2nd Order Derivative Research Articles

Impact of poly-gate depletion on MOS RF linearity

The distortion behavior for thin oxide MOS transistors can be degraded due to polysilicon-gate depletion effects. The nonlinear, bias-dependent gate capacitance for thin oxide MOSFET's results in significant 2nd-order derivatives in gate capacitance, (/spl part//sup 2/C(V/sub gs/)//spl part/V/sub gs//sup 2/), which in turn results in substantial 3rd-order derivative contributions to drain current, (/spl part//sup 3/I/sub ds///spl part/V/sub gs//sup 3/). This may restrict the use of very-thin oxide MOSFET's in RF applications.

Eigenvalue analysis of structures with flexible random connections

A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

Resolution of overlapping mid-infrared spectra using SIMPLISMA and a second-order derivative approach

Abstract Matrices of severely overlapping mid-infrared mixture spectra have been resolved into the pure compounds' spectra and concentration profiles using SIMPLISMA and a 2nd order derivative approach. For a three-compound mixture system of organic solvents, SIMPLISMA qualitatively resolves the spectra satisfactorily while it provides only semi-quantitative concentrations. Quantitative results are obtained by applying an additional iterative procedure. Applied to water spectra acquired in the temperature range 2–96°C, SIMPLISMA resolves two spectra. Using a discrete model, these spectra can be interpreted as corresponding to water structures constructed of H2O molecules with a relatively high and low average number of H-bonds. After an optimising procedure the estimated enthalpy was 2.3 kcal mol−1, which is in accordance with figures found in literature.

Simultaneous 2nd Order Derivative Spectrophotometry Determination of Sorbic and Benzoic Acids in Soft Drinks

Abstract A method is developed for the simultaneous 2nd order spectrophotometric determination of 1 to 7 μg.mL−1 of each of benzoic and sorbic acids in non vegetal soft drinks, using a blank prepared from the same soft drink to be analyzed in order to avoid the interferece from other additives and colouring matter present.

2nd and 3rd Order Derivative Spectrophotometric Determination of Ascorbic Acid in Soft Drinks

Abstract A method is developed for the 2nd and 3rd order derivative spectrophotometric determination of 0.5–6 and 0.5–7 μ.ml−1 of ascorbic acid, respectively. For its determination in soft drinks a blank solution is prepared from the soft drink to be analyzed in order to avoid the interference from the other additives and colouring matter present.

Curvature-dependent parameterization of curves and surfaces

An efficient way of drawing parametric curves and surfaces is to approximate the curve or surface by a sequence of straight-line segments or a mesh of polygons, respectively. In such an approximation, many small line segments or polygons are needed in regions of high curvature, and fewer and larger ones are needed in regions of low curvature. In the paper, special parameterizations of curves and surfaces, called angle parametrizations, are defined such that good approximations to curves and surfaces can be found by uniformly subdividing the parameter space, and applying the special parameterization. A pleasing feature of these parameterizations is that they are easily computed numerically. The numerical methods only require explicit expressions for the 1st- and 2nd-order derivatives of the original parameterization. This implies that the methods presented are applicable to the polynomial and rational curves and surfaces customarily used in computer-aided design, but are not limited to these. Some specific examples are presented. The numerical algorithm for surfaces is inherently suited to implementation on a network of processors operating in parallel, and such an implementation is briefly discussed.

A regularized boundary integral equation method for elastodynamic crack problems

This paper presents a double layer potential approach of elastodynamic BIE crack analysis. Our method regularizes the conventional strongly singular expressions for the traction of double layer potential into forms including integrable kernels and 0th, 1st and 2nd order derivatives of the double layer density. The manipulation is systematized by the use of the stress function representation of the differentiated double layer kernel functions. This regularization, together with the use of B-spline functions, is shown to provide accurate numerical methods of crack analysis in 3D time harmonic elastodynamics.

Numerical algorithms for solving nonlinearLр-norm estimation problems: part II - a mixture method for large residual and illo-conditioned problems

The nonlinear least squares algorithm of Gill and Murray (1978) is extended and modified to solve nonlinear L р-norm estimation problems efficiently. The new algorithm uses a mixture of 1st-order derivative (Guass-Newton) and 2nd-order derivative (Newton) search directions. A new rule for selecting the “grade” r of the p-jacobiab matrix Jp was also incorporated. This brought about rapid convergence of the algorithm on previously reported test examples.

Adaptive Density Flattening--A Metric Distortion Principle for Combating Bias in Nearest Neighbor Methods

With a wide variety of approaches to density estimation, it is profitable to perturb the data so as to make 2nd order derivatives of their density vanish. An adaptive transformation to local uniformity for instance will (for unchanged variance) lower bias to a vanishing fraction of what a Rosenblatt-Parzen or nearest neighbor estimator on the raw data yields; fractional pilot sampling, a common technical device of little practical appeal, can be shown by an embedding argument to be dispensable. An upshot is that MSE can be lowered by attacking the variance directly through extra smoothing, without the usual penalty from inflated bias.

2nd-Order Derivative Spectrometry in the Analysis of Formaldehyde (Applied for Exhaust Gases from an Alcohol Fueled S.I. Engine)

2nd-Order Derivative Spectrometry in the Analysis of Formaldehyde (Applied for Exhaust Gases from an Alcohol Fueled S.I. Engine)

On precision limits for derivatives numerically calculated from noisy data

This paper has three purposes. 1. (1) To verify an error formula from which the maximal precision in derivatives obtained from noisy measurement data can be calculated. The formula is verified by comparison with the resulting noise in derivatives obtained by local least squares polynomial fitting. It is also verified that differentiation by Fourier series expansion gives noise exceeding the minimum value according to the error formula. 2. (2) An index called the “Relative Noise Amplification” (RNA) is introduced. For an arbitrary differentiating filter it is defined as the noise transmission of the filter divided by the minimal noise transmission according to the above mentioned error formula. When the filter produces unbiased estimates the value of the RNA always exceeds one. The RNA can be used as a quality index for differentiating filters. The filter with the smallest value on the RNA also has the smallest amount of noise superimposed on the calculated derivatives provided the input noise is white and additive. 3. (3) The bandwidth and the Relative Noise Amplification of differentiating filters obtained by local least squares polynomial fitting are presented. The 0th, 1st and 2nd order derivatives have been investigated for polynomials up to 8th order. These results can be used for the determination of suitable filter parameters in various applications.