Magnetic relaxation in spinel Mo-ferrite and Ti substituted Mo-ferrite

A compensation temperature of 138 K was observed in the temperature-dependent magnetization curves of MoFe₂O₄. Relatively slow magnetization relaxation characterized the transitions between different spin states (compensated and uncompensated). Large magnetic after effect was found in time-dependent magnetization curves after heating or cooling from different characteristic temperatures for different spin states. The magnetic relaxation was nearly independent on magnetic field, supporting the presence of spin states and no involvement of domain structure. For the Ti substituted Mo_0.6Ti_0.4Fe₂O₄ sample, there were a compensation at ∼ 100 K and a maximum of magnetization at ∼ 175 K. Similar results of anomalous magnetic relaxation was observed in Ti substituted Mo-ferrite (Mo_0.6Ti_0.4Fe₂O₄). If the Mo_0.6Ti_0.4Fe₂O₄ sample was heated from 100 K to 235 K, the time-dependent magnetization curve could be considered as a combination of two magnetic relaxation processes. However, if the sample was heated from 100 K to 295 K, the time- dependent magnetization curve became complex. Received 30 October 2001 and Received in final form 21 January 2002     

Gorenstein Curves with Quasi-Symmetric Weierstrass Semigroups

We consider a canonical Gorenstein curve C of arithmetic genus g in P g-1 (K), that admits a non-singular point P, whose Weierstrass semigroup is quasi-symmetric in the sense that the last gap is equal to 2g-2. By making local considerations at the point P and the second point of the curve C on its osculating hyperplane at P we construct monomial bases for the spaces of higher order regular differentials. We give an irreducibility criterion for the canonical curve in terms of the coefficients of the quadratic relations. We also realize each quasi-symmetric numerical semigroup as the Weierstrass semigroup of a reducible canonical Gorenstein curve, but we give examples of such semigroups that cannot be realized as Weierstrass semigroups of smooth curves.     

Universal Hashing and Geometric Codes

We describe a new application of algebraic coding theory to universal hashing and authentication without secrecy. This permits to make use of the hitherto sharpest weapon of coding theory, the construction of codes from algebraic curves. We show in particular how codes derived from Artin-Schreier curves, Hermitian curves and Suzuki curves yield classes of universal hash functions which are substantially better than those known before.     

Isomorphism classes of elliptic and hyperelliptic curves over finite fields

We give the number and representatives of isomorphism classes of hyperelliptic curves of genus g defined over finite fields , g=1,2,3. These results have applications to hyperelliptic curve cryptography.     

Temperature dependent nano indentation of thin polymer films with the scanning force microscope

The scanning force microscope (SFM) was used to investigate the temperature dependent micro mechanical properties of polymethylmethacrylate (PMMA) films with a thickness of 35 nm in the range of the radius of gyration. Force-distance curves were performed in the glass transition range to create permanent nanometric indentations with maximal forces up to 4 μN. Quantitative measurements of the indentation depth during and after application of the force, hysteresis energy and slope of the loading part are carried out as function of sample temperature and applied force. The glass transition of the polymer film can be clearly identified by the change of the mechanical properties of the polymer. Surprisingly, only a small change of elasticity at the glass transition is observed.     

Degrees of the Elliptic Teichmüller Lift

The purpose of this paper is to find upper bounds for the degrees, or equivalently, for the order of the poles at O, of the coordinate functions of the elliptic Teichmüller lift of an ordinary elliptic curve over a perfect field of characteristic p. We prove the following bounds:ord₀(x_n)?−(n+2)pⁿ+npⁿ⁻¹, ord₀(y_n)?−(n+3)pⁿ+npⁿ⁻¹. Also, we prove that the bound for x_n is not the exact order if, and only if, p divides (n+1), and the bound for y_n is not the exact order if, and only if, p divides (n+1)(n+2)/2. Finally, we give an algorithm to compute the reduction modulo p³ of the canonical lift for p≠2,3.     

A Combinatorial Algorithm Related to the Geometry of the Moduli Space of Pointed Curves

As pointed out in Arbarello and Cornalba (J. Alg. Geom. 5 (1996), 705–749), a theorem due to Di Francesco, Itzykson, and Zuber (see Di Francesco, Itzykson, and Zuber, Commun. Math. Phys. 151 (1993), 193–219) should yield new relations among cohomology classes of the moduli space of pointed curves. The coefficients appearing in these new relations can be determined by the algorithm we introduce in this paper.     

Low-degree points on Hurwitz-Klein curves

We investigate low-degree points on the Fermat curve of degree 13, the Snyder quintic curve and the Klein quartic curve. We compute all quadratic points on these curves and use Coleman's effective Chabauty method to obtain bounds for the number of cubic points on each of the former two curves.

     

MFM study of magnetic vortex cores in circular permalloy dots: behavior in external field

In a circular dot of permalloy with an appropriate size, a vortex structure with perpendicular (turned-up) magnetization at the core is realized. The existence of the perpendicular magnetization spot has been confirmed and the direction of the magnetization, up or down, has been determined by magnetic force microscopy (MFM) for permalloy dots with the diameter of 0.1–1 μm. The switching field of turned-up magnetization is determined by applying external fields perpendicularly and in tilted directions to the plane. By comparing the MFM results and the magnetization curves measured by a SQUID magnetometer, the switching process of turned-up magnetization is argued.     

Reachability realization and stabilizability of switched linear discrete-time systems

In this paper, the reachability realization of a switched linear discrete-time system, which is a collection of linear time-invariant discrete-time systems along with some maps for “switching” among them, is addressed. The main contribution of this paper is to prove that for a switched linear discrete-time system, there exists a basic switching sequence such that the reachable (controllable) state set of this basic switching sequence is equal to the reachable (controllable) state set of the system. Hence, the reachability (controllability) can be realized by using only one switching sequence. We also discuss the stabilizability of switched systems, and obtain a sufficient condition for stabilizability. Two numeric examples are given to illustrate the results.