Showing papers on "Piecewise linear function published in 1975"

Evaluation of potential integral at singularity of exact kernel in thin-wire calculations

Abstract: A technique is presented for calculating the potential integral of thin-wire theory at the singularity of the exact kernel in cases where the current is representable as piecewise constant and/or piecewise linear over an interval containing the singularity. The integral of the rapidly varying portion of the kernel is converted to a highly convergent power series. Examples of how one employs the results in computations are given.

Error estimates for a finite element approximation of a minimal surface

Abstract: A finite element approximation of the minimal surface problem for a strictly convex bounded plane domain Q2 is considered. The approximating functions are continuous and piecewise linear on a triangulation of Q2. Error estimates of the form 0(h) in the H1 norm and 0(h 2) in the Lp-norm (p < 2) are proved,where h denotes the maximal side in the triangulation.

On the Calculation of the Piecewise Linear Approximation to a Discrete Function

Abstract: A repeated scanning algorithm for determining the minimax approximation to an arbitrary function by means of a piecewise linear function with a fixed number of variable knots is described, and it is compared to optimal and suboptimal methods.

A Method for Estimating the Number of Hours Below a Selected Temperature Threshold

Abstract: A method is presented for fitting climatic data with linear and piecewise linear equations. A least-squares technique was used to estimate hours below a selected temperature threshold. Three empirical equations were derived for estimating hours with temperatures below 45°F, the coefficients of correlation of which are 0.979, 0.988 and 0.989 respectively.

Extremum theorems for large displacement analysis of discrete elastoplastic structures with piecewise linear yield surfaces

Abstract: Discrete or discretized structures are considered in the range of large displacements. Elastic plastic behavior is assumed, under the hypothesis that both yield functions and hardening rules are piecewise linear. The structural response to a single finite loading step is assumed to involve regularly progressive yielding (no local unloading). An extremum property of this structural response is established, by recognizing that the relations governing the configuration change coincide with the Kuhn-Tucker conditions of a particular nonlinear constrained optimization problem, subject to sign constraints alone. This extremum property can be regarded as an extension of the theorem of minimum potential energy. Other properties, even if computationally less attractive, broaden the theory developed, so that some results previously obtained are derived as special cases.

Electronically programmable function generator

Abstract: An electronically programmable function generator with two dimensional programmability is provided which has an output, a current, which is a piecewise linear function ("transfer curve") of its input, a voltage. The transfer curve consists of contiguous straight line segments and the breakpoints between the line segments are electronically non-interactive and independently programmable. The generator in its preferred embodiment linearizes the response of a non-linear amplifier or can be utilized wherever an empirical non-linear function is needed in an analog system.

Energy Approach to Inelastic Cable-Structure Analysis

Abstract: A mew method is presented for the analysis of suspended structures in the presence of combined geometric and physical nonlinearities. Physical nonlinearity is due to loosening of cable numbers or their tensile yielding, or both, and is described by piecewise linear laws. It is shown that the solution can be attained by minimizing, under sign constraints only, an energy function of nodal displacements and “corrective” or “inelastic” strains (i.e., strains additional to the linear elastic ones). Thus a new generalization of the potential energy principle is achieved. The proposed numerical procedure consists of a fairly efficient algorithm in nonlinear programming. The irreversible nature of possible plastic deformations can be easily allowed for, from one loading step to another, by adjusting the piecewise linear cable law.

A Study of Marginal Oscillator Behavior

Abstract: In a magnetic resonance spectrometer, a marginal oscillator is used as a transducer to convert a minute change in the tank coil resistance into a change in the amplitude of oscillation. Thus one can define a conversion gain as the ratio of the fractional change in the amplitude of oscillation to the fractional change in the tank coil resistance. Since the change in the tank coil resistance is made periodic at a low frequency to facilitate phase-sensitive detection, a study of the transient behavior of the oscillator becomes important. In this paper, the conversion gain, bandwidth, and noise associated with the oscillator are studied as functions of the circuit parameters, utilizing a piecewise linear characteristic for the active device. Unlike the studies carried out by other authors making use of a polynomial expansion for the nonlinear characteristic, the piecewise linear characteristic has been chosen because it is more amenable to synthesis. The sensitivity of the amplitude of oscillation to the variation of the characteristics of the active device has also been evaluated, and the relationship between the stability requirement of the device characteristics and the conversion gain has been established.

Simplex analysis of grounded concave piecewise‐linear resistive networks

Abstract: The physical properties of the networks under consideration may be advantageously used for saving time and storage in analysing nonlinear networks. The algorithm proposed in the present paper represents an attempt in this direction. It concerns a particular class of piecewise linear resistive networks and it is based on a modification of the simplex as originally proposed by Dantzig. The algorithm requires: 1 The analysis of the linear network obtained by the given one by replacing the nonlinear resistances by linear ones. 1 The application of the modified simplex. This second step requires a number of arithmetical operations less than that necessary for analysing a linear resistive network having a number of nodes equal to the total number of break-points of the nonlinear resistances.

Piecewise approximation functions an educational note

Abstract: This paper gives a survey of piecewise approximation functions. Aside from the use of dummy variables, little research has employed such functions. Piecewise functions permit the dependent variable of a functional relationship to take on different forms with respect to the independent variable on various subintervals of the domain of the independent variable. Three types of piecewise approximation functions are considered: dummy variables, piecewise linear regressions and cubic splines. The theoretical and empirical properties of such functions are discussed within the context of an illustrative example involving the increase in ridership over time on urban mass transit systems. Dummy variables take account of shifts in the structural relation in a discontinuous fashion. Piecewise regressions and cubic splines allow for structural shifts without discontinuities arising. Tests are performed to determine whether a linear, quadratic, or cubic piecewise continuous function should be employed. In addition a test is employed to see if structural change occurs in the functional relation at the shift points.

An integrated function generator with two-dimensional electronic programming capability

Abstract: Describes a novel, electronically programmable function generator which has been designed, fabricated, and tested. Output is a piecewise linear function of the input and both coordinates of the function breakpoints can be independently programmed.

On a distance function between differentiable structures

Abstract: In this note, we investigate a relation between the connected sum of manifolds and the distance of manifolds ([2]). Since the smoothing of a piecewise linear equivalence is given by connected sum of exotic spheres ([1]), we have a certain estimate of the smoothing obstruction using the distance of manifolds (Proposition 3). In § 3, an application is given to show the impossibility of the 0.64-pinching of an exotic sphere.

Kolmogorov-smirnov-statistics under the alternative

Abstract: For the two sample problem the exact distributions of the one-sided and two-sided Kolmogorov-Smirnov-Statistics and being the empirical distribution functions of the samples) are derived for the family of apriori distributions (F, G), where F, G are both piecewise linear. In the second part approximation-therems are proved which can be used to approximated the distribution of Kolmogorov-Smirnov statistics in the case of general alternatives by means of these distributions for piecewise liner alternatives.

Novel analytic technique for obtaining the spectrum associated with piecewise-linear frequency modulation

Abstract: A new analytic method is presented for determining the frequency spectra associated with frequency-modulated waves. A piecewise-linear approximation to the modulation is used, the spectra being calculated for each piece. The sum of these spectra gives the total spectrum for the modulated signal.