Simple Procedure for Entanglement Transformation of Bipartite Pure States

An explicit procedure for transforming one bipartite entangled state into another via local operations and classical communication （LOCC） is presented. Our procedure is much simper than the previous ones in the sense that, it only involves two steps and the explicit expression of local general measurement used in the procedure can be obtained by solving a set of linear equations. Furthermore, this procedure is still applicable in high dimensional case.     

Scalar field quantization in stationary,non-static spacetimes

A quantization procedure is given for the scalar field on stationary, axisymmetric background spacetimes with orthogonal 2-surfaces. The procedure is based on observers orthogonal to surfaces of constant Killing time, and thus agrees with the usual procedure for static spacetimes. For stationary but nonstatic spacetimes the procedure differs from the usual one but nonetheless leads to a natural quantization scheme. Applying the procedure to flat space in rotating coordinates gives the standard, inertial Minkowski vacuum. For the Kerr spacetime, the procedure yields a particle definition which is well-defined everywhere outside the horizon. The above observers are just nonrotating ZAMO's, and the vacuum state smoothly interpolates between the “in” and “out” Boulware vacua.     

On the way towards a generalized entropy maximization procedure

We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Rényi and Tsallis entropies. The generalized entropy maximization procedure for Rényi entropies results in the exponential stationary distribution asymptotically for q∈(0,1] in contrast to the stationary distribution of the inverse power law obtained through the ordinary entropy maximization procedure. Another result of the generalized entropy maximization procedure is that one can naturally obtain all the possible stationary distributions associated with the Tsallis entropies by employing either ordinary or q-generalized Fourier transforms in the averaging procedure.     

The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids II: Extension to high order finite volume schemes

In this paper, the multidimensional limiter for the second order finite volume schemes on the unstructured grid, namely the Weighted Biased Average procedure developed in our previous paper is extended to high order finite volume schemes solving hyperbolic conservation laws. This extension relies on two key techniques: the secondary reconstruction and the successive limiting procedure. These techniques are discussed in detail in the present paper. Numerical experiments shows that this limiting procedure is very effective in removing numerical oscillations in the vicinity of discontinuities. And furthermore this procedure is efficient, robust and accuracy preserving.     

A Rayleigh–Chebyshev procedure for finding the smallest eigenvalues and associated eigenvectors of large sparse Hermitian matrices

A procedure is presented for finding a number of the smallest eigenvalues and their associated eigenvectors of large sparse Hermitian matrices. The procedure, a modification of an inverse subspace iteration procedure, uses adaptively determined Chebyshev polynomials to approximate the required application of the inverse operator on the subspace. The method is robust, converges with acceptable rapidity, and can easily handle operators with eigenvalues of multiplicity greater than one. Numerical results are shown that demonstrate the utility of the procedure.     

Estimation of the dynamical properties of polyurethane foam through use of Prony series

A system identification procedure is formulated for estimation of parameters associated with a dynamic model of a single-degree-of-freedom foam-mass system. The foam is modelled as a linear viscoelastic material, whose constitutive law is expressed by an exponential hereditary relaxation kernel. The identification procedure is based on modelling the free response of the system as a Prony series (sum of exponentials terms) and fitting this Prony series to the data. This estimated response model is then utilized to estimate the parameters in the system model based on an explicit solution of the model. The procedure is analyzed for its reliability under different sources of error and uncertainties, such as the presence of weak components and experimental noise, and some modifications are evaluated to improve the robustness of the procedure. Finally, the procedure is applied to experimental data to obtain relevant stiffness, viscous and viscoelastic parameters associated with the system. Variations in values of these parameters as a function of static compression are also investigated.     

A Newtonian procedure for the solution of the Kron characteristic value problem

In this paper a quadratically convergent Newtonian procedure is presented to determine the latent roots of the Kron matrix. The roots are found in ascending order with the certainty that none has been missed, since the procedure is allied to a Sturm sequence algorithm. The procedure has been programmed and it performs at least 50% faster than the bisection scanning method available for the Kron matrix. Examples of successful use of the procedure to solve for the natural frequencies of frames with large numbers of degrees of freedom are presented.     

Efficient implementation of high order inverse Lax–Wendroff boundary treatment for conservation laws

In [20], two of the authors developed a high order accurate numerical boundary condition procedure for hyperbolic conservation laws, which allows the computation using high order finite difference schemes on Cartesian meshes to solve problems in arbitrary physical domains whose boundaries do not coincide with grid lines. This procedure is based on the so-called inverse Lax–Wendroff (ILW) procedure for inflow boundary conditions and high order extrapolation for outflow boundary conditions. However, the algebra of the ILW procedure is quite heavy for two dimensional (2D) hyperbolic systems, which makes it difficult to implement the procedure for order of accuracy higher than three. In this paper, we first discuss a simplified and improved implementation for this procedure, which uses the relatively complicated ILW procedure only for the evaluation of the first order normal derivatives. Fifth order WENO type extrapolation is used for all other derivatives, regardless of the direction of the local characteristics and the smoothness of the solution. This makes the implementation of a fifth order boundary treatment practical for 2D systems with source terms. For no-penetration boundary condition of compressible inviscid flows, a further simplification is discussed, in which the evaluation of the tangential derivatives involved in the ILW procedure is avoided. We test our simplified and improved boundary treatment for Euler equations with or without source terms representing chemical reactions in detonations. The results demonstrate the designed fifth order accuracy, stability, and good performance for problems involving complicated interactions between detonation/shock waves and solid boundaries.     

An adaptive procedure for categorical loudness scaling

In this study, an adaptive procedure for categorical loudness scaling is introduced and evaluated. The procedure adjusts the presentation levels to the subject's individual auditory dynamic range without employing any premeasurement and presents levels in randomized order. The procedure has been named "Oldenburg-ACALOS" (Oldenburg-Adaptive CAtegorical LOudness Scaling). It was evaluated using repeated measurements with ten subjects with normal hearing and ten subjects with sensorineural hearing impairment. The results of this investigation revealed that the adaptive procedure provides greater reliability, while being more time efficient than a reference procedure that uses constant stimuli.     

A fuzzy finite element procedure for the calculation of uncertain frequency-response functions of damped structures: Part 1—Procedure

This work introduces a numerical algorithm to calculate frequency-response functions (FRFs) of damped finite element (FE) models with fuzzy uncertain parameters. Part one of this paper describes the numerical algorithm for the solution of the underlying interval finite element (IFE) problem. First, the IFE procedure for the calculation of undamped envelope FRFs is discussed. Starting from the undamped procedure, a strategy is developed to analyse damped structures based on the principle of Rayleigh damping. This is achieved by analysing the effect of the proportional damping coefficients on the subsequent steps of the undamped procedure. This finally results in a procedure for the calculation of fuzzy damped FRFs based on an analytical extension of the undamped algorithm. Part one of this paper introduces the numerical procedure. Part two of this paper illustrates the application of the methodology on four numerical case studies.     

Compensation for source nonstationarity in multireference,scan-based near-field acoustical holography

Multireference, scan-based near-field acoustical holography is a useful measurement tool that can be applied when an insufficient number of microphones is available to make measurements on a complete hologram surface simultaneously. The scan-based procedure can be used to construct a complete hologram by joining together subholograms captured using a relatively small, roving scan array and a fixed reference array. For the procedure to be successful, the source levels must remain stationary for the time taken to record the complete hologram; that is unlikely to be the case in practice, however. Usually, the reference signal levels measured during each scan differ from each other with the result that spatial noise is added to the hologram. A procedure to suppress the effects of source level, and hence reference level, variations is proposed here. The procedure is based on a formulation that explicitly features the acoustical transfer functions between the sources and both the reference and scanning, field microphones. When it is assumed that source level changes do not affect the sources' directivity, a nonstationarity compensation procedure can be derived that is based on measured transfer functions between the reference and field microphones. It has been verified both experimentally and in numerical simulations that the proposed procedure can help suppress spatially distributed noise caused by the type of source level nonstationarity that is characteristic of realistic sources.     

Calibration procedure for 3D measurement systems using two cameras and a laser line

In order to ensure the precision of the measurement of complex 3D object surfaces using non-contact laser scanning systems, a novel stereo vision calibration procedure based on a laser line projection plane is presented. This calibration procedure can also be used in measurement systems based on a single camera and a laser line projection. This procedure, while using only laser-coplanar points, is oriented towards laser line detection and allows the matching of two images on the laser projection plane without the use of a rigid motion equation. These features make this procedure very precise, simple and, consequently, easier to implement.     

金柱腔车削工序的贝叶斯质量控制模型

基于贝叶斯理论,针对小批量、少样本的金柱腔生产过程,讨论了生产质量控制模型的建立方法。利用大量历史数据和少量样本信息,建立了金柱腔车削工序的质量控制模型,并利用实际生产数据对该模型进行了验证。验证结果显示,当前金柱腔车削工序的生产过程处于统计控制状态,质量控制模型没有发出生产质量的虚警报,建立的质量控制模型是有效的,能够指导金柱腔车削工序的实际生产。     

Sequentially Estimating the Approximate Conditional Mean Using Extreme Learning Machines

This study examined the extreme learning machine (ELM) applied to the Wald test statistic for the model specification of the conditional mean, which we call the WELM testing procedure. The omnibus test statistics available in the literature weakly converge to a Gaussian stochastic process under the null that the model is correct, and this makes their application inconvenient. By contrast, the WELM testing procedure is straightforwardly applicable when detecting model misspecification. We applied the WELM testing procedure to the sequential testing procedure formed by a set of polynomial models and estimate an approximate conditional expectation. We then conducted extensive Monte Carlo experiments to evaluate the performance of the sequential WELM testing procedure and verify that it consistently estimates the most parsimonious conditional mean when the set of polynomial models contains a correctly specified model. Otherwise, it consistently rejects all the models in the set.     

Selection of shaker specifications in seismic qualification tests

A procedure that can be employed to determine suitable exciter specifications for seismic qualification tests is developed. Estimates for force, power, and stroke ratings of exciter are obtained by this procedure, the mass and the damping ratio of test package and the response spectrum of the excitation signal being used. Either an acceleration required response spectrum (RRS) or a velocity RRS may be used in this procedure to specify the dynamic environment for the test. Two numerical examples are given to demonstrate the procedure.     

Strongly interacting particles with strongly singular potentials

A statistical system of particles is considered for which interaction potentials are strongly singular so that the standard perturbation theory cannot be used. A regular procedure for constructing a mass operator is suggested, having no ultraviolet divergences and giving the possibility of finding corrections for any approximation chosen. In this procedure, the divergences connected with the potential singularity are eliminated with the help of a smoothing function, for which a simple equation is given and whose properties are analyzed both analytically and numerically. Two effective regularization methods are formulated, eliminating divergences occurring while iterating propagator equations. A continuous iterative procedure is invented for calculating observable quantities and the fast convergence conditions for this procedure are shown to be equivalent to the fixed-point conditions.     

An approximate block diagonalization for hermitian matrices as an improvement on successive Van Vleck transformations

A new approximate block diagonalization procedure for hermitian matrices is proposed. This iterative procedure generalizes the perturbation technique of the Van Vleck transformations.     

Minimum-Covariance Estimates of Signal Parameters

We show the existence of the only procedure ensuring the absolute minimum of an arithmetic mean covariance in a certain parameter-variation range and coinciding identically with the algorithm for calculating the estimate minimizing the mean risk for a quadratic loss function and a uniform a priory distribution of parameters. This procedure is compared with the standard method for obtaining maximum likely estimates. In particular, it is shown that the procedure ensures a significantly smaller random scatter of estimates during the estimation of deterministic-signal parameters against the background of Gaussian interference. In the case where the estimate covariance is independent of the parameter estimated for physical reasons, the use of the above procedure with an arbitrary sample size allows us to reach the actual attainable variance bound.     

Transient Photon Transport in Turbid Media with an Irregularly Shaped Foreign Object

A finite-volume method for the modeling of transient photon propagation in turbid media with an irregularly shaped foreign object is presented. The procedure can account for non-rectangular foreign object. Body-fitted coordinates are used to discretize the spatial domain. Absorbing, anisotropic scattering non-homogenous medium can be modeled. The procedure is validated using existing numerical results for a homogenous medium. The procedure produces physically possible trends for different optical properties of the foreign object.     

Diffeomorphism-invariant lattice actions

We present a lattice-discretization procedure which is based on the simplicial lattice preserves diffeomorphism invariance. The presented procedure is the straightforward generalization for the procedure used for discretization of the spinor gravity [7]. As a stable way to guarantee the removing of the lattice regularization, i.e. the continuum limit, for lattice diffeomorphism invariant theories, we propose to tune the system to point of the phase transition. We expect that the Einstein gravitation is achieved at this point.