Thomas Fincke und die <Emphasis Type="Italic">Geometria rotundi</Emphasis>

Thomas Fincke (January 6^th, 1561–April 24^th, 1656), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be „abreast of the mathematics of his time“.      

Dynamics of Vibroprotective Systems with Roller Dampers of Low-Frequency Vibrations

We study low-frequency vibrations of a vibroprotective system of solid bodies formed by a roller damper and a moving load-carrying body under the action of external harmonic excitations. The dynamic equations of combined motion of the working body of the damper over the hinged roller without sliding and the load-carrying body are deduced and numerically analyzed. A new procedure is proposed for the evaluation of the optimal parameters of adjustment of roller dampers in nonlinear systems.     

Stability of Circular Cylindrical Shells with a Single Local Dent

The theoretical-and-experimental investigation has been performed on the stability of smooth cylindrical shells of steel with a single local dent. All the shells manufactured using the same process were tested with the fulfillment of identical conditions for observations and measurements. Theoretical calculations were carried out by the mesh method with the use of the nonlinear theory of shells. A comparison of the experimental and theoretical values of the critical loads has been made. The theoretical-and-experimental approach proposed enables one to evaluate the quality of shells by studying local dents and other specific imperfections.     

Life Calculations for Header – PGV-1000 Steam Generator Connector Weld Joints under NPP Service Conditions

The procedure for calculating the life of header – steam generator connector weld joints is proposed. It allows for running out the material plasticity reserve upon static cyclic elastoplastic loading as well as operating conditions, local stress concentrations, and residual stresses after welding.     

Analysis of the Ductile Strength of Welds Weakened by Notches in Longitudinally Welded Pipes of Large Diameter by the Method of Slip Lines

We study the stressed state of an inhomogeneous welded joint containing an interlayer of a more high-strength material under the action of tensile loads. It is assumed that the contact boundary has a cracklike defect. We deduce analytic dependences of the fracture load on the mechanical inhomogeneity of the joint, thickness of the interlayer, and depth of the defect. The maximum depth of the defect to which the joint is insensitive is established. The proposed theoretical results are innovative and agree with the experimental data obtained for specimens cut out from a pipe of 14KhGS steel.     

A Mixed-Approach Analysis of Deformations in Pipe Bends. Part 3. Calculation of Bend Axis Displacements by the Method of Initial Parameters

A problem of deformation of a curved shell loaded by internal pressure, axial force, and temperature difference is discussed. Physical equations are derived whereby the displacements and angles of rotation of the line of centers of mass of cross sections of a shell are related to loading parameters. A general constitutive set of equations for a curved element during its deformation is given. Using a method of initial parameters, an analytical solution is obtained for the differential equations for displacements and angles of rotation of the center line allowing for the action of distributed forces and moments.     

Preparation and properties of heavy-metal halide glasses

We have studied the effect of In³⁺, Pb²⁺, Gd³⁺, and Cl (heavier ions) substitutions for Al³⁺, Ba²⁺, La³⁺, and F^? on the crystallization stability and UV/IR optical properties of HBLAN fluorohafnatc glasses (HfF₄-BaF₂-LaF₃-AlF₃-NaF system). We obtained stable glasses containing InF₃ and BaCl₂ instead of AlF₃ and BaF₂, respectively, and offering increased IR transmission. The presence of CCl₄ in the process atmosphere and the removal of oxygen-containing impurities via directional solidification are shown to have an advantageous effect on the optical quality of the glasses. The fluoride-chloride glasses are capable of accommodating about 1.5 times higher levels of rare-earth activators in comparison with their fluoride analogs.     

Novel Short-chain Crosslinked Cationomeric Polyurethanes

Summary Novel PUs containing pyridinium moieties were synthesized by chain extending isocyanate endcapped prepolymers with N, N’-bis (2-hydroxyethyl) isonicotinamide. The pyridinium moieties in the PUs were chemically crosslinked using short-chain divalent quaternising agents. The polyurethane cationomers were characterized by spectral, thermal and mechanical analysis. Spectral results confirmed the quaternisation of tertiary nitrogen leading to crosslinking. Compared to conventional PUs, the crosslinked PU networks exhibited improved thermal stability. The damping value (i.e.) tan δ for cationomers were improved over a broad temperature range when compared to conventional PU.     

Interaction of a ductile projectile with a brittle solid medium

The process of interaction of a ductile projectile with a many times harder brittle target is analyzed in the 500–1000 m/sec range of velocities. The effect of hardness of the target and its fragmentation on the penetration depth is shown.Translated from Problemy Prochnosti, No. 9, pp. 60–62, September, 1991.