The intertwining lifting theorem for ordered groups

Sz.-Nagy's dilation theorem for a contraction on a Hilbert space has been extended by Mlak to the case of a contraction semigroup whose indices are the positive elements of a totally ordered discrete group. We generalize to this case the intertwining lifting theorem of Sz.-Nagy and Foias. Some previous interpolation results on ordered groups are obtained as consequences.     

Low-temperature specific heat study of Ni85.5PxB18.5−x (0 ⩽ x ⩽ 18.5) metallic glasses

The low-temperature specific heat (LTSH) of the melt-quenched Ni_81.5P_x^- B_18.5?x amorphous alloy system, with 0 ? x ? 18.5, is presented. The decomposition of the LTSH into magnetic, lattice and electronic contributions shows that both Debye temperature θ_D and electronic specific heat coefficient decrease when the concentration of P increases.The electronic density of states N(E_F), deduced from γ for various Ni-metalloid alloys, is plotted as a function of the average electronic concentration xZ^M, where x is the metalloid concentration and Z^M is the chemical valence of M. Following Malozemoff et al.'s work, this plot is considered as a representation of the band structure and yields the change of the Fermi level with alloying.     

On an Extension Problem for Polynomials

Consider the following problem: given complex numbers a₁, ...,a_n, find an L function f of minimum norm whose Fourier coefficientsc_k(f) are equal to a_k for k between 0 and n. We show the uniquenessof this function, and we estimate its norm. The operator-valuedcase is also discussed. 2000 Mathematics Subject Classification30E05, 47A20, 47A56, 47A57.     

Analysis of the magnetoresistance contributions in a nanocrystallized Cr-doped FINEMET alloy

The magnetoresistance (MR) was measured at 200, 250 and 300 K in magnetic fields up to B=12 T for a nanocrystallized Fe_63.5Cr₁₀Nb₃Cu₁Si_13.5B₉ alloy. Both the longitudinal (LMR) and transverse (TMR) component of the magnetoresistance decreased from B=0 to about 0.1 T. This could be ascribed to a giant MR (GMR) effect due to spin-dependent scattering of conduction electrons along their path between two Fe-Si nanograins via the non-magnetic matrix. Such a scattering may occur if the nanograin moments are not or only weakly coupled in the absence of a strong exchange coupling (due to the high Cr content in the matrix) and/or only weak dipole-dipole coupling is present (due to sufficiently large separations between the nanograins). For larger fields, the GMR saturated and a slightly nonlinear increase in MR with B was observed due to a contribution by the residual amorphous matrix. The anisotropic MR effect (AMR≡LMR−TMR) was negative for all fields and temperatures investigated. By measuring the MR of melt-quenched Fe_100−xSi_x solid solutions with x=15, 18, 20, 25 and 28, the observed AMR could be identified as originating from the Fe-Si nanograins having a D0₃ structure.     

Determinantal formulae and nonsymmetric gaussian perfect elimination

Based upon certain key principal minors, a formula is given for the determinant of a nonsingular matrix in the case its inverse has a perfect elimination directed graph. The main result of [8] may be deduced from this formula. Our method allows us to construct a counterexample to a conjecture made in [8].     

The specific grain-boundary electrical resistivity of Ni

The purpose of the present study was to provide a reliable value for the specific grain-boundary resistivity ρ_SGBR of Ni metal. New results are presented on the room-temperature electrical resistivity of nanocrystalline (nc) Ni metal samples produced by electrodeposition with various grain sizes. These resistivity data were compared with previous reports on nc-Ni and all results were analysed according to the procedure of Andrews [Phys. Lett. 19, 558 (1965)] who found that the resistivity increment due to grain boundaries is proportional to the grain-boundary surface area per unit volume which is, on the other hand, inversely proportional to the grain size. It is pointed out that the grain size directly accessible by transmission electron microscopy imaging is the relevant parameter for the evaluation of ρ_SGBR whereas the crystallite size deduced from X-ray diffraction line broadening leads to an underestimation of ρ_SGBR because coherency-breaking intragrain defects not contributing significantly to the resistivity also cause a line broadening. From the evaluation of the nc-Ni resistivity data at room temperature, we find that 4.45·10^?16?Ω·m²?ρ_SGBR(Ni)??16?Ω·m² and our upper bound agrees exactly with the most recent calculated value in the literature.     

Temperature-dependent solvent effect on the kinetic energy distribution on p-cresol molecule as building block of calixarene capsules

The solvent effect on the kinetic energy distribution of p-cresol molecule was investigated by quantum-chemical (QM) method and molecular dynamics (MD) simulations, then the consequences were checked experimentally by photoluminescence (PL) and differential scanning calorimetry (DSC) methods. Results of QM calculations highlight the coupling of two vibrational normalmodes of p-cresol molecule in the presence of ethanol while no similar coupling was observed in methanol. MD simulations show that the normalmode coupling in ethanol is more pronounced at higher temperature and it is preferably based on the molecular friction of the cresol molecule with its environment. The theoretical observations were also proved experimentally. The dissociation rate of calixarene–phenol complexes were measured by DSC method. The decreased dissociation rate of the calixarene–phenol complexes observed in ethanol reflects the increased motion of the methyl groups of cresol units of calixarene in the ethanol solvent, a property which was predicted by the theoretical results. Our findings are applicable to many areas of chemistry where the formation and dissociation rates play important role: e.g., in the development of chemical molecular sensors or developing molecular containers for drugs towards pharmaceutical applications.     

Simple correlation between mechanical and thermal properties in TE-TL (TE = Ti,Zr,Hf;TL = Ni,Cu) amorphous alloys

We provide new data for the stiffness, hardness, Debye temperatures and crystallization and glass transition temperatures for fourteen Ti-TL and Hf-TL amorphous alloys (TL = Ni,Cu) covering wide composition range (x(TL) ≤ 70). These data increase linearly with x, as was previously observed for Zr-TL glassy alloys. Thus, the strength of interatomic bonding (reflected in stiffness) in all TE-TL amorphous alloys (TE = Ti,Zr,Hf) increases with x for x ≤ 65. The actual variations of studied properties depend on TE, being feeble for TE = Ti. The approximately linear variation of mechanical, vibrational and thermal parameters with x enables one to estimate these parameters for pure amorphous TEs, but does not indicate compositions at which bulk metallic glasses (BMG) form in these alloy systems. The reduced glass transition temperature T_rg is the property which roughly correlates with the formation of BMGs in glassy TE-TL alloys.     

Nehari and Carathéodory-Fejér type extension results for operator-valued functions on groups

Let be a compact abelian group having the property that its character group is totally ordered by a semigroup . We prove that every operator-valued function on of the form , such that the Hankel operator is bounded, has an essentially bounded extension with . The proof is based on Arveson's Extension Theorem for completely positive functions on -algebras. Among the corollaries we have a Carathéodory-Fejér type result for analytic operator-valued functions defined on such groups.