Recurrence Relations for the Coefficients in Series Expansions with Respect to Semi-Classical Orthogonal Polynomials

Let {P _k } be a sequence of the semi-classical orthogonal polynomials. Given a function f satisfying a linear second-order differential equation with polynomial coefficients, we describe an algorithm to construct a recurrence relation satisfied by the coefficients a _k [f] in f= _k a _k [f]P _k . A systematic use of basic properties (including some nonstandard ones) of the polynomials {P _k } results in obtaining a recurrence of possibly low order. Recurrences for connection or linearization coefficients related to the first associated generalized Gegenbauer, Bessel-type and Laguerre-type polynomials are given explicitly.     

Bounded solutions of second-order systems of differential equations

Sufficient conditions for the existence, uniqueness and stability of the bounded (in ) solution of the second-order systems of nonlinear differential equations are given.     

Some estimates for the normal structure coefficient in Banach spaces

Estimates for the normal structure coefficientN(X) are obtained in the case where the modulus of convexity ofX is larger than the modulus of convexity of a right hexagon orX is uniformly smooth.     

The applicability of DTA to the study of the crystallisation process of ceramic fibres

?esták's method for the determination of the activation energy of the crystallisation of mullite in ceramic fibres has been applied. The investigations performed proved that the mechanism of the crystallisation of mullite is far from the classical theories describing the devitrification process of glass. The determination of the kinetic parameters by ?esták's method requires the verification of the introduced simplification every single time.     

Crystal and molecular structure of the (−)-N-hydroxyimide of (10-pinene-2-yl) succinimic acid

Two independent molecules in the unit cell are the same enantiomer of the title compound but possess slightly different conformations. Both conformers are joined by H-bonds to one water molecule. The configuration at C11 was established asR.Crystal data: C₁₄H₁₉O₃N×1/2H₂O; trigonal,P3₂;a=17.486(2),b=17.486(2),c=8.024(1)Å;V=2124.72(6)ų;Z=6; (CuK)=1.54178 Å;F(000)=834; finalR=0.0495 for 2376 reflections (of 2747 unique data).     

Molecular nitrogen-N2 properties: the intermolecular potential and the equation of state

Quantum mechanical (QM) high precision calculations were used to determine N(2)-N(2) intermolecular interaction potential. Using QM numerical data the anisotropic potential energy surface was obtained for all orientations of the pair of the nitrogen molecules in the rotation invariant form. The new N(2)-N(2) potential is in reasonably good agreement with the scaled potential obtained by van der Avoird et al. using the results of Hartree-Fock calculations [J. Chem. Phys. 84, 1629 (1986)]. The molecular dynamics (MD) of the N(2) molecules has been used to determine nitrogen equation of state. The classical motion of N(2) molecules was integrated in rigid rotor approximation, i.e., it accounted only translational and rotational degrees of freedom. Fincham [Mol. Simul. 11, 79 (1993)] algorithm was shown to be superior in terms of precision and energy stability to other algorithms, including Singer [Mol. Phys. 33, 1757 (1977)], fifth order predictor-corrector, or Runge-Kutta, and was therefore used in the MD modeling of the nitrogen pressure [S. Krukowski and P. Strak, J. Chem. Phys. 124, 134501 (2006)]. Nitrogen equation of state at pressures up to 30 GPa (300 kbars) and temperatures from the room temperature to 2000 K was obtained using MD simulation results. Results of MD simulations are in very good agreement (the error below 1%) with the experimental data on nitrogen equation of state at pressures below 1 GPa (10 kbars) for temperatures below 1800 K [R. T. Jacobsen et al., J. Phys. Chem. Ref. Data 15, 735 (1986)]. For higher temperatures, the deviation is slightly larger, about 2.5% which still is a very good agreement. The slightly larger difference may be attributed to the vibrational motion not accounted explicitly by rigid rotor approximation, which may be especially important at high temperatures. These results allow to obtain reliable equation of state of nitrogen for pressures up to 30 GPa (300 kbars), i.e., close to molecular nitrogen stability limit, determined by Nellis et al. [Phys. Rev. Lett. 53, 1661 (1984)].     

Polarization and transmission of microwaves in the magnetic suspension in the applied magnetic field

The production method of magnetic suspension consisting of ferromagnetic particles dispersed in cedarwood oil is presented at the beginning of this article. Next, the set-up for microwaves generation using a klystron is described. The main part of this paper concerning microwave transmission and polarization during its passage in samples of the produced magnetic suspension placed in a magnetic field is based on the following parameters: induction of this field, filling factor of magnetic suspension by ferromagnetic particles, dimensions of particles, viscosity of liquid carrier, and ratio of the magnetic field changes. Conducted investigations show that microwaves are damped and polarized in these magnetic suspensions. Obtained results are discussed and observed effects are explained by ordering of ferromagnetic particles in magnetic suspension by applied magnetic field.     

Analysis of lumped models with contact and friction

We consider two mathematical models that describe the vibrations of spring-mass-damper systems with contact and friction. In the first model, both the contact and frictional boundary conditions are described with subdifferentials of nonconvex functions. In the second model, the contact is modeled with a Lipschitz continuous function, and the restitution force is described by a differential equation involving a Volterra integral term. The two models lead to second-order differential inclusions with and without an integral term, in which the unknowns are the positions of the masses. For each model, we prove the existence of a solution by using an abstract result for first-order differential inclusions in finite dimensional spaces. For the second model, in addition, we prove the uniqueness of the solution by using a fixed point argument. Finally, we provide examples of systems with contact and friction conditions for which our results are valid.     

A weak law of large numbers for maxima

A weak law of large numbers related to the classical Gnedenko results for maxima (see Gnedenko, Ann Math 44:423–453, 1943) is established.     

The effect of alloying on the H-atom adsorption on the (100) surfaces of Pd-Ag,Pd-Pt,Pd-Au,Pt-Ag,and Pt-Au. A theoretical study

The effect of alloying on the adsorption of atomic hydrogen was studied using density functional theory (DFT). In the study the (100) surfaces of Pd-Ag, Pd-Pt, Pd-Au, Pt-Ag, and Pt-Au alloys were considered by means of a cluster model. The structural and energetic properties of the H atom adsorbed on the Pd₄Me (Me = Ag, Pt, Au) and Pt₄Me (Me = Pd, Ag, Au) clusters were calculated and compared with the H-atom adsorption on monometallic clusters. The effect of alloying on the H-atom adsorption is evident for all the investigated bimetallic systems. However, it strongly depends on the second metal atom, Me, is placed in the surface layer or in the subsurface one. In general, the H atom adsorbed in a site containing the second metal exhibits different properties from those characteristic of its adsorption on Pd(100) and Pt(100). Hence, the modified interaction between atomic hydrogen and the alloyed surfaces may increase the selectivity of the catalytic hydrogenation reactions on such surfaces.