Self-adhesion of amorphous polymers and their miscible blends

The amorphous film surfaces of polystyrene (PS), poly(2,6-dimethyl 1,4-phenylene oxide) (PPO), and their miscible blends are brought into overlap contact below the glass transition temperature T _g for 10 min and 24 h in order to obtain PS—PS, PPO—PPO, and blend—blend self-adhesive joints. It is shown that after the contact of the blend surfaces, i.e., when the molecules of both PS and PPO are present at the interface, it is possible to attain higher values of shear strength as compared with those at PS—PS and PPO—PPO interfaces. This points to the contribution of a specific interaction between the segments of PS and PPO to the strength development at the interface. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 1, pp. 127–135, 2000.     

Morphology of fractured polymer surfaces self-bonded below the glass transition temperature

Previosly noncontact surfaces of polystyrene (PS) and poly(2,6-dimethyl 1,4-phenylene oxide) (PPO) were self-bonded in a lap shear joint geometry below the glass transition temperature T_g The joints were then fractured in tension at room temperature and the contact area was analyzed by means of scanning electron microscopy. Zones of plastic deformation were revealed on the surfaces of PS and PPO which had been bonded at T_g–33 and T_g–70°C, respectively, thus indicating interdiffusion across the interface. This result points to the lower T_g of the surface layer as compared with that of the bulk sample, in agreement with our previous studies. The unusually high self-bonding ability of PPO (at very low temperatures related to the bulk T_g) is presumably due to the low depth of penetration required to establish entanglements.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 665–672, September–October, 1998.     

Relationship between the Contact Time of Polymer Surfaces and Their Bond Strength

Films of amorphous polystyrene (PS) (mono- and polydisperse polymers) and poly(phenylene oxide) (PPO) were brought into contact at a low pressure (0.8 MPa) under temperatures T _h from 62 to 156°C. The contact time t was varied from 2 min to 96 h. Partially healed PS-PS, PPO-PPO, and PS-PPO contacts were broken at room temperature and the shear strength in the contact zone was measured. The experimental -t curves were analyzed in double logarithmic coordinates. The value of for the three interfaces investigated was within 0.07-0.32 at T _h < T _g, where is the glass transition temperature. In the same way, the data on strength development taken from the literature for a number of polymer-polymer contacts formed both above and below T _g were analyzed, and the range of variations in proved to be roughly the same (0.05-0.35). The results obtained are discussed within the framework of theories of molecular dynamics for the polymer bulk and the interface.     

Investigation of the friction of rubber under constant compressive strain conditions at low pressure

A vacuum tribometer was developed which was used to investigate the maximum friction force occurring at the initial instant of slipping in rubber-metal friction pairs under conditions of a given (from 5 to 40%) compressive strain at a low pressure in the temperature range from +100 to –100°C. Filled rubbers on a base of nitrile-butadiene rubbers were studied. Up to the glass transition temperature T_g the vacuum had practically no effect on the maximum friction frocef _m; at temperatures T_g and lower the values off _m obtained in a vacuum were 10–15% higher than those obtained in the atmosphere. It is shown that with a decrease of temperature from 20°C to the glass transition temperature T_g the slope of the dependence of the maximum friction force on the degree of deformation increases, and below T_g decreases. The effect of the slipping speed v on the maximum friction forcef _m was also studied.Laboratory of Polymer Physics, V. I. Lenin Moscow State Pedagogical Institute. Leningrad Branch, Scientific Research Institute of the Rubber Industry. Translated from Mekhanika Polimerov, No. 3, pp. 486–492, May–June, 1970.     

Effective action and collective bose-excitations in the T-J-model

The two-dimensional (2D) t-T-model is investigated using the functional integration method. The effective action is obtained, and the spectrum of collective Bose-excitations in the superconductive phase of the system is calculated both in the phase-transition vicinity (Ginsburg-Landau region |T−T_c| ≪ T_c) and in the low-temperature region T ≪ T_c. Bibliography: 26 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 224, 1995, pp. 300–309. Translated by P. A. Sevastianov.     

Controllability in a filled domain for the multidimensional wave equation with a singular boundary control

In accordance with the demands of the so-called local approach to inverse problems, the set of “waves” u^f (·, T) is studied, where u^f (x,t) is the solution of the initial boundary-value problem u_tt−Δu=0 in Ω×(0,T), u|_t<0=0, u|_∂Ω×(0,T)=f, and the (singular) control f runs over the class L²((0,T); H^−m (∂Ω)) (m>0). The following result is established. Let Ω^T={x ∈ Ω : dist(x, ∂Ω)<T)} be a subdomain of Ω ⊂ ℝⁿ (diam Ω<∞) filled with waves by a final instant of time t=T, let T_*=inf{T : Ω^T=Ω} be the time of filling the whole domain Ω. We introduce the notation D_m=Dom((−Δ)^m/2), where (−Δ) is the Laplace operator, Dom(−Δ)=H²(Ω)∩H ₀ ¹ (Ω);D_−m=(D_m)′;D_−m(Ω^T)={y∈D_−m:supp y ⋐ Ω^T. If T<T., then the reachable set R _m ^T ={u^t(·, T): f ∈ L₂((0,T), H^−m (∂Ω))} (∀m>0), which is dense in D_−m(Ω^T), does not contain the class C ₀ ^∞ (Ω^T). Examples of a ∈ C ₀ ^∞ , a ∈ R _m ^T , are presented. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 7–21. Translated by T. N. Surkova.     

Collective excitations in the ferro-and antiferromagnetic states of the two-dimensional repulsive Hubbard model

Collective excitations in the antiferromagnetic and ferromagnetic states of the two-dimensional repulsive Hubbard model are investigated both in the phase transition vicinity (Ginsburg-Landau region |T−T_c|≪T_c) and in the low-temperature region T≪T_c using the functional integration method. The spectrum of collective excitation consists of one branch at T>T_c, and another branch (Goldstone branch) arises at T<T_c. The Goldstone branch at T≪T_c in the antiferromagnetic state is calculated including the anisotropic correction term to the linear dispersion law. The value of the nonphonon branch at the zero momentum is equal to the double gap of the fermion energy 2Δ. All the spectrum branches in the ferromagnetic state vanish at zero momentum . Bibliography: 6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 229–259. Translated by P. A. Sevastianov.     

Existence principles for higher-order nonlocal boundary-value problems and their applications to singular Sturm-Liouville problems

We present existence principles for the nonlocal boundary-value problem (φ(u^(p−1)))′=g(t,u,...,u^(p−1), α_k(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α _k: C ^p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)ⁿ(φ(u⁽²ⁿ⁻⁾))′=f(t,u,...,u⁽²ⁿ⁻¹⁾), u^(2k)(0)=0, α_ku^(2k)(T)+b_ku^(2k=1)(T)=0, 0≤k≤n−1, is given. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008.     

Fourier Series with the Continuous Primitive Integral

Fourier series are considered on the one-dimensional torus for the space of periodic distributions that are the distributional derivative of a continuous function. This space of distributions is denoted A_c(\mathbbT){\mathcal{A}}_{c}(\mathbb{T}) and is a Banach space under the Alexiewicz norm, ||f||_\mathbbT=sup_{|I| ￡ 2p}|ò_I f|\|f\|_{\mathbb{T}}=\sup_{|I|\leq2\pi}|\int_{I} f|, the supremum being taken over intervals of length not exceeding 2π. It contains the periodic functions integrable in the sense of Lebesgue and Henstock–Kurzweil. Many of the properties of L ¹ Fourier series continue to hold for this larger space, with the L ¹ norm replaced by the Alexiewicz norm. The Riemann–Lebesgue lemma takes the form [^(f)](n)=o(n)\hat{f}(n)=o(n) as |n|→∞. The convolution is defined for f ? A_c(\mathbbT)f\in{\mathcal{A}}_{c}(\mathbb{T}) and g a periodic function of bounded variation. The convolution commutes with translations and is commutative and associative. There is the estimate ||f*g||_￥ ￡ ||f||_\mathbbT ||g||_BV\|f\ast g\|_{\infty}\leq\|f\|_{\mathbb{T}} \|g\|_{\mathcal{BV}}. For g ? L¹(\mathbbT)g\in L^{1}(\mathbb{T}), ||f*g||_\mathbbT ￡ ||f||_{\mathbb T} ||g||₁\|f\ast g\|_{\mathbb{T}}\leq\|f\|_{\mathbb {T}} \|g\|_{1}. As well, [^(f*g)](n)=[^(f)](n) [^(g)](n)\widehat{f\ast g}(n)=\hat{f}(n) \hat{g}(n). There are versions of the Salem–Zygmund–Rudin–Cohen factorization theorem, Fejér’s lemma and the Parseval equality. The trigonometric polynomials are dense in A_c(\mathbbT){\mathcal{A}}_{c}(\mathbb{T}). The convolution of f with a sequence of summability kernels converges to f in the Alexiewicz norm. Let D _n be the Dirichlet kernel and let f ? L¹(\mathbbT)f\in L^{1}(\mathbb{T}). Then ||D_n*f-f||_\mathbbT?0\|D_{n}\ast f-f\|_{\mathbb{T}}\to0 as n→∞. Fourier coefficients of functions of bounded variation are characterized. The Appendix contains a type of Fubini theorem.     

Influence of the gravity on interface shape during crystal growth of LICAF

A Galerkin finite element method, together with the boundary conformal mapping technique, is used to investigate the change of melWcrystal interface under low gravity during the growth of LEAF system. Results have shown that strong convection can cause a deeply concave interface toward the crystal, and significantly increase radial thermal gradients near the interface. The flow intensity and the change of the gravity have a linear relationship under low gravity (g _o u = 10⁻²-10⁻⁶). At smallMa number, the maximum acceleration for keeping a planar growth interface is g_max = 1 × 10⁻³ g under our given conditions. In addition, the growth velocity may have some influence on the growth interface shape even atpg gravity level, indicating that the growth velocity cannot be too fast even when convection is very weak.     

A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.     

Temperature inversion symmetry in gauge-Higgs unification models

We study the temperature inversion symmetry R → 1/T for the finite-temperature effective potential of the N=1, d=5 supersymmetric SU(3) _c ×SU(3) _w model on the orbifold S ¹ /Z ₂ . For the value of the Wilson line parameter α = 1 (SU(2) _L breaks to U′(1)), we show that the effective potential contains a symmetric part and an antisymmetric part under ξ → 1/ξ, ξ = RT. For α = 0 (SU(2) _L is preserved in this case), we find that the only contribution to the effective potential that breaks the temperature inversion symmetry comes from the fermions in the fundamental representation of the gauge group with the Z ₂ parities (+, +) or (−,−). This is interesting because it implies that the bulk effective potential corresponding to models with fundamental fermions localized at a fixed point in the orbifold (and models with no bulk fundamental fermions) has the temperature inversion symmetry. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 1, pp. 109–130, April, 2009.     

Some remarks on the (f, g)-linear connections

In this note we consider structures defined on a differentiable manifoldM by a tensor fieldf of type (1,1) satisfying the conditionf ⁴+f ²=0 and by a Riemannian structureg such thatg(f(X),Y)=−g(Xf(Y)) for all vector fieldsX,YεT ¹ ₀(M). Then we determine linear connections compatible with those structures. Facultatea de Matematica, Str. Academiei 14, 70109 Bucaresti, Romania. Published in Lietuvos Matematikos Rinkinys, Vol. 37, No. 3, pp. 383–387, July–September, 1997.     

On optimal condition numbers for Markov chains

Let T and be arbitrary nonnegative, irreducible, stochastic matrices corresponding to two ergodic Markov chains on n states. A function κ is called a condition number for Markov chains with respect to the (α, β)–norm pair if . Here π and are the stationary distribution vectors of the two chains, respectively. Various condition numbers, particularly with respect to the (1, ∞) and (∞, ∞)-norm pairs have been suggested in the literature. They were ranked according to their size by Cho and Meyer in a paper from 2001. In this paper we first of all show that what we call the generalized ergodicity coefficient , where e is the n-vector of all 1’s and A ^# is the group generalized inverse of A = I − T, is the smallest condition number of Markov chains with respect to the (p, ∞)-norm pair. We use this result to identify the smallest condition number of Markov chains among the (∞, ∞) and (1, ∞)-norm pairs. These are, respectively, κ ₃ and κ ₆ in the Cho–Meyer list of 8 condition numbers. Kirkland has studied κ ₃(T). He has shown that and he has characterized transition matrices for which equality holds. We prove here again that 2κ ₃(T) ≤ κ(6) which appears in the Cho–Meyer paper and we characterize the transition matrices T for which . There is actually only one such matrix: T = (J _n  − I)/(n − 1), where J _n is the n × n matrix of all 1’s. This research was supported in part by NSERC under Grant OGP0138251 and NSA Grant No. 06G–232.     

An example concerning the nonlinear pointwise ergodic theorem

It is shown that the pointwise ergodic theorem for Markov operators inL ₁, having a finite invariant measure, fails to extend to the case of nonlinear operators. Recall thatT is called nonexpansive inL _p if ‖Tf – Tg ‖ _p ≦‖f – g‖ _p holds for allf andg.     

Cellulose-Based Composite Films

The mechanical and optical properties of cellulose-based composite films are investigated.It is shown that the use of toluene diisocyanate as a coupling agent and Avicel fibers as reinforcing elements give films with the highest mechanical characteristics. Using differential scanning calorimetry, it is also found that the glass transition temperature T _g of all the materials studied is below the room temperature and that the T _g increased with cross-linking and introduction of Avicel.     

Description of weakly periodic Gibbs measures for the isingmodel on a cayley tree

We introduce the concept of a weakly periodic Gibbs measure. For the Ising model, we describe a set of such measures corresponding to normal subgroups of indices two and four in the group representation of a Cayley tree. In particular, we prove that for a Cayley tree of order four, there exist critical values T _c < T _cr of the temperature T > 0 such that there exist five weakly periodic Gibbs measures for 0 < T < T _c or T > T _cr , three weakly periodic Gibbs measures for T = T _c , and one weakly periodic Gibbs measure for T _c < T ≤ T _cr . __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 292–302, August, 2008.     

The solvability of a boundary-value periodic problem

In the space of functions B _a³⁺={g(x, t)=−g(−x, t)=g(x+2π, t)=−g(x, t+T₃/2)=g(x, −t)}, we establish that if the condition aT ₃ (2s−1)=4πk, (4πk, a (2s−1))=1, k ∈ ℤ, s ∈ ℕ, is satisfied, then the linear problem u _u −a ² u _xx =g(x, t), u(0, t)=u(π, t)=0, u(x, t+T ₃ )=u(x, t), ℝ², is always consistent. To prove this statement, we construct an exact solution in the form of an integral operator. Ternopol’ Pedagogical Institute, Ternopol’. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 302–308, Feburary, 1997 Ternopol’ Pedagogical Institute, Ternopol’. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 302–308, Feburary, 1997     

Coboundaries of irreducible markov operators onC(K)

LetK be a compact Hausdorff space, and letT be an irreducible Markov operator onC(K). We show that ifgεC(K) satisfies sup _N ‖Σ _j ^=0N T ^j g‖<∞, then (and only then) there existsfεC(K) with (I − T)f=g. Generalizing the result to irreducible Markov operator representations of certain semi-groups, we obtain that bounded cocycles are (continuous) coboundaries. For minimal semi-group actions inC(K), no restriction on the semi-group is needed.