Hille and Nehari type criteria for third-order dynamic equations

In this paper, we extend the oscillation criteria that have been established by Hille [E. Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948) 234-252] and Nehari [Z. Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957) 428-445] for second-order differential equations to third-order dynamic equations on an arbitrary time scale T, which is unbounded above. Our results are essentially new even for third-order differential and difference equations, i.e., when T=R and T=N. We consider several examples to illustrate our results.     

An improved algorithm for computing topological entropy

A new algorithm is presented for computing the topological entropy of a unimodal map of the interval. The accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed.     

Extension of the Sommerfeld diffraction integral to the case of extremely short optical pulses

The Sommerfeld diffraction theory is extended to the case of extremely short pulses. It is shown that a simple qualitative analysis and a quantitative solution of a wide class of diffraction problems are possible for pulses with durations of the order of the period of the light oscillations and an arbitrary initial distribution of the light field. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 5, 323–326 (10 September 1997) Deceased     

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.     

The semidirect products of finite cyclic groups that areI-E groups

AnI-E group is a group in which the endomorphism near-ring generated by the group's inner automorphisms equals the endomorphism near-ring generated by its endomorphisms. In this paper we shall completely determine the finite groups that are semidirect products of cyclic groups and areI-E groups.     

Anticancer agent development: X-ray crystal structure and keto-enol tautomerism of dimethyl 1-hydroxy-6,7-methylenedioxy-4-(3′,4′,5′-trimethoxyphenyl-trans-3,4-dihydronaphthalene-2,3-dicarboxylate

Structural and conformational information obtained from the crystal structure and solution¹H nmr investigations of the title compound are compared. The 4-aryltetralone, C₂₄H₂₄O₁₀, crystallizes as a chloroform solvate in the monoclinic space group, P2₁/n, witha=12.519(4),b=17.938(6),c=12.534(9)Å,=111.90(5)°, and D_calc=1.51 g cm^–3 forZ=4. The data for this compound were collected at –150°C. Least-squares refinement of 2796 observed [F _o5(F _o)] reflections led to the final agreement index ofR=0.062. A threefold static disorder was observed for one of the carboxyl groups. The second carboxyl group participates in an intramolecular hydrogen bond and is thus ordered. The¹H nmr spectrum revealed the title compound to exist as a keto-enol tautomeric mixture in solution. Vicinal hydrogen coupling constant analysis proved reliable in ascertaining B-ring stereochemistry of 2,3-disubstituted-4-aryltetralones.