On an Extremal Problem About the Arc-Length of Algebraic Polynomials

In this work we investigate polynomials of maximal (minimal) arc-length in the interval [−1, 1] amongst all monic polynomials of fixed degree n with n real zeros in [−1, 1].     

Nuclear orientation study of54Mn impurity in Pt100-x Fe x alloy

The low temperature nuclear orientation of⁵⁴Mn in Pt_99.95Fe_0.05, Pt_99.9Fe_0.1, Pt₉₉Fe₁ and Pt₈₈Fe₁₂ has been studied in the temperature range 12–50 mK and in the external magnetic field range 0–1.2 T. The strong temperature and external magnetic field dependence of the effective fieldB _eff on⁵⁴Mn has been observed even in the range where the host itself is magnetically saturated. This behaviour is interpreted by noncollinearity of the Mn magnetic moments with respect to the macroscopic magnetisation direction.     

Angular anisotropy of the alpha emission from241Am nuclei oriented by magnetic hyperfine interaction

Angular anisotropy of the alpha emission from²⁴¹Am nuclei oriented by magnetic hyperfine interaction at low temperatures in ZrFe₂-host have been observed. The sign of the anisotropy indicates unambiguously the enhanced alpha emission from the poles of²⁴¹Am nucleus. The value of magnetic hyperfine field on²⁴¹Am nuclei have been estimated from the temperature dependence of the anisotropy.     

Transfinite interpolation on the medians of a triangle and best L 1-approximation

Let be a triangle in and let be the set of its three medians. We construct interpolants to smooth functions using transfinite (or blending) interpolation on The interpolants are of type f(₁)+g(₂)+h(₃), where (₁,₂,₃) are the barycentric coordinates with respect to the vertices of . Based on an error representation formula, we prove that the interpolant is the unique best L¹-approximant by functions of this type subject the function to be approximated is from a certain convexity cone in C³().Received: 17 December 2003     

Geodesic Equivalence via Integrability

We suggest a construction that, given an orbital diffeomorphism between two Hamiltonian systems, produces integrals of them. We treat geodesic equivalence of metrics as the main example of it. In this case, the integrals commute; they are functionally independent if the eigenvalues of the tensor g ⁱg¯_j are all different; if the eigenvalues are all different at least at one point then they are all different at almost each point and the geodesic flows of the metrics are Liouville integrable. This gives us topological obstacles to geodesic equivalence.     

The fourfold escape threshold law

The dependence of an ionization function on the total energy near the break-up threshold has been derived making use of the classical theory. The threshold exponent for the triple ionization by electron impact on neutral target assumes the value κ = 3.525.     

Localization of the electromagnetic field in the vicinity of gold nanoparticles: Surface modification of different substrates

Theoretical predictions and experimental results for nanosized modification of metal (Au), semiconductor (Si), or dielectric (soda lime glass) substrates using near-electromagnetic field enhancement in the vicinity of gold nanoparticles are presented. The near field properties for the system consisting of an isolated gold nanoparticle or nanoparticle aggregate deposited on the substrates, which is irradiated by electromagnetic wave, are investigated using Finite Difference Time Domain Simulation technique. The influence of the substrate material on the near field distribution characteristics is predicted. The results reveal that the field on the substrate surface is enhanced in the three investigated cases, but its spatial distribution and magnitude depend on the substrate material. In the case of the metal and semiconductor substrate the enhanced near field is strongly localized in the vicinity of the contact point with the particle, in an area with diameter smaller than the particle's one. The intensity of the enhanced field on the glass is more than an order of magnitude lower than the case of using silicon substrate. The properties of the near field on the substrate surface also depend on the particle arrangement. For a two-dimensional gold nanoparticle array, when the particles are closely arrayed, the intensity of the enhanced field on the substrate surface is minimal. With the increase of the interparticle distance the near field intensity increases. The validity of the obtained theoretical results is confirmed experimentally.     

Low-Regularity Solutions of the Periodic Camassa–Holm Equation

We prove local existence and uniqueness of weak solutions of the Camassa–Holm equation with periodic boundary conditions in various spaces of low-regularity which include the periodic peakons. The proof uses the connection of the Camassa–Holm equation with the geodesic flow on the diffeomorphism group of the circle with respect to the L ² metric.     

Synthesis and Characterization of Novel Cycloalkanespiro-5-Hydantoin Phosphonic Acids

A series of new cycloalkanespiro-5-hydantoin phosphonic acids have been synthesized and characterized. The mixture of [(2,4-dioxo-1,3-diazaspiro-alkane-3-yl)-methyl]phosphonic acids and [(2,4-dioxo-1,3-diazaspiro-alkane-1,3-diyl)dimethyl]diphospho-nic acids was obtained from cycloalkanespiro-5-hydantoins, formaldehyde, and phosphorus trichloride in a molar ratio of 1:2:2, by a procedure modified by us. Their structures were proved by means of IR, ¹H, ¹³C{¹H} and ³¹P NMR spectroscopy.     

Optimal strong Mal’cev conditions for omitting type 1 in locally finite varieties

We show that the class of locally finite varieties omitting type 1 has the following properties. This class is:

1. definable by an idempotent, linear, strong Mal’cev condition in a language with one 4-ary function symbol;
2. not definable by an idempotent, linear, strong Mal’cev condition in a language with only one function symbol of arity strictly less than 4;
3. definable by an idempotent, linear, strong Mal’cev condition in a language with two 3-ary function symbols;
4. not definable by an idempotent, linear, strong Mal’cev condition in a language with function symbols of arity less than 4 unless at least two of the symbols have arity 3.