Beurling algebra analogues of the classical theorems of Wiener and Levy on absolutely convergent Fourier series

Let $f$ be a continuous function on the unit circle $\Gamma$, whose Fourier series is $\omega$-absolutely convergent for some weight $\omega$ on the set of integers $\mathcal{Z}$. If $f$ is nowhere vanishing on $\Gamma$, then there exists a weight $\nu$ on $\mathcal{Z}$ such that $1/f$ had $\nu$-absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary, it follows that if $\phi$ is holomorphic on a neighbourhood of the range of $f$, then there exists a weight $\chi$ on $\mathcal{Z}$ such that \hbox{$\phi\circ f$} has $\chi$-absolutely convergent Fourier series. This is a weighted analogue of L\'{e}vy's generalization of Wiener's theorem. In the theorems, $\nu$ and $\chi$ are non-constant if and only if $\omega$ is non-constant. In general, the results fail if $\nu$ or $\chi$ is required to be the same weight $\omega$.Comment: 4 page

Fatigue behavior of SiC reinforced titanium composites

The low cycle axial fatigue properties of 25 and 44 fiber volume percent SiC/Ti(6Al-4V) composites were measured at room temperature and at 650 deg C. The S-N curves for the composites showed no anticipated improvement over bulk matrix behavior at room temperature. Although axial and transverse tensile strength results suggest a degradation in SiC fiber strength during composite fabrication, it appears that the poor fatigue life of the composites was caused by a reduced fatigue resistance of the reinforced Ti(6Al-4V) matrix. The reduced matrix behavior was due, to the presence of flawed and fractured fibers created near the specimen surfaces by preparation techniques and to the large residual tensile stresses that can exist in fiber reinforced matrices. The effects of fatigue testing at high temperature are discussed

Infinite disorder scaling of random quantum magnets in three and higher dimensions

Using a very efficient numerical algorithm of the strong disorder renormalization group method we have extended the investigations about the critical behavior of the random transverse-field Ising model in three and four dimensions, as well as for Erd\H os-R\'enyi random graphs, which represent infinite dimensional lattices. In all studied cases an infinite disorder quantum critical point is identified, which ensures that the applied method is asymptotically correct and the calculated critical exponents tend to the exact values for large scales. We have found that the critical exponents are independent of the form of (ferromagnetic) disorder and they vary smoothly with the dimensionality.Comment: 6 pages, 5 figure

A Study of starless dark cloud LDN 1570: Distance, Dust properties and Magnetic field geometry

We wish to map the magnetic field geometry and to study the dust properties of the starless cloud, L1570, using multi-wavelength optical polarimetry and photometry of the stars projected on the cloud. We made R-band imaging polarimetry of the stars projected on a cloud, L1570, to trace the magnetic field orientation. We also made multi-wavelength polarimetric and photometric observations to constrain the properties of dust in L1570. We estimated a distance of 394 +/- 70 pc to the cloud using 2MASS JHKs colours. Using the values of the Serkowski parameters namely $\sigma_{1}$, $\bar \epsilon$, {\lambda}max and the position of the stars on near infrared color-color diagram, we identified 13 stars that could possibly have intrinsic polarization and/or rotation in their polarization angles. One star, 2MASS J06075075+1934177, which is a B4Ve spectral type, show the presence of diffuse interstellar bands in the spectrum apart from showing H{\alpha} line in emission. There is an indication for the presence of slightly bigger dust grains towards L1570 on the basis of the dust grain size-indicators such as {\lambda}max and Rv values. The magnetic field lines are found to be parallel to the cloud structures seen in the 250{\mu}m images (also in 8{\mu}m and 12{\mu}m shadow images) of L1570. Based on the magnetic field geometry, the cloud structure and the complex velocity structure, we believe that L1570 is in the process of formation due to the converging flow material mediated by the magnetic field lines. Structure function analysis showed that in the L1570 cloud region the large scale magnetic fields are stronger when compared with the turbulent component of magnetic fields. The estimated magnetic field strengths suggest that the L1570 cloud region is sub-critical and hence could be strongly supported by the magnetic field lines.Comment: 26 pages, 22 figures, and 7 tables; Accepted for its publication in A&

Structural, Magnetic and Magneto-caloric studies of Ni50Mn30Sn20Shape Memory Alloy

We have synthesized a nominal composition of Ni50Mn30Sn20 alloy using arc melting technique. Rietveld refinement confirms the austenite L21 structure in Fm-3m space group. Electrical resistivity has been found to clearly exhibiting two different phenomena viz. a magnetic transition from paramagnetic to ferromagnetic and a structural transition from austenite to martensitic phase. Thermo-magnetization measurements M(T) confirms ferromagnetic transition temperature TC at 222 K and martensitic transition starting at 127 K(MS). Magnetization measurement M(H) at 10 K confirms the ferromagnetic state. Frequency dependence of ac susceptibility \c{hi}' at low temperature suggests spin glass behavior in the system. The isothermal magnetic entropy change values have been found to be 1.14 J/Kg.K, 2.69 J/Kg.K and 3.9 J/Kg.K, with refrigeration capacities of 19.6 J/kg, 37.8 J/kg and 54.6 J/kg for the field change of 1, 2 and 3 Tesla respectively at 227 K.Comment: 16 pages text + Figs. Ni50Mn30Sn20 alloy: reasonable refrigeration capacity tunable to Room