Modification of magnetic anisotropy in metallic glasses using high-energy ion beam irradiation

Heavy ion irradiation in the electronic stopping power region induces macroscopic dimensional change in metallic glasses and introduces magnetic anisotropy in some magnetic materials. The present work is on the irradiation study of ferromagnetic metallic glasses, where both dimensional change and modification of magnetic anisotropy are expected. Magnetic anisotropy was measured using Mössbauer spectroscopy of virgin and irradiated Fe₄₀Ni₄₀B₂₀ and Fe₄₀Ni₃₈Mo₄B₁₈ metallic glass ribbons. 90 MeV ¹²⁷I beam was used for the irradiations. Irradiation doses were 5×10¹³ and 7.5×10¹³ ions/cm². The relative intensity ratios D ₂₃ of the second and third lines of the Mössbauer spectra were measured to determine the magnetic anisotropy. The virgin samples of both the materials display in-plane magnetic anisotropy, i.e., the spins are oriented parallel to the ribbon plane. Irradiation is found to cause reduction in magnetic anisotropy. Near-complete randomization of magnetic moments is observed at high irradiation doses. Correlation is found between the residual stresses introduced by ion irradiation and the change in magnetic anisotropy.     

Pyridine N-alkylation by lithium, magnesium, and zinc alkyl reagents: synthetic, structural, and mechanistic studies on the bis(imino)pyridine system

The 2,6-bis(alpha-iminoalkyl)pyridines 2,6-[ArNC(CR(3))](2)C(5)H(3)N [R = H, D; Ar = 2,6-i-Pr(2)C(6)H(3) (DIPP), 2,6-Me(2)C(6)H(3) (DMP)] react with MeLi in Et(2)O to give a binary mixture of products: the pyridine N-methylated species 2,6-[ArNC(CR(3))](2)C(5)H(3)N(Me)Li(OEt(2)) and the deprotonated/dedeuterated species 2-[ArNC(CR(3))],6-[ArNC(=CR(2))]C(5)H(3)NLi(OEt(2)). For R = D, the product ratio is 2:1 in favor of the N-methylated product, while, for R = H, the deprotonated product is favored by 5:1, increasing to 8:1 in toluene solvent. Warming solutions of the N-methylated species leads to clean conversion to the thermodynamically preferred deprotonated species. Crossover experiments show that MeLi is re-formed and dissociates from the terdentate ligand before deprotonating the ketimine methyl unit. For MgR(2) (R = Et, i-Pr) and ZnR(2) (R = Et) reagents, N-alkylation products are formed exclusively, but derivatives containing bulky aryl substituents are found to undergo further rearrangement to 2-alkylated species, arising by migration of the alkyl group of the N-alkyl moiety to the adjacent ring carbon atom. The reversibility of the N-alkylation process has been probed using deuterio-labeled Mg alkyl reagents and mixed alkyl zinc species. A cationic zinc derivative is shown to undergo "reverse" alkyl migration, from the heterocycle nitrogen atom to the zinc center. EPR spectroscopy reveals a paramagnetic intermediate in which the unpaired electron is delocalized over the heterocycle and di-imine moieties of the ligand, indicating that the N-alkylation reactions proceed via single electron-transfer processes.     

Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg then the state complexity of is equal to the Wolf bound. For deg , we use Clifford's theorem to give a simple lower bound on the state complexity of . We then derive two further lower bounds on the state space dimensions of in terms of the gonality sequence of . (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.     

A novel piezo-optical styrene sensor incorporating polymer-supported tribromide ion

Encapsulation of Amberlyst A-26 supported tribromide in a 10,000 MW polyethylene glycol matrix gives a robust colour-sensitive reagent matrix which can be deposited on indium-tin oxide coated polyvinylidene fluoride (PVDF) piezoelectric film for the detection of styrene (and other alkene) vapours.     

An early Chinese derivation of the volume of a pyramid: Liu Hui,third century A.D.

The Chiu-chang suan-shu (“Arithmetic in nine chapters”) is a mathematical book of the late first century A.D. It gives practical problems and states algorithms for their solution, with no explanation. A commentary attributed to Liu Hui, of the third century A.D., gives an explanation of each algorithm; these explanations satisfy many of the criteria for what we would call a proof. In this article Liu Hui's explanation of the formula for the volume of a particular kind of pyramid is translated and discussed.     

On the lax solution to the Hamilton-Jacobi equation. Part I

The review article of Crandall, Ishii, and Lions [Bull. AMS,27, No. 1, 1–67 (1992)] devoted to viscosity solutions of first- and second-order partial differential equations contains the exact Lax formula

The influence of a transverse magnetic field on a subnormal glow discharge in air

In subnormal glow discharge under d.c. excitation at different pressure in a varying transverse magnetic field (0 to 30 G) some measurements have been carried out for various initial average tube currents. The voltage across the discharge increases and average tube current and residual current decreases in the magnetic field. With the help of Beckman’s expression [4] for the axial field and the electron density distribution in a transverse magnetic field the observed variation of current and voltage can be satisfactorily explained. The variation of axial electric field with transverse magnetic field can be represented to a fair degree of accuracy by the derived equation. The behaviour of residual current with magnetic field has been observed in these oscillations.