Line graphs of bipartite graphs with Hamiltonian paths

It is shown that, if t is an integer ≥3 and not equal to 7 or 8, then there is a unique maximal graph having the path P_t as a star complement for the eigenvalue ?2. The maximal graph is the line graph of K_m,m if t = 2m?1, and of K_m,m+1 if t = 2m. This result yields a characterization of L(G ) when G is a (t + 1)‐vertex bipartite graph with a Hamiltonian path. The graphs with star complement P_r ∪ P_s or P_r ∪ C_s for ?2 are also determined. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 137–149, 2003     

Acoustic waves in random fields

The effect of space- and time-dependent random mass density, velocity, and pressure fields on frequencies and amplitudes of acoustic waves is considered by means of the analytical perturbative method. The analytical results, which are valid for weak fluctuations and long wavelength sound waves, reveal frequency and amplitude alteration, the effect of which depends on the type of random field. In particular, the effect of a random mass density field is to increase wave frequencies. Space-dependent random velocity and pressure fields reduce wave frequencies. While space-dependent random fields attenuate wave amplitudes, their time-dependent counterparts lead to wave amplification. In another example, sound waves that are trapped in the vertical direction but are free to propagate horizontally are affected by a space-dependent random mass density field. This effect depends on the direction along which the field is varying. A random field, which varies along the horizontal direction, does not couple vertically standing modes but increases their frequencies and attenuates amplitudes. These modes are coupled by a random field which depends on the vertical coordinate, but the dispersion relation remains the same as in the case of the deterministic medium.     

Universal Models For Real Submanifolds

In previous papers by the present author, a machinery for calculating automorphisms, constructing invariants, and classifying real submanifolds of a complex manifold was developed. The main step in this machinery is the construction of a “nice” model surface. The nice model surface can be treated as an analog of the osculating paraboloid in classical differential geometry. Model surfaces suggested earlier possess a complete list of the desired properties only if some upper estimate for the codimension of the submanifold is satisfied. If this estimate fails, then the surfaces lose the universality property (that is, the ability to touch any germ in an appropriate way), which restricts their applicability. In the present paper, we get rid of this restriction: for an arbitrary type (n,K) (where n is the dimension of the complex tangent plane, and K is the real codimension), we construct a nice model surface. In particular, we solve the problem of constructing a nondegenerate germ of a real analytic submanifold of a complex manifold of arbitrary given type (n,K) with the richest possible group of holomorphic automorphisms in the given class.     

Crystallographic report: A new polymorph for bis[bis(N,N‐dibenzyldithiocarbamato)cadmium(II)]

The title compound is a centrosymmetric dimer with each cadmium in a distorted CdS₅ square pyramidal geometry. The Cd–S bond distances range from 2.5626(11) to 2.8459(11) Å. Copyright © 2004 John Wiley & Sons, Ltd.     

Experimental characterization of hexatic smectic phases through electro-optic studies and dielectric relaxation spectroscopy

The electro-optic and complex dielectric behaviour of an antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)phenyl 4'-(n-butanoyloxyprop-1-oxy)biphenyl-4-carboxylate, having chiral SmC_A* and hexatic smectic phases, have been investigated. Complex dielectric permittivities were measured as a function of frequency, d.c. bias field and temperature. Spontaneous polarization was measured by the current reversal technique; tilt angle was measured under a polarizing microscope using a low frequency electric field. The electro-optic properties and dielectric behaviour of the material are compared with results obtained by DSC and polarizing optical microscopy. Dielectric relaxation processes in SmC_A* and hexatic smectic phases were determined. The dielectric strength at the SmC_A* to hexatic smectic phase transition is discussed in terms of coupling between the long range bond orientational order and smectic C director. It seems from the results of spontaneous polarization and dielectric relaxation spectroscopy that the material might possess an additional phase between the SmC_A* and hexatic smectic I* phases.     

Effect of short glass fiber on structure and viscoelastic behavior of olefinic polymers synthesized with metallocene catalyst

Several composites were prepared on the basis of an ethylene homopolymer and different copolymers of ethylene and 1‐hexene, synthesized with a metallocene catalyst, as matrices and a content of a 5 wt % of short glass fiber. The effect of the fiber incorporation on the structure and mechanical and viscoelastic behaviors was analyzed for the different samples. The glass fibers induced a slightly higher crystallinity, and the crystallite morphology significantly changed (long spacings and crystal orientation). The incorporation of fibers did not reinforce the different matrices under study at this low content; consequently, the mechanical parameters, such as Young's modulus, yielding stress, and microhardness, were lower in the composites as compared with those values found in the neat polyolefins. The location and apparent activation energies of distinct relaxation processes are also discussed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1244–1255, 2003     

Ultrasonic spectroscopic evaluation of the ring‐opening metathesis polymerization of dicyclopentadiene

An in situ ultrasonic spectroscopy technique was used to study the ring‐opening metathesis polymerization of dicyclopentadiene catalyzed by bis(tricyclohexylphosphine)benzylidene ruthenium dichloride. A reaction cell employing a flexible poly(ethylene terephthalate) window for pulse echo ultrasonic spectroscopy was used to monitor the polymerization. The changes in the density, wave speed, acoustic modulus, and attenuation were all simultaneously monitored. In comparison with Fourier transform infrared (FTIR) spectroscopy data, the changes in the density, velocity, and modulus only accurately measured the rate constant for the metathesis of the cyclopentyl unsaturation. The ultrasonic values were within 6% of the values determined by FTIR. The activation energy for metathesis of the cyclopentyl unsaturation was 84 kJ mol^?1, following first‐order kinetics. Rate constants for the polymerization of the norbornyl unsaturation could not be determined by ultrasound. The gel point, vitrification, and qualitative information about the reaction rate could be determined from the change in the attenuation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1323–1333, 2003     

Estimate for the Best Approximation of Summable Functions of Several Variables with a Certain Symmetry of Fourier Coefficients

An upper bound for the best approximation of summable functions of several variables by trigonometric polynomials in the metric of L is determined in terms of Fourier coefficients. We consider functions representable by trigonometric series with certain symmetry of coefficients satisfying a multiple analog of the Sidon–Telyakovskii conditions.