Effect of the molecular weight of the polystyrene matrix on the physicomechanical properties of impact polystyrene

The effect of the molecular weight of the polystyrene on the properties of impact polystyrene obtained by mechanical mixing of polystyrene and rubber has been investigated. As the molecular weight of the polystyrene increases, the physicomechanical properties of the impact polystyrene improve and its rheological properties deteriorate. There is a definite correlation between the physicomechanical properties of the polystyrene and those of the impact polystyrene.Scientific-Research Institute of Synthetic Rubber, Kralupy-on-Vltava, Czechoslovakia. Translated from Mekhanika Polimerov, No. 3, pp. 545–546, May–June, 1971.     

Wavelet-type Transform and Bessel Potentials Associated with the Generalized Translation

Wavelet–type transform associated with singular Laplace–Bessel differential operator is introduced and the relevant Calderón–type reproducing formula is established. Representations of the generalized Bessel potentials 0)$ " align="middle" border="0"> and their inverses via the wavelet–type transform are obtained.     

A Family of Semi-Regular Divisible Difference Sets

We give a construction of semi-regular divisible difference sets with parametersm = p2a(r–1)+2b (pr – 1)/(p – 1), n = pr, k = p(2a+1)(r–1)+2b (pr – 1)/(p – 1)1 = p(2a+1)(r–1)+2b (pr–1 – 1)/(p-1), 2 = p2(a+1)(r–1)–r+2b (pr – 1)/(p – 1)where p is a prime and r a + 1.     

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.     

Effect of fillers and solvents on the properties of polystyrene coatings

The mechanism of coating formation from solutions of atactic polystyrene in xylene and carbon tetrachloride has been investigated. It has been established that, as the filler content increases, in coatings formed from polystyrene solutions containing an evaporating solvent the growth of the internal stresses and the thermophysical characteristics is characterized by similarity of slope, as distinct from the case of coatings obtained from systems containing a polymerizing solvent. It is shown that the nature of the solvent has an important effect on the character of the interaction at the polymer—filler interface and on the structure and properties of the coatings.Kucherenko Central Scientific-Research Institute of Structural Design. Institute of Physical Chemistry, AS USSR, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1127–1129, November–December, 1968.     

On the Spectrum of the Sizes of Maximal Partial Line Spreads in <Emphasis Type="Italic">PG</Emphasis>(2<Emphasis Type="Italic">n</Emphasis>,<Emphasis Type="Italic">q</Emphasis>), <Emphasis Type="Italic">n</Emphasis> ≥ 3

A lot of research has been done on the spectrum of the sizes of maximal partial spreads in PG(3,q) [P. Govaerts and L. Storme, Designs Codes and Cryptography, Vol. 28 (2003) pp. 51–63; O. Heden, Discrete Mathematics, Vol. 120 (1993) pp. 75–91; O. Heden, Discrete Mathematics, Vol. 142 (1995) pp. 97–106; O. Heden, Discrete Mathematics, Vol. 243 (2002) pp. 135–150]. In [A. Gács and T. Sznyi, Designs Codes and Cryptography, Vol. 29 (2003) pp. 123–129], results on the spectrum of the sizes of maximal partial line spreads in PG(N,q), N 5, are given. In PG(2n,q), n 3, the largest possible size for a partial line spread is q^2n-1+q^2n-3+...+q³+1. The largest size for the maximal partial line spreads constructed in [A. Gács and T. Sznyi, Designs Codes and Cryptography, Vol. 29 (2003) pp. 123–129] is (q²ⁿ⁺¹–q)/(q²–1)–q³+q²–2q+2. This shows that there is a non-empty interval of values of k for which it is still not known whether there exists a maximal partial line spread of size k in PG(2n,q). We now show that there indeed exists a maximal partial line spread of size k for every value of k in that interval when q 9.J. Eisfeld: Supported by the FWO Research Network WO.011.96NP. Sziklai: The research of this author was partially supported by OTKA D32817, F030737, F043772, FKFP 0063/2001 and Magyary Zoltan grants. The third author is grateful for the hospitality of Ghent University.     

Light absorption and laser-crack development. 2

Conclusions 1. The gray color of a laser crack in PMMA (black in polystyrene) is caused by carbon-black particles that adhere to its walls.2. Further experimentation under an electron microscope is necessary to determine the size of the carbon-black particles. Making use of these new data and the results described here, we can define their absorption index more precisely.3. The absorption index of the gaseous medium between the walls of the crack in a layer 30–100 µ thick is 20 cm^–1; this is 1000 times smaller than that of graphite, but approximately 1000 times greater than that of the ordinary block polymer.4. As a result of photochemical and photothermal reactions, the laser source creates a gray (PMMA) or black (polystyrene) absorbent layer located in the crack and on its walls. Thus, the energy of the laser beam is absorbed due to "self-inductive" opacity. This leads to an increase in the mass of the "gas wedge," to a pressure increase, and ultimately, to crack propagation.For communication 1, see [1].Institute of the Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 409–412, May–June, 1977.     

On Inversion Of Bessel Potentials Associated With The Laplace–Bessel Differential Operator

Explicit inversion formulas of Balakrishnan–Rubin type and a characterization of Bessel potentials associated with the Laplace–Bessel differential operator are obtained. As an auxiliary tool the B-metaharmonic semigroup is introduced and some of its properties are investigated.     

Some properties of the quasimomentum of the one-dimensional Hill operator

In this paper, a study is made of the properties of the energy E(k) of the Hill operator, as a function of the global quasimomentum k, running over the Riemann surface of the quasimomentumK. A study is made of , Ë on the straight line Im k=0, and of the location of the zeros of Ë. For example: 1) the function on the straight line Im k=0 between zeros has only one local maximum or minimum, 2) in the case of an N-zone potential, the function Ë has exactly 6(N–1) zeros inK, N–1 zeros both on the positive (negative) semiaxes, and in each quadrant.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 195, pp. 48–57, 1991.     

Stability of a Pivoting Strategy for Parallel Gaussian Elimination

Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by _n <#60; 3 ^n–1, as compared to 2 ^n–1 for the standard partial pivoting. This bound _n, close to 3 ^n–2, is attainable for class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting.This revised version was published online in October 2005 with corrections to the Cover Date.     

Structural susceptibility of strength characteristics of polystyrene under uniaxial stretching

The structural susceptibility of the strength characteristics of polystyrene under uniaxial stretching and under test conditions with = const and v_elong = const was studied at 20–100°C. The low structural susceptibility of the durability and durability-equation parameters is due to a change in the elementary fracture volume at different test conditions. It was proposed to characterize the degree of participation of chemical and intermolecular forces by the value U₀/.Moscow Technological Institute of Meat and Milk Industry. Translated from Mekhanika Polimerov, No. 6, pp. 979–984, November–December, 1974.     

Density changes in stretched polymers

Data are presented on the relation between the density of polystyrene and polyvinyl alcohol specimens and the relative elongation. The change in density observed during the stretching of polyvinyl alcohol specimens is associated with changes in the optical density of the 1146 cm^–1 band and the crystalline phase content of the polymer.Mekhanika Polimerov, Vol. 3, No. 5, pp. 777–781, 1967     

Implicit function theorems for generalized equations

We show that Lipschitz and differentiability properties of a solution to a parameterized generalized equation 0 f(x, y) + F(x), wheref is a function andF is a set-valued map acting in Banach spaces, are determined by the corresponding Lipschitz and differentiability properties of a solution toz g(x) + F(x), whereg strongly approximatesf in the sense of Robinson. In particular, the inverse map (f + F)^–1 has a local selection which is Lipschitz continuous nearx ₀ and Fréchet (Gateaux, Bouligand, directionally) differentiable atx ₀ if and only if the linearization inverse (f (x ₀) + f (x₀) (× – x₀) + F(×))^–1 has the same properties. As an application, we study directional differentiability of a solution to a variational inequality.This work was supported by National Science Foundation Grant Number DMS 9404431.     

New Families of Complete Caps, and the Asymptotic Size of the Largest Caps, of Quadrics over Prime Fields

A cap of a quadric is a set of its points whose pairwise joins are all chords. Such a cap is complete if it is not part of a larger one. Few examples of complete caps are known except for quadrics in low dimensions. In this paper, we consider the case when the coordinate field is GF(p), with p an odd prime, and construct, in each projective space GF(n,p) with n p – 1 and n – 2(mod p), a cap on one of its nonsingular quadrics. We use this in two ways. Firstly, we combine its size with the recent Blokhuis–Moorhouse upper bound for quadric caps to show that the size of the largest cap of any nonsingular quadric in PG(N,p) is asymptotic to Np – 1/(p – 1) ! as N tends to infinity. Secondly, by establishing situations when our cap is complete, we produce various infinite families of complete quadric caps over GF(p) for each p. Earlier work determined all complete caps of all nonsingular quadrics over GF(2).     

Supersymmetric p-branes at finite temperature

The regularized free energy of open and closed supersymmetric p-branes in (D – 1)-dimensional flat space is calculated by the method of quasiclassical quantization. The critical temperature, indicating a phase transition, is obtained. It is shown that the quantum properties of bosonic p-branes (open and closed) with p = D – 1 are identical to the properties of a massless scalar particle.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akademii Nauk SSSR, Vol. 180, pp. 36–40, 1990.     

Properties of reinforced polystyrene in short-time tension,compression, and bending

The mechanical properties of reinforced polystyrene in short-time tension, compression, and bending have been experimentally investigated. Specimens of nine different reinforced-polystyrene compositions with reinforcement ratios of 18.7, 12, and 6.75% and wire diameters of 2, 1, and 0.5 mm were tested. The reinforcement consisted of steel or brass wire. The method of preparing the laboratory specimens is described. The principal results of machine tests on reinforced- and unreinforced-polystyrene specimens are presented. It is shown that certain reinforced-polystyrene compositions possess the properties of a Cosserat medium.Kharkov Structural Engineering Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1059–1064, November–December, 1968.     

The acoustic properties of polymers with an asymmetric potential barrier at liquid-helium temperatures

The pulse-phase compensation method has been used to measure the propagation velocities of longitudinal and shear waves in polyvinyl chloride, polyvinyl fluoride, and polystyrene at frequencies of 1 and 5 MHz on the temperature interval 2.1–240°K. It has been established that as the temperature falls to 2.1°K the speed of ultrasound in these polymers monotonically increases, the dispersion (frequency dependence) of the speed of sound being preserved over the entire temperature interval. Two possible causes of the viscoelastic relaxation observed in the investigated polymers in the region of helium temperatures are considered.Scientific-Research Institute of Plastics, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 749–751, July–August, 1973.     

Ebene algebraische Kurven vom Typ p,q

Let p,q be relatively prime integers with 2pr ^p,q be the numerical semigroup generated by p,q,{(p–1) (q–1)–1–(ip+jq)¦i+jr–2}. Then there exists a smooth projective curve X and a point x on X, such that H _r ^p,q is the set of orders of poles of the rational functions on X, which are regular on X\{x}; in other words: H _r ^p,q is a Weierstraß semigroup.     

Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames

This paper is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [17]. The paper [17] derives, by means of a three-scale matched asymptotics, starting from the classical thermo-diffusive model with high activation energies, an integro-differential equation for the flame radius. In the derivation, it is essential for the Lewis Number – i.e. the ratio between thermal and molecular diffusion – to be strictly less than unity. If is the inverse of the – reduced – activation energy, the idea underlying the construction of [17] is that (i) the time scale of the radius motion is ^-2, and that (ii) at each time step, the solution is -close to a steady solution.In this paper, we give a rigorous proof of the validity of this model under the restriction that the Lewis number is close to 1 – independently of the order of magnitude of the activation energy. The method used comprises three steps: (i) a linear stability analysis near a steady – or quasi-steady – solution, which justifies the fact that the relevant time scale is ^-2; (ii) the rigorous construction of an approximate solution; (iii) a nonlinear stability argument. Mathematics Subject Classification (2000) Primary 80A25, Secondary 35K57, 47G20     

Effect of cyclic cooling to low temperatures on the adhesive strength of fiber-thermoplastic matrix joints

The adhesive strength of the interface between the polyarylene sulfone PSK-1 and a steel wire 150 mm in diameter was measured using a pull-out technique after cyclic cooling of the joints from room temperature down to liquid nitrogen temperature. All specimens were prepared under isothermal conditions (300 °C, 30 min) without applying pressure. The number of cycles N of plunging in liquid nitrogen reached 900. All measurements were taken at room temperature with constant loading rate. The joint areas S were varied within a wide range. It was found that ten cooling cycles do not cause any appreciable change in the values of (Figs. 1–3). After 100 cooling cycles, the adhesive strength losses reached 30–45% (Figs. 1–3). After 810 cycles, the fiber-matrix interface is almost totally destroyed (Fig. 1). As the number of cycles N increases, the character of the dependence of the adhesive strength on the joint area changes: when N < 100, the values of are reduced as the interfacial surface area increases; when N = 810, the adhesive strength does not depend on S. The main factor that governs the reduction in adhesive strength is assumed to be residual thermal stresses. Analysis of the data obtained here and earlier shows that the behavior of polymer-fiber systems after cyclic cooling down to low temperatures is the same for both network and linear polymer matrices. The origin of this behavior also seems to be the same for all polymer-fiber adhesive joints.Report presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 156–162, March–April, 1995.This work was done with the support of the International Science Foundation (the G. Soros Foundation), grant NED000.