f(R) theories of gravity in the Palatini approach matched with observations

We investigate the viability of f(R) theories in the framework of the Palatini approach as solutions to the problem of the observed accelerated expansion of the universe. Two physically motivated popular choices for f(R) are considered,: power law, f(R) = β R ⁿ , and logarithmic, f(R) = α ln R. Under the Palatini approach, both Lagrangians give rise to cosmological models comprising only standard matter and undergoing a present phase of accelerated expansion. We use the Hubble diagram of type Ia Supernovae and the data on the gas mass fraction in relaxed galaxy clusters to see whether these models are able to reproduce what is observed and to constrain their parameters. It turns out that they are indeed able to fit the data with values of the Hubble constant and of the matter density parameter in agreement with some model independent estimates, but the today deceleration parameter is higher than what is measured in the concordance ΛCDM model.     

Time variation of the electromagnetic transfer function of the earth estimated by using wavelet transform

In order to accurately estimate the geomagnetic transfer functions in the area of the volcano Mt. Iwate (IWT), we applied the interstation transfer function (ISTF) method to the three-component geomagnetic field data observed at Mt. Iwate station (IWT), using the Kakioka Magnetic Observatory, JMA (KAK) as remote reference station. Instead of the conventional Fourier transform, in which temporary transient noises badly degrade the accuracy of long term properties, continuous wavelet transform has been used. The accuracy of the results was as high as that of robust estimations of transfer functions obtained by the Fourier transform method. This would provide us with possibilities for routinely monitoring the transfer functions, without sophisticated statistical procedures, to detect changes in the underground electrical conductivity structure.     

Application of the finite Hankel transform to a diffusion problem without azimuthal symmetry

The problem treated in this paper concerns calculating the evolution of the pressure in a single-phase, slightly compressible fluid in a porous medium consisting of communicating layers. The fluid is produced through a point sink located on the side of an otherwise sealed cylindrical wellbore. This location of the sink causes the flow around the wellbore to be azimuthally asymmetric.The problem is solved through successive application of Laplace, finite Fourier and finite Hankel transforms. Although apparently straightforward, this approach leads to serious numerical difficulties. The published form of the inversion formula for the finite Hankel transform leads to inaccurate computation for the higher azimuthal modes even with 128 bit arithmetic. An alternative form is developed which enables accurate evaluation of the solution with the more practical 64 bit arithmetic. The technique for two-layer solution presented here can be directly extended to a problem with a larger number of communicating layers. This is the first instance of successful application of the finite Hankel transform to an azimuthally asymmetric diffusion problem.     

Aliasing Effects and Sampling Theorems of Spherical Random Fields when Sampled on a Finite Grid

Aliasing effects are investigated for spherical random fields sampled on a finite grid. Using the spherical harmonics expansion, it is shown that for a band-limited spherical random field its trend and spectrum can be uniquely reconstructed from the sampled field if the sampling points are judiciously designed. Analytical expressions are also obtained for aliasing errors in the trend and the spectrum when the field is not band-limited.     

Modeling of drug molecule orientation within a receptor cavity in the BiS algorithm framework

The BiS algorithm is suggested for modeling the drug molecule orientation within a receptor cavity. It is based on the assumption of complementarity of the field created by biologically active compounds and the field of the responsive receptor. The comparison of predicted orientations of various biologically active compounds on the relevant receptors with the data of X-ray structural studies (Protein Data Bank) reveals that the results obtained with this approach surpasses those reported in the literature. The suggested technique made it possible to elucidate the details of the action mechanism of DNA antimetabolites, dihydrofolate reductase inhibitors. The dependence of the activity on the structural parameters of “ligand-receptor” complexes is determined.     

蒙特卡罗哈密顿新方案及其检验

蒙特卡罗哈密顿方法(MCH)是研究量子理论的数值模拟新方法, 其优点是可求出超出基态的能谱和波函数. 旧MCH方案需要自由粒子的信息, 较难推广应用于格点规范理论. 本文提出克服这个困难的新方案. 首先介绍这一方案的思想, 并以1维量子力学模型V(x)=μ²x²+λx⁴(其中μ²< 0,λ>0)为例说明实现这一新方案的具体计算步骤和方法.     

The semiclassical limit of a quantum Fermi accelerator

A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions.     

双光子吸收效应对孤子和孤子对传输的影响

用分步傅立叶变换法求解含双光子吸收效应的光孤子NLS方程,研究了双光子吸收效应对一阶孤子和孤子对传输的影响,发现双光子吸收效应除对孤子产生等效损耗外,还影响了孤子对在传输中的相互作用。在特定的双光子吸收系数条件下双光子吸收效应可以使孤子对平行地向前传输。     

Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations

We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature.     

Flow Search Approach and New Bounds for the m-Step Linear Conjugate Gradient Algorithm

A flow search approach is presented in this paper. In the approach, each iterative process involves a subproblem, whose variables are the stepsize parameters. Every feasible solution of the subproblem corresponds to some serial search stages, the stepsize parameters in different search stages may interact mutually, and their optimal values are determined by evaluating the total effect of the interaction. The main idea of the flow search approach is illustrated via the minimization of a convex quadratic function. Based on the flow search approach, some properties of the m-step linear conjugate gradient algorithm are analyzed and new bounds on its convergence rate are also presented. Theoretical and numerical results indicate that the new bounds are better than the well-known ones.