twenty extracted upper first premolars for orthodontic reason were used in this study; depending on weather thermocycled or not, the sample was divided into two main groups, then within each group 30 teeth were used for stainless-steel brackets (Bionic®) and for sapphire brackets (Pure®). Both groups were subdivided into three

      It is frequently asserted that an advantage of a binary search tree implementation of a set over linked list implementation is that for reasonably well balanced binary search trees the average search time (to discover whether or not a particular element is present in the set) is O(log N) to the base 2 where N is the number of element in the set (the size of the tree).  This paper presents an experiment for measuring and comparing the obtained binary search tree time with the expected time (theoretical), this experiment proved the correctness of the hypothesis, the experiment is carried out using a program in turbo Pascal with recursion technique implementation and a statistical method  to prove th

This paper concentrates on employing the -difference equations approach to prove another generating function, extended generating function, Rogers formula and Mehler’s formula for the polynomials , as well as thegenerating functions of Srivastava-Agarwal type. Furthermore, we establish links between the homogeneous -difference equations and transformation formulas.