Fixed points and graph images for minimal maps on the once punctured torus

A fixed point detection theorem for a family of maps defined on the once punctured torus is proved. As a consequence, we produce an example of a homotopy class [f] of self-maps on the once punctured torus that illustrates the following: (i) there is a map in the homotopy class that has no fixed points, and (ii) if the image of f lies in a 1-complex that embeds as a homotopy equivalence, then f must have a fixed point.     

On homotopy groups of quandle spaces and the quandle homotopy invariant of links

For a quandle X, the quandle space BX is defined, modifying the rack space of Fenn, Rourke and Sanderson (1995) [13], and the quandle homotopy invariant of links is defined in Z[π₂(BX)], modifying the rack homotopy invariant of Fenn, Rourke and Sanderson (1995) [13]. It is known that the cocycle invariants introduced in Carter et al. (2005) [3], Carter et al. (2003) [5], Carter et al. (2001) [6] can be derived from the quandle homotopy invariant.In this paper, we show that, for a finite quandle X, π₂(BX) is finitely generated, and that, for a connected finite quandle X, π₂(BX) is finite. It follows that the space spanned by cocycle invariants for a finite quandle is finitely generated. Further, we calculate π₂(BX) for some concrete quandles. From the calculation, all cocycle invariants for those quandles are concretely presented. Moreover, we show formulas of the quandle homotopy invariant for connected sum of knots and for the mirror image of links.     

A piecewise-linearized algorithm based on the Krylov subspace for solving stiff ODEs

Numerical methods for solving Ordinary Differential Equations (ODEs) have received considerable attention in recent years. In this paper a piecewise-linearized algorithm based on Krylov subspaces for solving Initial Value Problems (IVPs) is proposed. MATLAB versions for autonomous and non-autonomous ODEs of this algorithm have been implemented. These implementations have been compared with other piecewise-linearized algorithms based on Padé approximants, recently developed by the authors of this paper, comparing both precisions and computational costs in equal conditions. Four case studies have been used in the tests that come from stiff biology and chemical kinetics problems. Experimental results show the advantages of the proposed algorithms, especially when the dimension is increased in stiff problems.     

Global and bifurcation analysis of a structure with cyclic symmetry

This article combines the application of a global analysis approach and the more classical continuation, bifurcation and stability analysis approach of a cyclic symmetric system. A solid disc with four blades, linearly coupled, but with an intrinsic non-linear cubic stiffness is at stake. Dynamic equations are turned into a set of non-linear algebraic equations using the harmonic balance method. Then periodic solutions are sought using a recursive application of a global analysis method for various pulsation values. This exhibits disconnected branches in both the free undamped case (non-linear normal modes, NNMs) and in a forced case which shows the link between NNMs and forced response. For each case, a full bifurcation diagram is provided and commented using tools devoted to continuation, bifurcation and stability analysis.     

一阶线性模糊微分方程的解

利用文[8]中的扩展原理求解了一阶线性模糊微分方程,给出了解可表示的条件,讨论了同其他求解方法之间的关系,最后给出了具体算例。     

Palladium Release in Electrothermal Atomic Absorption Spectrometry

The absorbance signal in electrothermal atomic absorption spectrometry is a result of the processes of atom formation and dissipation and first of all depends on the initial generation of atoms from the surface. The rising part of the absorbance time profiles can be used for characterization of the release of the metals like Pd, Ag, Au etc. The method is applied to investigate the palladium release from a pyrocoated graphite support at different initial masses of the Pd. The kinetic parameters are evaluated and conclusions about the distribution of palladium on the graphite surface are made. The estimated values of apparent activation energies depend on the initial mass of analyte. The advantages and limitations of the present approach are discussed.     

Equation of state and thermal expansivity of LiF and NaF

The high-pressure and high-temperature behaviors of LiF and NaF have been studied up to 37 GPa and 1000 K. No phase transformations have been observed for LiF up to the maximum pressure reached. The B1 to B2 transition of NaF at room temperature was observed at ～28 GPa, this transition pressure decreases with temperature. Unit-cell volumes of LiF and NaF B1 phase measured at various pressures and temperatures were fitted using a P–V–T Birch–Murnaghan equation of state. For LiF, the determined parameters are: α₀ = 1.05 (3)×10^?4 K^?1, dK/dT = ?0.025 (2) GPa/K, V ₀ = 65.7 (1) Å³, K ₀ = 73 (2) GPa, and K′ = 3.9 (2). For NaF, α₀ = 1.34 (4)×10^?4 K^?1, dK/dT = ?0.020 (1) GPa/K, V ₀ = 100.2 (2) Å³, K ₀ = 46 (1) GPa, and K′ = 4.5 (1).     

Stability of MgAl 2 O 4 Under High-Pressure Conditions

A theoretical investigation of the MgAl 2 O 4 crystal response to high-pressure conditions has been carried out to determine its stability against decomposition towards MgO and f -Al 2 O 3 , and towards recently observed orthorhombic phases. We have evaluated total energy versus volume curves using the density functional formalism under the non-local B3LYP approximation, as implemented in the CRYSTAL package. Numerical and analytical fittings have been carried out to determine the equilibrium unit cell geometry and equation of state parameters for all the structures and compounds involved in the phase diagram. The macroscopic compressibility of the spinel phase is interpreted considering the compressibility of its elementary MgO 4 and AlO 6 coordination polyhedra, and implications to understand the phase stability are suggested.     

Ultrahigh pressure equation of state of tantalum to 310 GPa

ABSTRACT

The isothermal compression of transition metal tantalum (Ta) was studied in a diamond anvil cell by X-ray diffraction utilizing rhenium (Re) and gold (Au) as internal X-ray pressure standards. The Re pressure marker was employed during non-hydrostatic compression to pressures up to 310?GPa while the Au pressure marker was used during quasi-hydrostatic compression in a neon pressure-transmitting medium to 80?GPa. Two ultra-high pressure experiments were conducted on Ta and Re mixtures utilizing focused-ion beam machined toroidal diamond anvils with central flats varying from 8 microns to 16 microns in diameter. The Ta metal was observed to be stable in the body-centered-cubic phase to a volume compression V/V₀?=?0.581. The measured equations of state (EOS) of Ta using two different calibrations of the Re pressure marker are compared with the ambient temperature isotherm derived from shock compression data. We provide a detailed analysis of EOS fit parameters for Ta under quasi-hydrostatic and non-hydrostatic conditions.