Ferromagnetic Zr1−xMnxCo2 laves phase compounds

Structure and magnetic properties of the Zr_1−xMn_xCo_2+δ alloys were studied for 0 x <0.7, δ=0, 0.45. The cubic C15 Laves phase structure shows Mn solubility up to x≈0.4. The other Laves phase with the hexagonal C36 structure found for x0.5 apparently has a small region of Mn solubility in the vicinity of Zr_0.4Mn_0.6Co₂. Though the parent Mn-free compounds are known to be paramagnetic, the Mn-substituted alloys show ferromagnetic behavior with the Curie temperatures up to 625 K and the room-temperature saturation magnetization of about 100 emu/g. The onset of ferromagnetism with the Mn substitution for Zr may be caused by polarization of itinerant 3d electrons, like it was earlier supposed for the off-stoichiometric ZrCo_2+δ. The universal composition dependencies of the intrinsic magnetic properties for different δ can be obtained, if plotted against the amount of zirconium atoms missing in its sublattice. The room-temperature anisotropy with the noticeable anisotropy field of 24 kOe and the 1 1 0 easy magnetization direction laying in a basal plane was found in the hexagonal Zr_0.5Mn_0.5Co₂.     

Hypernormal form theory: foundations and algorithms

Hypernormal forms (unique normal forms, simplest normal forms) are investigated both from the standpoint of foundational theory and algorithms suitable for use with computer algebra. The Baider theory of the Campbell-Hausdorff group is refined, by a study of its subgroups, to determine the smallest substages into which the hypernormalization process can be divided. This leads to a linear algebra algorithm to compute the generators needed for each substage with the least amount of work. A concrete interpretation of Jan Sanders’ spectral sequence for hypernormal forms is presented. Examples are given, and a proof is given for a little-known theorem of Belitskii expressing the hypernormal form space (in the inner product style) as the kernel of a higher-order differential operator.     

Propriétés statistiques des entiers friables

Let Ψ(x,y) (resp. Ψ_m(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψ_m(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which supersede all previously known results. Applications are given to averages of various arithmetic functions over friable integers which in turn improve corresponding results from the literature. The technique employed rests mainly on the saddle-point method, which is an efficient and specific tool for the required design.2000 Mathematics Subject Classification: Primary—11N25; Secondary—11K65, 11N37     

Ergodic properties and thermodynamic behavior of elementary reversible cellular automata. I. Basic properties

This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.     

Probability Interpretation of the Integral of Fractional Order

We establish a relation between stable distributions in probability theory and the fractional integral. Moreover, it turns out that the parameter of the stable distribution coincides with the exponent of the fractional integral. It follows from an analysis of the obtained results that equations with the fractional time derivative describe the evolution of some physical system whose time degree of freedom becomes stochastic, i.e., presents a sum of random time intervals subject to a stable probability distribution. We discuss relations between the fractal Cantor set (Cantor strips) and the fractional integral. We show that the possibility to use this relation as an approximation of the fractional integral is rather limited.     

一类混合型微分差分方程的周期解

利用Fenchel变换,我们推出一类微分差分方程存在周期解等价于某泛函具有临界点,并求出方程具有周期解的充分条件.     

在高密度下核物质的色超导性

建立了相变热力学理论和场论的关系. 强调在量子场论中必须引进序参量场， 则相变的讨论就类似于Goldstone bosons 的产生. 如果只讨论一级相变， Goldstone bosons场就足够了; 如果要讨论二级相变， 则必须讨论一系列的场， 这些场构成一个对称群的表示. 另外, 也将这一思想用到色超导中. In this paper we built a relation between the thermodynamical theory of the phase transition and field theory. We emphasized that in the quantum field theory we have to introduce the order parameter fields. Then the discussion of the phase transition is closed to the creation of the Goldstone bosons. If we only discuss the first order transition, the Goldstone bosons fields are sufficient. If we want to discuss the second order transition, we have to discuss a set of fields that constructs a representation of a symmetry group. We also apply this concept to color superconductivity.     

Electronic transport properties of bismuth nanobridges through silicon-nitride membranes

The electronic transport through nanostructured bismuth nanobridges has been investigated at low temperatures (T<2 K) and in magnetic fields B up to 8.5 T. The samples show reproducible resistance fluctuations as a function of B, superimposed on a large magnetoresistance of up to 50%. In addition, time-dependent resistance fluctuations in zero magnetic field demonstrate the presence of bistable scatterers in the constriction region of our samples, which are described by two-level systems. Their dynamics are shown to be sensitive to subtle modifications of the static scatterer configuration in their vicinity, which cannot be detected in the sample magnetofingerprint.     

A model study for the steady state error of numerical approximations of inviscid flow equations on Cartesian grid

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. In this paper we consider the influence of the refined interfaces on the steady state errors for second‐order three‐point difference approximations of flow equations. Since the various characteristic components of the Euler equations should behave similarly on such grids with regard to refinement‐induced errors, it is sufficient enough to conduct the analysis on a scalar model problem. The error we consider is a global error, different to local truncation error, and reflects the interaction between multiple interfaces. The steady state error will be compared to the errors on smooth refinement grids and on uniform grids. The conclusion seems to support the numerical findings of Yamaleev and Carpenter (J. Comput. Phys. 2002; 181: 280–316) that refinement does not necessarily reduce the numerical error. Copyright © 2005 John Wiley & Sons, Ltd.     

ITERATIVE APPROXIMATION OF FIXED POINTS OF NON-LIPSCHITZIAN ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS

The purpose of this paper is to investigate the problem of approximating fixed points of non-Lipschitizian asymptotically pseudocontractive mappings in an arbitrary real Banach space by the modified Ishikawa iterative sequences with errors.