Anisotropy of the elastic and strength properties of reinforced plastics

The method and results of experimental investigation of anisotropy of the elastic and strength properties of reinforced plastics are discussed. A method of determining the mechanical characteristics in different directions on tubular test pieces is proposed. A special testing machine is described. It is shown that determining the strength and elastic properties of reinforced materials in directions other than the directions of reinforcing on flat test pieces cut mechanically leads to distorted results.Mekhanika Polimerov, Vol. 3, No. 3, pp. 461–466, 1967     

Testing the nullspace property using semidefinite programming

Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results either rely on computing sparse eigenvalues of the design matrix or on properties of its nullspace. So far, no tractable algorithm is known to test these conditions and most current results rely on asymptotic properties of random matrices. Given a matrix A, we use semidefinite relaxation techniques to test the nullspace property on A and show on some numerical examples that these relaxation bounds can prove perfect recovery of sparse solutions with relatively high cardinality.     

External capacitive probes for the nondestructive determination of the dielectric properties of polymeric materials

The effect of the finite dimensions of the test object on the results of nondestructive determination of the dielectric properties of polymers with external capacitive probes has been investigated. Recommendations are made for eliminating the effect of the air gap between the electrodes and the surface of the test object.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1098–1104, November–December, 1969.     

On the Generation of Markov Decision Processes

Comparisons of the performance of solution algorithms for Markov decision processes rely heavily on problem generators to provide sizeable sets of test problems. Existing generation techniques allow little control over the properties of the test problems and often result in problems which are not typical of real-world examples. This paper identifies the properties of Markov decision processes which affect the performance of solution algorithms, and also describes a new problem generation technique which allows all of these properties to be controlled.     

Spaces appearing in the construction of infinite-dimensional analysis according to the biorthogonal scheme

We study properties of annihilation operators of infinite order that act in spaces of test functions. The results obtained are used for establishing the coincidence of spaces of test functions.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 977–990, July, 2004.     

Estimation of the stability of the strength of glass-reinforced plastics in conical shells

On the basis of a statistical analysis of the test data it is shown that there is a difference between the mechanical characteristics (in tension and compression) of laminated glass-reinforced plastics obtained under laboratory and industrial conditions by impregnation under pressure in a closed mold. The stability of the strength properties of the glass-reinforced plastic in various conical shells, produced in large batches, is considered. Certain experimental relations between the material properties and the total number of shells produced are also established.Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 102–108, January–February, 1970.     

Comparison of the asymptotic stability properties for two multirate strategies

This paper contains a comparison of the asymptotic stability properties for two multirate strategies. For each strategy, the asymptotic stability regions are presented for a 2×2 test problem and the differences between the results are discussed. The considered multirate schemes use Rosenbrock type methods as the main time integration method and have one level of temporal local refinement. Some remarks on the relevance of the results for 2×2 test problems are presented.     

Identification of chaos in a cutting process by the 0–1 test

We have examined the cutting process by using a two degrees of freedom non-smooth model with a friction component. Instead of the standard Lyapunov exponent treatment a statistical ‘0–1’ test based on the asymptotic properties of a non-harmonic Brownian motion chain has been successively applied to reveal the nature of the cutting process. In this test we calculated the control parameter K which is approaching asymptotically to 0 or 1 for regular and chaotic motions, respectively. The presented approach is independent on the integration procedure as we defined a characteristic distance between the points forming the time series used in the test separately.     

Testing exponentiality against a class of alternatives which includes the RNBUE distributions based on the empirical laplace transform

A scale-free test for exponentiality is proposed which is consistent within an extended set of models, including, but not limited to, the “renewal new better than used in expectation” (RNBUE) class of life distributions. The limiting null distribution of the test statistics is derived, and the approximate local Bahadur efficiency is calculated for several families of alternatives. Finite-sample properties of the proposed procedures are investigated via simulation. Bibliography: 24 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 63–77.     

On the sensitivity of the one-sided test to covariance misspecification

Sensitivity analysis stands in contrast to diagnostic testing in that sensitivity analysis aims to answer the question of whether it matters that a nuisance parameter is non-zero, whereas a diagnostic test ascertains explicitly if the nuisance parameter is different from zero. In this paper, we introduce and derive the finite sample properties of a sensitivity statistic measuring the sensitivity of the t statistic to covariance misspecification. Unlike the earlier work by Banerjee and Magnus [A. Banerjee, J.R. Magnus, On the sensitivity of the usual t- and F-tests to covariance misspecification, Journal of Econometrics 95 (2000) 157–176] on the sensitivity of the F statistic, the theorems derived in the current paper hold under both the null and alternative hypotheses. Also, in contrast to Banerjee and Magnus’ [see the above cited reference] results on the F test, we find that the decision to accept the null using the OLS based one-sided t test is not necessarily robust against covariance misspecification and depends much on the underlying data matrix. Our results also indicate that autocorrelation does not necessarily weaken the power of the OLS based t test.     

On the stability of the one-step exact collocation methods for the numerical solution of the second kind Volterra integral equation

The purpose of this paper is to analyze the stability properties of one-step collocation methods for the second kind Volterra integral equation through application to the basic test and the convolution test equation.Stability regions are determined when the collocation parameters are symmetric and when they are zeros of ultraspherical polynomials.     

Shape preserving representations and optimality of the Bernstein basis

This paper gives an affirmative answer to a conjecture given in [10]: the Bernstein basis has optimal shape preserving properties among all normalized totally positive bases for the space of polynomials of degree less than or equal ton over a compact interval. There is also a simple test to recognize normalized totally positive bases (which have good shape preserving properties), and the corresponding corner cutting algorithm to generate the Bézier polygon is also included. Among other properties, it is also proved that the Wronskian matrix of a totally positive basis on an interval [a, ) is also totally positive.Both authors were partially supported by DGICYT PS90-0121.     

Asymptotic power properties of the Cramér-von Mises test under contiguous alternatives

The asymptotic power of the Cramér-von Mises test (CvM test) when parameters are estimated from the data is studied under certain local (contiguous) alternatives. The notion of (asymptotic) direction and distance from the null hypothesis of alternatives is introduced, and it is shown that there exist directions with maximum, minimum, and arbitrary intermediate power. For each direction, there exists a natural asymptotic testing problem with an uniformly most powerful test that is compared with the CvM test. For that, the notion of asymptotic local efficiency (ALE) of the CvM test is introduced. finally, the influence of more information on the (unknown) parameter is studied for three tests of the CvM-type for independence. it is shown that for certain directions, a better knowledge of the parameter may increase the power, and for other ones decrease it. These properties are analogous to that of the X²-test in similar situations.     

On the semicontinuity problem of fibers and global F-regularity

In this article, we discuss the semicontinuity problem of certain properties on fibers for a morphism of schemes. One aspect of this problem is local. Namely, we consider properties of schemes at the level of local rings, in which the main results are established by solving the lifting and localization problems for local rings. In particular, we obtain the localization theorems in the case of seminormal and F-rational rings, respectively. Another aspect of this problem is global, which is often related to the vanishing problem of certain higher direct image sheaves. As a test example, we consider the deformation of the global F-regularity.     

Numerical analysis of the states of deformation and stress in the compact tension specimen (CT)

This work presents a new method of determination of the states of stresses and strains in the compact tension specimen (CT). The numerical analysis was carried out in ANSYS/LS–DYNA programme. The Cowper–Symond's material model was applied in the computational analysis. Selected mechanical properties executed from the uniaxial tension test were used in the numerical calculations. The main aim of this paper is to determinate the influence of the dimensions and vertical notch angle of CT on the stresses and strains states. The present application allows a calculation of the states of stresses and strains in arbitrarily specimen place, and at any time of the duration of the tensile test process. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spline solution of the generalized Burgers'-Fisher equation

A numerical method based on exponential spline and finite difference approximations is developed to solve the generalized Burgers'-Fisher equation. The error analysis, stability and convergence properties of the method are studied via energy method. The method is shown to be unconditionally stable and accurate of orders 𝒪(k?+?kh?+?h ²) and 𝒪(k?+?kh?+?h ⁴). Some test problems are given to demonstrate the applicability of the purposed method numerically. Numerical results verify the theoretical behaviour of convergence properties. The main superiority of the presented scheme is its simplicity and applicability in comparison with the existing well-known methods.     

On the definition of viscosity solutions for parabolic equations

In this short note we suggest a refinement for the definition of viscosity solutions for parabolic equations. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behavior prior to the given moment of time and ignore what happens at times after that.

     

Nonparametric tests of independence between random vectors

A nonparametric test of the mutual independence between many numerical random vectors is proposed. This test is based on a characterization of mutual independence defined from probabilities of half-spaces in a combinatorial formula of Möbius. As such, it is a natural generalization of tests of independence between univariate random variables using the empirical distribution function. If the number of vectors is p and there are n observations, the test is defined from a collection of processes R_n,A, where A is a subset of {1,…,p} of cardinality |A|>1, which are asymptotically independent and Gaussian. Without the assumption that each vector is one-dimensional with a continuous cumulative distribution function, any test of independence cannot be distribution free. The critical values of the proposed test are thus computed with the bootstrap which is shown to be consistent. Another similar test, with the same asymptotic properties, for the serial independence of a multivariate stationary sequence is also proposed. The proposed test works when some or all of the marginal distributions are singular with respect to Lebesgue measure. Moreover, in singular cases described in Section 4, the test inherits useful invariance properties from the general affine invariance property.     

The composite Milstein methods for the numerical solution of Stratonovich stochastic differential equations

In this paper, we present two composite Milstein methods for the strong solution of Stratonovich stochastic differential equations driven by d-dimensional Wiener processes. The composite Milstein methods are a combination of semi-implicit and implicit Milstein methods. The criterion for choosing either the implicit or the semi-implicit method at each step of the numerical solution is given. The stability and convergence properties of the proposed methods are analyzed for the linear test equation. It is shown that the proposed methods converge to the exact solution in Stratonovich sense. In addition, the stability properties of our methods are found to be superior to those of the Milstein and the composite Euler methods. The convergence properties for the nonlinear case are shown numerically to be the same as the linear case. Hence, the proposed methods are a good candidate for the solution of stiff SDEs.