The paper investigates a number of Incomplete exact roots of a series of natural numbers, in relation to the Pythagorean theorem that in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the legs. It uses the fact that the equation x^2+y^2=z^n,n=2,3,4,.. always has an solution (x,y,z) in integer numbers x,y,z∈Z={0,±1,±2,…}.

Background: Uterine rupture at the site of a previous cesarean scar is an uncommon but catastrophic complication of pregnancy, which is associated with significant maternal and fetal morbidity and mortality.Case Presentation: A 30-year old woman at 24th week of gestation and complaint of pain, contractions and spotting was admitted in Royan Institute in Tehran, Iran. She had a past medical history of an EP and a cesarean section delivery, respectively 4 and 2 years before hospitalization. Herniation of an amniotic membrane into the maternal bladder was found on ultrasound examination.Conclusion: Risk factors of cesarean scar rupture should be considered in women undergoing subsequent pregnancies as they need extra care. Ultrasonography can be used to evaluate women with previous cesarean section to assess the risks of scar rupture during subsequent pregnancies.

In respect of make a distinction between Incomplete crime (Attempt, Failed crime and Impossible crime) as well as distinguish of other similar institutions, have not presented a clear and detailed criteria because, if does not provide specific and clear criterion, would be effective in determining the type and level of response against defendant. Accordingly, the most comprehensive measure that can be offered in this regard, the possibility or impossibility of the crime in time to start running, which follows, the first is, when the arrival time of operation (to perform) the crime, it is impossible to be committed if to be for the reason of the inherent inadequacy of action, it is not any instances of Incomplete crime and consequently the amount of action, was not entitled criminal reaction because has not been achieved start perform as a condition for Incomplete crime in this situation, and if to be cause the impossibility of crime the lack if subject matter, the existence of hindrance or lack of the relative adequacy of act, has occurred impossible crime. While the second is, when the time begging to run, commit of the crime be possible, if despite of possibility, in fact was not any and it be for existence and creation of hindrance it is a Attempt, and if the fault or defect of accused caused it, failed crime has occurred.

This is a rare case of prostatic agenesia with Incomplete urethral duplication. A 63 year old man was reffered to us with LUTS (Lower Urinary Tract Symptoms). Bladder ultra sonography and retrograde urthrography showed bladder neck obstruction with a prostatic diverticula and Incomplete bulbar urethral duplication. The final diagnosis "prostatic agenesia" was made following pathological study on bladder neck resected pieces and Incomplete urethral duplication by urethrography.

In this paper, we explain a new generalized contractive condition for multivalued mappings and prove a  xed point theorem in metric spaces (not necessary complete) which extends some well{ known results in the literature. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection ful lling the corresponding functional equation.