Oscillation of higher order delay differential equations

A sufficient condition was obtained for oscillation of all solutions of theodd-order delay differential equation $$x^{(n)} (t) + \sum\limits_{i = 1}^m {p_i (t)} x(t - \sigma _{_i } ) = 0,$$ wherep _i (t) are non-negative real valued continuous function in [T ∞] for someT≥0 and σ_i,∈(0, ∞)(i = 1,2,…,m). In particular, forp _i (t) =p _i ∈(0, ∞) andn > 1 the result reduces to $$\frac{1}{m}\left( {\sum\limits_{i = 1}^m {(p_i \sigma _i^m )^{1/2} } } \right)^2 > (n - 2)!\frac{{(n)^n }}{e},$$ implies that every solution of (*) oscillates. This result supplements forn > 1 to a similar result proved by Ladaset al [J. Diff. Equn.,42 (1982) 134–152] which was proved for the casen = 1.     

Dispersion characteristics of broadside coupled dielectric image guide at millimeter wave frequencies

Dispersion characteristics and wave impedance for the even and odd modes of the broad side coupled dielectric image guides are computed by using mode matching techniques. Dispersion curves for broadside image guide are plotted for various dielectric materials and dimensional parameters as a function of frequency. Normalized electric field for dominant electric field component E of TM even and odd modes for various half spacings between two dielectric slabs of broadside coupled image guide have been plotted. Polysterene ( r=2.56) and Stycast ( r=3.4) have been used as dielectric materials in fabricating broadside coupled image guide. This broadside coupled dielectric guide is very convenient as compared to the other dielectric guides. Since in case of broadside coupled image guide the dielectric slab can be bonded to the side metallic walls using some low loss adhesive material, while in other coupled dielectric guides the dielectric slab have to be supported by some low dielectric constant material (Eccofoam with r=1.02) to maintain the proper distance of side metallic walls from the dielectric slab. Since this structure is symmetrical, this configuration can be analysed in terms of even and odd mode phase velocities. The difference in these even and off mode phase velocities can be used to determine the coupling between coupled dielectric slab. Various couplers in this configuration can be realised.     

Formation of YAG from coprecipitated yttrium aluminium hydroxides

Thermal decomposition of the amorphous coprecipitate of yttrium and aluminium hydroxides forming yttrium aluminium garnet has been investigated employing thermal analyses, X-ray diffraction and IR spectroscopy. On heating, the coprecipitate progressively loses water forming a stable but highly disordered hydroxy garnet which crystallizes at 1180 K and decomposes to YAG at 1290 K. Nucleation of the crystalline phase appears to begin at 800 K.The authors thank Dr. P. V. Ravindran of the Analytical Chemistry and Shri N. K. Kulkarni of the Fuel Chemistry Divisions of BARC for their assistance in the thermoanalytical experiments.     

Formation andstability of magnetic moment on isolated Rh impurities in dilute PtFe alloys

The local susceptibilities (T) of isolated Rh impurities in paramagnetic dilute Pt(Fe) alloys have been measured using the TDPAC method. The results show existence of 4d magnetic moment for Rh with reduced spin fluctuation temperatures (T _sf). It is suggested that moment stability scaled byT _sf is governed mainly by the interatomic d-d exchange interaction caused by induced ferromagnetic polarization of host d band electrons.     

Local magnetism of Rh in Ni-Rh alloys near the critical composition for ferromagnetism

Local magnetic behaviour of Rh implanted into Ni-Rh alloys near the critical Rh compositionx=0.37 has been studied using the TDPAC method. The observed Curie-Weiss type local susceptibility reflects the presence of large d spin polarization around Rh yielding a total moment of 4.7 _B. Our results show that the magnetism of Rh in the alloys depends strongly on the number of Ni near neighbour atoms.     

Rapid dissolution procedure for base-metals-bearing complex materials for quality control assessment

A less labour-intensive method, involving a mixture of 1.0 g MnO₂ + 20 mL HCl (11), is proposed for decomposing seven ores and six metallurgical products for accurate and precise estimation of copper, lead, zinc, cobalt and nickel for quality control assessment. Twentyone international reference materials were also analysed. Results of regression analyses are presented and intermethod comparison studies reveal that the probability of results being different compared with a reference method was less than 1%. Sample decomposition is straightforward and the method has been found to be very simple, rapid and easily adaptable, as it involves no separation of the analyte from the matrix elements.