Vibrational frequency shifts in the stretched polypropylene molecule

The GF matrix method is used to compute the changes in the skeletal vibration frequencies for a simplified model of isotactic polypropylene stretched by a loadf. The series of frequencies obtained atf=0 are identified with those experimentally observed. A linear approximation is used for the deformation potential energy atf=0–2·10^–4 dyneperchain. The results of the calculations are presented in graph form.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 586–594, July–August, 1968.     

An Assmus–Mattson-Type Approach for Identifying 3-Designs from Linear Codes over Z 4

The complete weight enumerator of the Delsarte–Goethals code over Z ₄ is derived and an Assmus–Mattson-type approach at identifying t-designs in linear codes over Z ₄ is presented. The Assmus–Mattson-type approach, in conjunction with the complete weight enumerator are together used to show that the codewords of constant Hamming weight in both the Goethals code over Z ₄ as well as the Delsarte–Goethals code over Z ₄ yield 3-designs, possibly with repeated blocks.     

Automated thermomechanograph for investigating polymer microsamples

An instrument has been developed for recording the thermomechanical curves of microsamples of polymers (30 mg) by the penetration method in the continuous heating regime. The thermomechanical curves are recorded by a PDS-021 two-coordinate recorder; the effective temperature range is 20–400°C.Institute of High-Molecular Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 746–749, July–August, 1968.     

Thermal effects in a glass laminate in tension

The results of a calorimetric investigation of a glass-reinforced textolite in uniaxial tension are presented. The specimens were deformed on the interval of strain rates from 0.3 to 10.5 mm/min at test temperatures from –30 to 80°C. The thermal effects are shown to depend on strain rate and test temperature.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 599–604, July–August, 1971.     

Infinite series of combinatorially regular polyhedra in three-space

The paper discusses polyhedral realizations in ordinary Euclidean 3-space of Coxeter's regular skew polyhedra {4, p|4 ^p/2]–1} and their duals on an orientable surface of genus 2 ^p–3(p–4)+1. Our considerations are based on work of Coxeter, Ringel and McMullen et al., revealing that certain polyhedral manifolds discovered by the last three authors are in fact the polyhedra in question. We also describe Kepler-Poinsot-type polyhedra in 3-space obtained by projections from Coxeter's regular skew star-polyhedra in 4 dimensions.     

Investigation of the adiabatic elasticity of polystyrene in the glass-transition region

Experimental results are presented for the density, absorption coefficient, and speed of ultrasound in a morphous polystyrene at frequencies of 375, 910, and 2350 kHz on the temperature interval 15–140°C. The glass-transition temperature does not depend on frequency. The adiabatic elasticity and characteristic impedance are calculated.Kolomna Branch of the All-Union Correspondence Polytechnic Institute. Translated from Mekhanika Polimerov, No. 4, pp. 746–749, July–August, 1973.     

Contact problems for beams and plates with low shear stiffness

The low shear stiffness and strength of unidirectionally reinforced plates and beams predetermines the choice of calculation model in specific problems [4]. The contact problem is considered for a glass-reinforced plastic plate resting on a Winkler foundation; the deformation properties of the plate are described by the equations of an orthotropic material; the investigation is based on generalized applied theories of the Timoshenko and Ambartsumyan types [5–8], which permit the high shear compliance of thin-walled structures to be taken into account.L'vov Polytechnic Institute; Ivan Franko Institute of Petroleum and Gas. Translated from Mekhanika Polimerov, No. 4, pp. 715–720, July–August, 1970.     

Investigation of the extremal directions in a glass-reinforced plastic

The extremal directions in an orthotropic material are investigated on the basis of six experimentally determined values of the investigated characteristic in the three planes of symmetry of the material.Translated from Mekhanika Polimerov, No. 4, pp. 742–745, July–August, 1971.     

Hyperbolic Manifolds, Harmonic Forms, and Seiberg–Witten Invariants

New estimates are derived concerning the behavior of self-dual harmonic 2-forms on a compact Riemannian 4-manifold with nontrivial Seiberg–Witten invariants. Applications include a vanishing theorem for certain Seiberg–Witten invariants on compact 4-manifolds of constant negative sectional curvature.     

Vibrations of a viscoelastic cylinder with an elastic shell

The nonlinear vibrations of a viscoelastic cylinder with an elastic shell subjected to two harmonic forces are investigated using the averaging scheme described in [3, 4]. Nonresonance, resonance, and subharmonic vibrations are examined. It is shown that the presence of viscosity in the system leads to a single stationary equilibrium position for which the stability conditions are given.V. I. Lenin Tashkent State University. Translated from Mekhanika Polimerov, No. 4, pp. 691–697, July–August, 1973.     

Polyethylene autohesion under simultaneous deformation

The strength of polyethylene autohesion joints obtained by simultaneous deformation is compared with that of compressed specimens of monolithic LPP. The probable mechanisms of polyethylene autohesion under these conditions are discussed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 656–660, July–August, 1968.     

Temperature-time dependence of the adhesion strength for polymer — Polymer systems

The temperature — time dependence of the adhesion strength has been studied for polymer systems differing in the thermodynamic compatibility of the substrate and adhesive and in the rate of polymerization of the latter. The fracture-activation energies of these systems have been calculated. It is shown that the temperature — time dependence of the adhesion strength varies depending on whether chemical intermolecular forces are responsible for the strength of the joint.Perm Scientific-Research Institute of Polymer Materials. A. M. Gor'kii Ural State University. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 665–671, July–August, 1968.     

State of stress and strain of plates with two equal openings in the presence of high-elastic deformation

The apparatus of the nonlinear theory of elasticity [1–3] is used to investigate the high-elastic deformation of a plate with two equal circular openings and a massive block with two cylindrical channels. Computer-calculated stress concentration factors are given for compressible and incompressible materials.Translated from Mekhanika Polimerov, No. 4, pp. 687–692, July–August, 1969.     

Stability of hinged viscoelastic rods under dynamic loading

Equations of Mathieu type describing the transverse vibrations of a straight viscoelastic rod compressed by a periodic longitudinal force are examined. The resonance regime is investigated by means of the method of averaging [2–4] in the case of a hinged viscoelastic rod acted upon by a periodic force.Institute of Cybernetics and Computer Center, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 6, pp. 1126–1129, November–December, 1973.     

Continuous-time mean–variance portfolio selection with liability and regime switching

A continuous-time mean–variance model for individual investors with stochastic liability in a Markovian regime switching financial market, is investigated as a generalization of the model of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean–variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466–1482]. We assume that the risky stock’s price is governed by a Markovian regime-switching geometric Brownian motion, and the liability follows a Markovian regime-switching Brownian motion with drift, respectively. The evolution of appreciation rates, volatility rates and the interest rates are modulated by the Markov chain, and the Markov switching diffusion is assumed to be independent of the underlying Brownian motion. The correlation between the risky asset and the liability is considered. The objective is to minimize the risk (measured by variance) of the terminal wealth subject to a given expected terminal wealth level. Using the Lagrange multiplier technique and the linear-quadratic control technique, we get the expressions of the optimal portfolio and the mean–variance efficient frontier in closed forms. Further, the results of our special case without liability is consistent with those results of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean–variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466–1482].     

Universal (Co) Homology Theories

It is shown that the homology and cohomology theories on separable C*–algebras given by nonstable E–theory are the universal such theories. By specializing to Abelian C*–algebras, we obtain a family of extraordinary Steenrod homology and cohomology theories on pointed compact metric spaces which are the universal such theories in the same way. For each of the extraordinary Steenrod (co)homology theories considered, we describe an –spectrum which represents the theory.     

Effect of small additives of oligomer on the viscoelastic properties of carbon fiber plastics

The viscoelastic properties of carbon fiber composites whose phenol-formaldehyde matrix is modified by thermodynamically incompatible isocyanate derivatives have been investigated. Data are given on fiber wetting (Table 11), internal stress (Table 2), viscoelastic properties (Fig. 1), and tensile strength (Fig. 2). The modified composites are strengthened by the addition of 0.5–4% oligomer additive. This process involves the formation of a two-phase structure, in which the additive phase microparticles act as a polymer filler. Due to selective interactions, the intermediate layer formed at the fiber-binder interface leads to changes in the viscoelastic properties and tensile strength of the matrix and improved maintenance characteristics for the material as a whole.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 440–445, July–August, 1993.     

The chemistry of coordinate polymerization of dienes

Conclusions This review has brought together the diverse ionic initiators for dienes into a consistent series of four polymerization mechanisms. The ionic freedom characteristic of the electrophilic and free anionic initiators catalyze the rapid formation of 1–4 trans structures. Coordinate initiation produces 1–4 cis structures via a cyclic transition state while anionic initiation produces 1–2 (3–4) structures.The catalytic activity in the coordinate and anionic catalysts depends largely on complex formation. The equilibrium characteristics of complex formation produces the different rate, structure and molecular weight effects observed in coordinate initiation studies.I wish to thank Drs. P. H.Moyer and M. R.Frederick for many helpful discussions of the mechanisms of coordinate polymerizations.     

Properties of multicomponent polymers systems

In order to design materials having different mechanical properties combined with a permittivity of 2.2–2.6 and tg =2·10^–4-4.10^–4 at 20±1° C and 10⁶ Hz, it is possible to use compositions consisting of polystyrene, polyisobutylene and polyethylene. Projections of the three-dimensional triangular composition-property diagrams are presented for selecting the composition corresponding to spcified properties (hardness at 20 and 50° C and breaking stress and elongation).Central Scientific-Research Institute of Communications, Moscow. Moscow Krupskaya Regional Pedagogical Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 133–1135, November–December, 1968.     

Decomposing the complete graph into cycles of many lengths

For all oddv 3 the complete graph onvK _v vertices can be decomposed intov – 2 edge disjoint cycles whose lengths are 3, 3, 4, 5,...,v – 1. Also, for all oddv 7,K _v can be decomposed intov – 3 edge disjoint cycles whose lengths are 3, 4,...,v – 4,v – 2,v – 1,v. Research supported by Australian Research Council grant A49130102