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In this article the creation of a four-dimensional model of dry friction in the interaction of two wheels of a mobile robot with a rough plane is discussed. A study is performed of the dynamics of a two-wheeled robot on a horizontal surface, taking into account the inertial properties of its design and using the combined model of dry friction developed. The contact between the wheels and the horizontal surface is continuous. The movement of the wheels occurs under the conditions of combined dynamics. Combined dynamics involves sliding, spinning, and rolling motion. To formulate the equation of motion, Appel's equation is used. The proposed model of sliding, spinning, and rolling friction is given for the case when the contact area is a circle. To simplify cumbersome integral equations, linear-fractional Pade approximations are used, which accurately describe the behavior of the components of the friction model. A mathematical model is proposed that describes the movement of a mobile robot, the wheels of which perform simultaneous sliding, spinning, and rolling. [ABSTRACT FROM AUTHOR]

The accumulation of gadolinium in human brain gliomas is estimated after a single intravenous administration of Magnevist. The study is conducted using samples excised during standard surgeries on human brain gliomas. Gadolinium is present in all five examined samples at concentrations of 0.0093 to 0.2384 ng mg–1 (ppm) of tumor tissue. [ABSTRACT FROM AUTHOR]

This paper is devoted to solving the problem of motion of a rigid body with a cylindrical surface on a plane. The plane moves according to the harmonic law in the horizontal direction. The phenomenon of vibrational translation and its nature are described. The applicability of the problem and the main weak points in its study are determined. The law of motion of a cylindrical body on a vibrating base is derived, and the algorithm for solving the problems in MatLab is developed. The graphs of velocity variation in time are plotted for different frequency values. The results are presented in the form of the frequency response. [ABSTRACT FROM AUTHOR]

We consider the boundary-value problem on a finite interval for a class of second-order operator-differential equations with a linear operator in one of its boundary conditions. We obtain sufficient conditions for the regular solvability of the boundary-value problem under consideration; these conditions are expressed only in terms of its operator coefficients. [ABSTRACT FROM AUTHOR]

We present conditions of solvability of a boundary value problem for a class of second order operator-differential equations on a finite segment, study the behavior of the resolvent of the corresponding operator pencil, prove the double completeness of a system of the derived chains of eigenvectors and associated vectors corresponding to a boundary value problem on a segment, and establish the completeness of elementary solutions to the homogeneous equation in the solution space. [ABSTRACT FROM AUTHOR]

We have developed a radiochemical neutron activation analysis technique (RNAA) of pure uranium with using extraction chromatographic separation of 239Np from impurity elements in TBP-6M HNO3 media. The estimation of influence of fission products of 235U on the results by radiochemical neutron activation analysis has been carried out. For it we have performed NAA with preconcentration of impurity elements. Experiments show that in this case the apparent concentration of Y, Zr, Mo, Cs, La, Ce, Pr, Nd exceeds the true concentration by 2500–3000 times. Therefore, determination of these elements is not possible by RNAA. This technique allowed to use the determination of 26 impurity elements with detection limit 10−5–10−9% by mass. This developed technique may be used for the determination of impurities in uranium and its compounds. [ABSTRACT FROM AUTHOR]

A procedure for the radiochemical neutron activation analysis of rhenium and ammonium perrhenate samples was developed. The procedure provides the determination of about 30 impurity elements present in concentrations of n× 10–4to n× 10–8mass % with RSD of 20–30%. An AV-17 anion exchanger–nitric acid solution system was used, which allows the selective separation of rhenium from a wide variety of elements. [ABSTRACT FROM AUTHOR]