Investigation of the alumina properties with adsorbed polyvinyl alcohol

The influence of solution pH on the structure of polyvinyl alcohol adsorption layer on the alumina surface was investigated. The spectrophotometry, viscosimetry, thermogravimetry, potentiometric titration and microelectrophoresis were applied in experiments. These methods enable determination of the following parameters: adsorbed amount of PVA, stability of suspension without and with polymer, thickness of its adsorption layers, changes in thermal characteristics of Al₂O₃ surface with the adsorbed polymer, surface charge density and zeta potential of solid particles in the presence and absence of PVA, respectively. All measurements were carried out in the pH range 3–9. The obtained results indicate that pH has a great influence on the conformation of PVA chains adsorbed on the alumina surface. It is due to incomplete hydrolysis of acetate groups of polyvinyl alcohol macromolecules (degree of hydrolysis 97.5%), which dissociate with the increasing pH. Moreover, the polymer adsorption on the alumina surface causes changes in the course of thermogravimetric curves. The effect of weight loss for Al₂O₃–PVA systems is smaller than that of Al₂O₃ without polymer. It is due to elimination of water molecules from the solid surface by adsorbed polymer.     

History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics

We consider a class of subdifferential inclusions involving a history-dependent term for which we provide an existence and uniqueness result. The proof is based on arguments on pseudomonotone operators and fixed point. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Such kind of problems arises in a large number of mathematical models which describe quasistatic processes of contact between a deformable body and an obstacle, the so-called foundation. To provide an example we consider a viscoelastic problem in which the frictional contact is modeled with subdifferential boundary conditions. We prove that this problem leads to a history-dependent hemivariational inequality in which the unknown is the velocity field. Then we apply our abstract result in order to prove the unique weak solvability of the corresponding contact problem.     

Analysis of a time-dependent scheduling problem by signatures of deterioration rate sequences

In the paper a single machine time-dependent scheduling problem is considered. The processing time p_j of each job is described by a function of the starting time t of the job, p_j=1+α_jt, where the job deterioration rate α_j?0 for j=0,1,…,n and t?0. Jobs are nonpreemptable and independent, there are no ready times and no deadlines. The criterion of optimality of a schedule is the total completion time.First, the notion of a signature for a given sequence of job deterioration rates is introduced, two types of the signature are defined and their properties are shown. Next, on the basis of these properties a greedy polynomial-time approximation algorithm for the problem is formulated. This algorithm, starting from an initial sequence, iteratively constructs a new sequence concatenating the previous sequence with new elements, according to the sign of one of the signatures of this sequence.Finally, these results are applied to the problem with job deterioration rates which are consecutive natural numbers, α_j=j for j=0,1,…,n. Arguments supporting the conjecture that in this case the greedy algorithm is optimal are presented.     

Hemivariational inequalities for stationary Navier-Stokes equations

In this paper we study a class of inequality problems for the stationary Navier-Stokes type operators related to the model of motion of a viscous incompressible fluid in a bounded domain. The equations are nonlinear Navier-Stokes ones for the velocity and pressure with nonstandard boundary conditions. We assume the nonslip boundary condition together with a Clarke subdifferential relation between the pressure and the normal components of the velocity. The existence and uniqueness of weak solutions to the model are proved by using a surjectivity result for pseudomonotone maps. We also establish a result on the dependence of the solution set with respect to a locally Lipschitz superpotential appearing in the boundary condition.     

A model for so(5) = sp(4) lie algebra

The paper is the continuation of a previous one [Physica Scripta22 (1980), 545–555] devoted to quadrupling in the shell model. We consider here a simple model of the ten- dimensional quasi-spin Lie algebra which is spectrum generating for the quadrupling Hamiltonian. The model allows us to investigate many concrete aspects of the theory of linear representations of the quasi-spin algebra. In particular, we present an explicit construction of the irreducible representation module for the finite dimensional representations, and we consider the direct product of the such irreducible modules.     

Frequency doubling of laser light in an isotropic medium with electrically destroyed centre of inversion

The non-zero non-linear susceptibility tensor components ² (E ⁰)which account for frequency doubling of laser light in a naturally isotropic medium immersed in a DC efectric field (E ⁰) are discussed. The conditions for extremal second harmonic generation (SHG) are derived, which depend onE ⁰ and on the incident laser intensity but primarily on the microstructure of the medium. With growingE ⁰, the susceptibilities ² (E ⁰) increase for cigar-like microsystems but decrease for disc-shaped ones, according to whether the induced dipole helps or hinders the permanent dipole in reorienting the microsystem along (E ⁰). Non-linear electronic distortion alone is insufficient for explaining the anomalous experimental results.Generally, upon the electrically induced anisotropy, an anisotropy self-induced by the laser beam is superimposed, with optical axis along the propagation direction if the beam is circularly polarised or unpolarised, or along the oscillation direction of the light vector if it is linearly polarised.Extremal anisotropy of the medium occurs at saturation of electric or optical reorientation. This is experimentally inachievable in molecular substances even with very strong fields but is easy to obtain in solutions of macromolecules or colloid particles, where yet other opto-electronic processes intervene significantly.     

Analysis of a dynamic contact problem for electro-viscoelastic cylinders

We consider a mathematical model which describes the antiplane shear deformations of a piezoelectric cylinder in frictional contact with a foundation. The process is mechanically dynamic and electrically static, the material behavior is described with a linearly electro-viscoelastic constitutive law, the contact is frictional and the foundation is assumed to be electrically conductive. Both the friction and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is of the form of a system coupling a second order hemivariational inequality for the displacement field with a time-dependent hemivariational inequality for the electric potential field. Then we prove the existence of a unique weak solution to the model. The proof is based on abstract results for second order evolutionary inclusions in Banach spaces. Finally, we present concrete examples of friction laws and electrical conductivity conditions for which our result is valid.     

Phase behavior of four homologous compounds of 4-n-alkyl-4′-isothiocyanatobiphenyl (nBT) under pressure

The phase behavior of four homologous compounds of 4-n-nonyl-, 4-n-decyl-, 4-n-undecyl-, and 4-n-dodecyl-4′-isothiocyanatobiphenyl (9BT, 10BT, 11BT, and 12BT) was re-investigated to characterize their high-pressure mesophases under pressures up to 150 MPa using a polarizing optical microscope equipped with a high-pressure optical cell and a wide-angle X-ray diffractometer equipped with a high-pressure sample vessel. The pressure-induced mesophases of 9BT and 10BT appearing under pressures above about 60 and 100 MPa, respectively, were identified as nematic (N) and SmA phases, which indicate the reversible Cr–CrE–N–I and Cr–CrE–SmA–I phase transitions under elevated pressure. 11BT and 12BT exhibited the reversible transition of Cr–CrE–SmA–I in the low-pressure regions below about 5 and 23 MPa, respectively. Both the stable CrE phases changed into the monotropic (and metastable) one under higher pressures, in which the Cr–SmA–I and I–SmA–CrE–Cr phase transitions on heating and cooling processes, respectively, were recognized.