STRONG DERIVATIVE AND ITS CONSEQUENCES

We introduce strong derivative, the corresponding Z-integrable and other related concepts. Also, we give an improved version of the fundamental theorem of calculus.     

Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part I. Derivation of different formulations and constant density limit

The paper presents various formulations of characteristics-based schemes in the framework of the artificial-compressibility method for variable-density incompressible flows. In contrast to constant-density incompressible flows, where the characteristics-based variables reconstruction leads to a single formulation, in the case of variable density flows three different schemes can be obtained henceforth labeled as: transport, conservative and hybrid schemes. The conservative scheme results in pseudo-compressibility terms in the (multi-species) density reconstruction. It is shown that in the limit of constant density, the transport scheme becomes the (original) characteristics-based scheme for incompressible flows, but the conservative and hybrid schemes lead to a new characteristics-based variant for constant density flows. The characteristics-based schemes are combined with second and third-order interpolation for increasing the computational accuracy locally at the cell faces of the control volume. Numerical experiments for constant density flows reveal that all the characteristics-based schemes result in the same flow solution, but they exhibit different convergence behavior. The multigrid implementation and numerical studies for variable density flows are presented in Part II of this study.     

Hurst exponent footprints from activities on a large structural system

This paper presents Hurst exponent footprints from pseudo-dynamic measurements of significantly varied activities on a damaged bridge structure during rehabilitation through continuous monitoring. The system is interesting due to associated uncertainty in large-scale structures and significant presence of human intervention arising from fundamentally different processes. Investigations into the variation of computed Hurst exponents on time series of limited lengths are carried out in this regard. The Hurst exponents are compared with respect to specific events during the rehabilitation, as well as with the data collection locations. The variations of local Hurst exponents about the values computed for each activity are presented. The scaling of Hurst exponents for different activities is also investigated; these are representative of the extent of multifractality for each event. The extent of multifractality is assessed along with its source and time dependency.     

Measuring the self-similarity exponent in Lévy stable processes of financial time series

Geometric method-based procedures, which will be called GM algorithms herein, were introduced in [M.A. Sánchez Granero, J.E. Trinidad Segovia, J. García Pérez, Some comments on Hurst exponent and the long memory processes on capital markets, Phys. A 387 (2008) 5543-5551], to efficiently calculate the self-similarity exponent of a time series. In that paper, the authors showed empirically that these algorithms, based on a geometrical approach, are more accurate than the classical algorithms, especially with short length time series. The authors checked that GM algorithms are good when working with (fractional) Brownian motions. Moreover, in [J.E. Trinidad Segovia, M. Fernández-Martínez, M.A. Sánchez-Granero, A note on geometric method-based procedures to calculate the Hurst exponent, Phys. A 391 (2012) 2209-2214], a mathematical background for the validity of such procedures to estimate the self-similarity index of any random process with stationary and self-affine increments was provided. In particular, they proved theoretically that GM algorithms are also valid to explore long-memory in (fractional) Lévy stable motions.     

On the quantum Lorentz group

The quantum analog of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indices we construct a quantum Minkowski metric. In this framework we show explicitly the correspondence between the SL(2,C) and Lorentz quantum groups. Five matrices of the quantum Lorentz group are constructed in terms of the R matrix of SL(2,C) group. These matrices satisfy Yang–Baxter equations and two of which have adequate properties tied to the quantum Minkowski space structure as the reality conditions of the coordinates and the symmetrization of the metric. It is also shown that the Minkowski metric leads to invariant and central lengths of four-vectors.     

Self-regulation in infinite populations with fission-death dynamics

The evolution of an infinite population of interacting point entities placed in ${\mathbb{R}}^d$ is studied. The elementary evolutionary acts are death of an entity with rate that includes a competition term and independent fission into two entities. The population states are probability measures on the corresponding configuration space and the result is the construction of the evolution of states in the class of sub-Poissonian measures, that corresponds to the lack of clusters in such states. This is considered as a self-regulation in the population due to competition.     

Semiclassics around a phase space caustic: An illustration using the Nelson Hamiltonian

The semiclassical formula for the coherent-state propagator is written in terms of complex classical trajectories of an equivalent classical system. Depending on the parameters involved, more than one trajectory may contribute to the calculation. Eventually, however, two contributing trajectories coalesce, characterizing what is called phase space caustic. In this case, the usual semiclassical formula for the propagator diverges, so that a uniform approximation is required to avoid this singularity. In this Letter, we present a non-trivial numerical application illustrating this scenario, showing the accuracy of the uniform formula that we have previously derived.     

Clement-Desormes实验之不足

通过分析实验数据发现，Clement-Desormes的测量结果接近理论值存在某种巧合，该实验所用的测量原理并不能充分解释其实验现象。