Some NP-Hard Problems for the Simultaneous Coprimeness of Values of Linear Polynomials

The algorithmic-time complexity of some problems connected with linear polynomials and coprimeness relation on natural numbers is under consideration in the paper. We regard two easily stated problems. The first one is on the consistency in natural numbers from the interval of a linear coprimeness system. This problem is proved to be NP-complete. The second one is on the consistency in natural numbers of a linear coprimeness and discoprimeness system for polynomials with not greater than one non-zero coefficient. This problem is proved to be NP-hard. Then the complexity of some existential theories of natural numbers with coprimeness is considered. These theories are in some sense intermediate between the existential Presburger arithmetic and the existential Presburger arithmetic with divisibility. In a form of corollaries from the theorems of the second section we prove NP-hardness of the decision problem for the existential theories of natural numbers for coprimeness with addition and for coprimeness with successor function. In the conclusion section we give some remarks on the NP membership of the latter problem

Child health status — the future of the country (part 2)

The article deals with the problems of increasing the incidence and prevalence of childhood diseases during 1994–2016 against the background of a global reduction in the staffing of children’s specialists by 1.7 times, with an extremely inadequate supply of the regions of the South-East, Donetsk and Luhansk regions. All of this has a negative impact on the proper medical care of the child population, including the detection of childhood diseases. The authors substantiate the need to restore the personnel and material-technical potential of the pediatric service, the development of modern diagnostic and treatment technologies, the preservation of immunization and the prevention of disability of common childhood diseases that is an important component of the national health care and safety system of the country as a whole

Status of child population health — the future of the country (part 1)

The article of the team of scientists of pediatricians and organizers of pediatric health care of Ukraine is devoted to the study of the main trends in the health status of children over last 22 years. The results of the analysis of the incidence and prevalence of diseases among Ukrainian child population, infant mortality rates over the past two decades demonstrates that they remain significantly higher than the average European indicators against the background of a progressive decrease in the number of child population at 3,16 million people. The prevalence of childhood diseases in Ukraine over past 22 years has grown by 41 %, the incidence of childhood diseases arose by 36 %. The article considers the ways of solving a number of new social and medico-ecological problems that negatively affect child health