Higher-order Ones Research Articles

Method for measuring properties of high relative dielectric constant materials in a cutoff waveguide cavity

In this paper, a method for measuring properties of ceramic materials with relative dielectric constant value of 20-150 is proposed. It permits us to eliminate the operating TM/sub 01/spl delta//-mode degeneration due to its frequency coincidence with other modes, including ones of higher order. Both that fact and the possibility of precise calculation of an unloaded quality factor for a cavity permit one to execute the accurate measurements of loss tangent values as low as (1/spl divide/0, 5)/spl times/10/sup -4/, the error of dielectric constant measurement being equal to or less than 1%. The feasibility of precise measurement of the loaded Q-factor of a cavity by the readings of micrometric probe makes the use of frequency meters unnecessary.

Numerical treatment of the nerve conduction equation

This paper is devoted to study the numerical solution of a pair of differential equations which are of the FitzHugh–Nagumo (F–N) type. Existence and uniqueness for such system has been given in 1978 by Rauch and Smoller. Our main concern in this article is to use high ordered splines as basis for the collocation method to solve numerically such differential equations. Finite difference methods were used in 1979 by Khalifa as well as collocation with cubic and quadratic splines but higher order ones were not used because of the discontinuity in the second derivative of the solution. In this paper, we considered the problem under the same basis in three separate regions and end up with a forced parameter in the quintic splines to satisfy the solution in the first and third subregions after getting the solution in the middle region, in which we overcome the difficulty of the discontinuity in the second derivative. Numerical results obtained are good and more accurate than the previous ones.

SUBMODELS OF NONLINEAR GRASSMANN SIGMA MODELS IN ANY DIMENSION AND CONSERVED CURRENTS, EXACT SOLUTIONS

In the preceding paper,1 we constructed submodels of nonlinear Grassmann sigma models in any dimensions and, moreover, an infinite number of conserved currents and a wide class of exact solutions. In this letter, we first construct almost all conserved currents for the submodels and all those for CP1-model. We next review the Smirnov and Sobolev construction for the equations of CP1-submodel and extend the equations, the S-S construction and conserved currents to higher order ones.

On the validity of the elastic expansion of the free energy of nematic liquid crystals

The elastic free energy F el of nematic liquid crystals is a truncated power expansion of the free energy F in the gradients of the director field n(r) . In principle, the cut-off distortion length for F el could be estimated from the direct comparison between the elastic terms and the higher order ones. However, in the case of dispersion interactions, the higher order elastic constants diverge and this comparison is not possible. The divergence of the higher order constants poses some doubt about the internal consistency of the elastic expansion itself. In this paper, we use a molecular model of a nematic liquid crystal to calculate the total free energy and its elastic approximation. The two free energies are calculated numerically for some director configurations as a function of the characteristic distortion length L dis. A good agreement between the two free energies is found for slow director fields, and large deviations are observed only if L dis ≈ a, where a is the molecular length. This result demonstrates the validity of the elastic expansion and shows that the higher order terms affect only the behavior at very short length scales.

On the implementation of boundary conditions for the method of lines

The method of lines for difference approximations of hyperbolic first order systems of partial differential equations is analyzed. The approximations are based on strictly semibounded difference operators including high order ones. The formulation of the ODE-system requires that the implementation of the boundary conditions is done carefully. We shall illustrate how different ways of implementation give rise to different stability properties. In particular, we derive a way of implementation that leads to an approximation that is strongly stable.

Dynamics of the ordered structure formation in a thermal dusty plasma

The dynamics of the ensemble of interacting dust grains under conditions of thermal plasma was studied, and the formation of the liquidlike structure observed in the experiment was investigated. The simulation results showed that ordering of the dust structure manifested in the experiment with thermal dusty plasmas can be explained by the electric interaction of dust grains. It is found that the structure obtained in the experiment is far from equilibrium because the plasma flight time is less than the time of structure formation. It conforms to the emergence of the experimental correlation function characterized by a sharp main peak with no highorder ones. It is shown through experimental measurements of the diffusion coefficient that the thermal energy of dust grains is close to the gas temperature, and the friction force acting on grains is determined via the expression obtained in the kinetic limit. @S1063-651X~98!03606-X#

Nonlocal Behavior in Polynomial Regressions

Polynomial regression is a common technique for estimating conditional mean functions of unknown form. Increasing the order of the polynomial increases the flexibility of the estimated function. This note shows with an example how these estimated polynomials, even (perhaps especially) higher-order ones, display undesirable nonlocal effects. That is, values of the response corresponding to a particular value or range of the predictor may have a large and undesirable influence on the predicted response at a very different value of the predictor.

The enemy within: Autocorrelation bias in content analysis of narratives

Many content analysis studies involving temporal data are biased by some unknown dose of autocorrelation. The effect of autocorrelation is to inflate or deflate the significant differences that may exist among the different parts of texts being compared. The solution consists in removing effects due to autocorrelation, even if the latter is not statistically significant. Procedures such as Crosbie's (1993) ITSACORR remove the effect of at least first-order autocorrelations and can be used with small samples. The AREG procedure of SPSS (1994) and the AUTOREG procedure of SAS (1993) can be employed to detect and remove first-order autocorrelations, and higher-order ones too in the case of AUTOREG, while several methods specifically intended for small samples (Huitema and McKean, 1991, 1994) have been developed. Four examples of content analysis studies with and without autocorrelation are discussed.

Deformation structures in ball milled copper

The deformation structures of copper powder induced by ball milling were studied in detail by using high resolution electron microscopy. It was found that copper powder after 20 h of milling shows the formation of shear bands and a number of mechanical twins. The observed twins belong to two types, i.e. multiple twins and high-order ones. It is suggested that Venables' model on mechanical twins in face-center-cubic metals is reasonable in this case. The generation of mechanical twins could be explained as follows: the shear stress ( P max) induced by ball milling exceeds the critical shear stress for twinning (τ); the grain size decreases to a critical value below which twinning rather than slip is the preferred mode of deformation as well as the high strain rates induced by ball milling. The formation of subgrains was found to occur via two routes: they were formed both in the shear bands and at the tip of them or at the tip of the twin boundaries, or at the edge of the larger grains. The subgrains formed via the two ways are in nanometer scale (10–100 nm), and their orientations are completely random. The as-received nanograins contained high density of dislocations. The grain boundaries (GBs) of nanocrystalline (NC) Cu are usually ordered, curved and strained, and disordering, lattice distortion and nanovoids in local regions were observed too.

Linkers and Nonlinkers: Goal Beliefs as a Moderator of the Effects of Everyday Hassles on Rumination, Depression, and Physical Complaints1

We blocked subjects on their tendency to link the attainment of lower order goals (e.g., being one's ideal weight) to the attainment of a higher‐order goal (i.e., being happy). We then assessed the number of everyday hassles these subjects experienced, the amount of rumination they reported, their level of depression, and the extent to which they were bothered by a number of physical symptoms. These measures were taken at 2 time periods, 2 weeks apart. In the first session, subjects who tended dispositionally to link lower‐order goals to higher order ones were more likely than were those who did not make this link to ruminate, experience depression, and complain of physical symptoms. At Session 2, linkers who had experienced a high number of hassles in Session 1 reported higher depression and more bother from physical symptoms than did any of the other groups. These results are consistent with the growing body of evidence indicating a relation between rumination and depression and suggest that one factor that determines rumination is the extent to which people link the attainment of lower‐order goals to the attainment of higher‐order goals.

Special finite elements for use with high-order boundary conditions

A hierarchy of special two-dimensional finite elements is constructed for use in a layer near a boundary or an interface B . The construction of the elements guarantees high-order ( C N ) regularity along B and C 0 regularity elsewhere. All the elements in the hierarchy are proved to be fully conforming. The most important finite element in this class is the first-order one, which provides C 1 regularity on B and C 0 regularity elsewhere. It is used here to improve the numerical solution of Dirichlet problems, by prescribing the tangential derivative of the solution on B in addition to the solution itself. This element and higher-order ones are also useful near artificial boundaries where high-order local non-reflecting boundary conditions are used, and as transition elements near the interface between a domain governed by a ‘ C 0 theory’ and a domain governed by a ‘ C N theory.’

Higher-order structure in regularity detection

In three experiments a simple Euclidean transformation (reflection, translation, rotation) was applied to collections of twelve dots in such a way that they contained equal lower-order structure, defined on the pairwise grouping of elements with their partner following transformation (e.g. parallel virtual lines), but differed in the presence vs absence of higher-order structure, defined on pairs of pairwise groupings (e.g. virtual quadrangles with correlated angles). Based on the much better performance levels ( d′) in the case of additional higher-order structure, we conclude that global regularities are easier to detect when the local correspondences are supported by higher-order ones formed between them. These enable the lower-order groupings to spread out across the whole pattern very rapidly (called bootstrapping). As a preliminary attempt to specify these principles, we proposed a working model with two basic components: first, a function expressing the cost of a perceptual grouping or the lack of regularity, and, secondly, an algorithm based on simulated annealing to minimize the cost function. The simulation results obtained with our current implementation of these principles showed satisfactory qualitative agreement with human regularity detection performance. Finally, the theory was shown to capture the essence of a large number of grouping phenomena taken from diverse domains such as detection of symmetry in dot patterns, global structure in Glass and vector patterns, correspondence in stereoscopic transparency and apparent motion. Therefore, we are convinced that, in principle, the mechanism used by the human visual system to detect regularity incorporates something like bootstrapping based on higher-order structure. We regard this as a promising step towards unraveling the intriguing mechanisms of classic Gestalt phenomena.

An investigation of the phenomenon of double high water or double low water at some harbours

Double high water or double low water results from a subtle interaction between the fundamental and the higher harmonics, which need amplitudes of only a few percents of that of the fundamental, to distort markedly the levels around high water or low water. The fundamental is usually M2, whose harmonics are M4, M6, M8, M10, etc. of order 2, 3, 4, 5. The capacity of a higher harmonic to modulate an extremum depends on the square of its order, thus making the higher order ones much more effective. Contrary to widespread belief, the second harmonic M4 alone, cannot be responsible for the effect since this would require it to have an amplitude exceeding 25% of that M2, which occurs very rarely. The presence of the other harmonics, especially of odd order, which are generated in shallow water by bottom friction, is essential, while theoretically at least, M4 is completely expendable. Such distortions are rarely encountered in nature because the higher harmonics must be either in or out of phase with the fundamental, a very stringent requirement. When double high water, double low water or stands do occur, they should be found in open water, near the coast or in shallow estuaries, not inside rivers discharging fresh water. Theoretical cases are considered as well as the actual conditions prevailing at some European harbours.

Calculation of moment invariants via hadamard transform

The calculation of moment invariants via the Hadamard transform is proposed. First of all, the relationship between moments and coefficients of a Hadamard transformed image is established. Moments can then be calculated from these coefficients via addition and shift operations except for a negligible amount of multiplication operations. Furthermore, based on the relationship among moments, the higher order ones can be computed from the lower order ones. For the simply connected binary image regions, the amount of computation can be further reduced by projecting the original two-dimensional (2D) image to the x- and y-direction one-dimensional (1D) arrays and tracing the object's boundary to get the values. Simulation results indicate that the amount of computation required for the proposed algorithm is only about 50% of Li's algorithm.

Uniqueness and bifurcation in elastic-plastic solids

The present work is concerned with the problems of uniqueness and bifurcation in a time-independent elastic-plastic material obeying the normality flow rule with a smooth yield surface. Rate n constitutive relations are formulated for the corresponding material. Under self-adjoint boundary conditions, it is shown that every solution of the rate n boundary value problem is governed by a variational principle and the corresponding functional reaches a strict absolute minimum if the solution satisfies a sufficient uniqueness condition. In order to analyse uniqueness and bifurcation, a series of linear comparison solids are constructed. It is shown that Hill's exclusion condition excludes not only rate one bifurcations but also higher order ones.

SET-VALUED DERIVATIVES OF ONE-DIMENSIONAL DISTRIBUTIONS

By using harmonic representations of distributions, set-valued derivatives of one-dimensional distributions are introduced in this paper. And several equivalent definitions of the set-valued derivative are given for continuous real functions. The set-valued derivative of a local Lipschitz function coincides with the generalized gradient defined by F. H. Clarke. A distribution is Lipschitz near a point if and only if its set-valued derivative at this point is finite. When the set-valued derivative at some point of a distribution on R does not contain both +∞ and -∞ its distributional derivative is a Radon measure on some neighbourhood of this point. By using the first order'set-valued derivatives, an existence theorem of inverse functions of continuous functions is proved; and by using higher order ones, two very general sufficient conditions for a distribution to attain extremal values are obtained. A distribution is convex on an open interval if and only if its second order set-valued derivatives at all points of the interval are contained in [0, +∞]. Therefore, a satisfactory differential theory of nondifferentiable functions is developed.

Statistical field theory of multiparticle density fluctuations.

We present a three-dimensional statistical field theory of density fluctuations motivated by the Ginzburg-Landau theory of superconductivity. The free-field theory yields Yukawa-type two-particle cumulant correlations and no higher-order ones, in agreement with high-energy heavy-ion data. We mention the extension of our model to describe hadronic reactions and indicate how it may be related to QCD. We predict the multiplicity distribution of particles produced in heavy-ion collisions.

Systematic comparison of statistical analyses of electronic and vibrational circular dichroism for secondary structure prediction of selected proteins

The electronic (ultraviolet) circular dichroism (UVCD) and vibrational circular dichroism (VCD) of 20 proteins are systematically compared as to their relationship to the secondary structures of these proteins. The UVCD spectra are statistically treated by use of the same factor analysis methods used previously for VCD. The UVCD spectra can be reproduced as linear combinations of five subspectra. The first subspectrum reflected the expected alpha-helical UVCD shape, particularly at longer wavelengths, while the higher order ones had less obvious similarity to standard bandshapes. Cluster analysis on the UVCD factor analysis coefficients reflected the clustering on the basis of the fractional secondary structure parameters (from X-ray) but was less clear than VCD. Qualitative complementarity of protein VCD and UVCD spectra was demonstrated by combined cluster analysis of their respective factor analysis coefficients. Quantitative relationships between spectral coefficients and fractional secondary structure were determined by multiple regression analyses using only statistically important coefficients. These resulted in an ability to reproduce four of the structural parameters with errors for individual proteins comparable to the VCD result. In UVCD, the standard deviations of the regression fit for beta-sheet were worse and for the undefined part of the structure were better than in VCD. Parallel analyses using the partial least-squares method showed UVCD in that case to have more error than VCD in reproducing the training set structural parameters. Comparison of the regression and partial least-squares methods illustrated limitations of total back-transformation of the UVCD spectra into structural parameters.

Detection of generalized principal axes in rotationally symmetric shapes

Automatic detection of the principal axes of given shapes with known symmetry properties is studied in this paper. The inapplicability of a well-known equation, which is used to compute the direction of the principal axis of a given shape using moment functions, to a class of so-called degenerate shapes is first pointed out. Rotationally symmetric shapes often encountered in real applications are shown to belong to this class. This problem is solved by extending the notion of principal axis to higher order ones in terms of higher order moment functions. Analytic equations for computing the direction of high-order principal axes are derived. They include the well-known equation for computing the direction of the (second-order) principal axis as a special case. Some experimental results are included finally to show the effectiveness of the derived analytic equations.

A note on the modified stability table for linear discrete time systems

It is shown how to obtain the inner determinants of the stability determinantal criterion from the entries of the modified stability table. This requires the expansion of only 2*2 determinants instead of higher-order ones. This constitutes a computational simplification of the determinantal criterion. The results are the discrete analog of obtaining the Hurwitz minors from the Routh table.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>