The probability of large deviations for the sum functions of spacings

Let 0=U0,n≤U1,n≤⋯≤Un−1,n≤Un,n=1 be an ordered sample from uniform [0,1] distribution, and Din=Ui,n−Ui−1,n, i=1,2,…,n; n=1,2,…, be their spacings, and let f1n,…,fnn be a set of measurable functions. In this paper, the probabilities of the moderate and Cramer-type large deviation theorems for statistics Rn(D)=f1n(nD1n)+⋯+fnn(nDnn) are proved. Application of these theorems for determination of the intermediate efficiencies of the tests based on Rn(D)-type statistic is presented here too

On Asymptotic Expansion in the Random Allocation of Particles by Sets

We consider a scheme of equiprobable allocation of particles into cells by sets. The Edgeworth type asymptotic expansion in the local central limit theorem for a number of empty cells left after allocation of all sets of particles is derived.Comment: 15 page

System of preparing the personnel for railway of Uzbekistan

The paper, by the example of training for the railway industry in Uzbekistan, focuses on the experiences and characteristics of Uzbekistan's integration into the international system of education, a framework of qualifications of the European Commission. Tashkent Institute of Railway Engineering has: rated the students' knowledge of the possibility of mutual recognition and accreditation based on the comparability of disciplines and curricula; included in its institutional strategy doctoral program, which has national features aimed at providing career opportunities for young researchers and university teachers based on the fundamental nature and the humanization of education, providing the preparation of the highly qualified specialists, ensures the interconnection and interdependence at all levels of technical education: secondary, undergraduate, graduate, doctoral and post-graduate training and re-training to maintain the knowledge and skills of teachers at the level of requests engineering and production of the XXI century

Miswak: An Alternative Approach to Traditional Oral Hygiene Care

Dental professionals recommend many methods such as tooth brushing, flossing and mouth rinse in order to maintain healthy teeth and gingival tissue. Patient compliance is crucial in implementing these three steps in an oral care and may be challenging to many patients. A simple regime requires a toothbrush and toothpaste, and still proves to be difficult for patients. Chlorhexidine is prescribed to patients who have abundant amount of biofilm, or even for just chronic gingival inflammation. This rinse carries many side effects and can be avoided by using another method to keep the oral cavity healthy. An alternative such as Miswak, is an effective natural tool, a solution to maintaining oral health and overcome the gold standards drawbacks. Miswak has been used as a toothbrush by the Babylonians since 7000 BC. Studies have extensively shown that Miswak contains several components that benefit the oral health, including analgesic, antiplaque, antifungal, anticariogenic, and antimicrobial properties. Studies suggests that the individuals who use Miswak sticks have less biofilm than those patients who use regular toothbrushes. Comparing the efficacy of Miswak to a toothbrush was evaluated and associated with a significant reduction of dental biofilm and gingivitis. Based on the patient’s preference, Miswak comes in different forms such as a mouth rinse that carries the effectiveness as if using the chewing stick. Overall, Miswak is an inexpensive oral hygiene regime, and can be a great recommendation for individuals who are eager for a natural and simple approach to incorporate in their oral health care

Physicochemical method of fixing mobile sands with local materials

Impregnating composition with water-soluble binders has been elaborated, with the help of which the source of deflation of mobile sands is blocked, and the protective crust obtained on the sandy surface is characterized by resistance to the effects of wind-sand flow, assessed by plastic strength and thickness. The free-flow movement of a binder in a porous body of sand depends mainly on the equivalent diameter of the particles obtained by the joint solution of the internal and external problems of hydrodynamics and the shape factor of the particles. To interpret the experimental results empirically, an indicator of the saturation of the protective crust sand characterizing the impregnation as an unstable process proceeding under the predominant influence of the gravity field with an uneven movement of the liquid front was revealed. The prevalence of the elastic-plastic properties of the protective crust is evidenced by a slight and smooth change in physical and mechanical indicators over time by the third year of operation