Showing papers on "Tangent published in 1984"

A new method for linearizing non-linear systems : the pseudolinearization†

Abstract: Consider the single-input non-linear system x = f(x, u). It has been shown that, under mild conditions, there exist transformations z=T[x), v = S(x, u) such that, in the z-space, the linear tangent model is independent of the operating point. A constructive procedure to obtain the above transformations is described. This new method is computationally attractive and effective in many practical cases.

A maximum-dissipation principle in generalized plasticity

Abstract: It is shown that in large-deformation generalized plasticity a local maximum-dissipation postulate is equivalent to the condition that the plastic strain rate (in the sense of Rice) cannot oppose the total strain rate, when strain space is regarded as a Riemannian manifold with the instantaneous Lagrangian tangent elastic stiffness as the metric tensor. From this condition, normality conditions in strain space (in this sense) and in the space of the second Piola-Kirchhoff stress (in the usual sense) are derived. With the additive decomposition of strain, the loading surface has essentially the same properties as in infinitesimal-strain plasticity. For the multiplicative decomposition, approximate normality rules are derived.

A representation for image curves

Abstract: A representation for image curves and an algorithm for its computation are introduced. The representation is designed to facilitate matching of image curves to completely specified model plane curves and estimation of their orientation in space, despite the presence of noise, variable resolution, or partial occlusion. This is an important subproblem of model-based vision. A curve may be represented at a variety of scales, and a strategy for selecting natural scales is proposed. At each scale, the representation is simply a list of positions in the plane, with tangent directions and curvatures specified at each position; each curvature is cither a zero or an extremum (hereafter critical points). The algorithm for computing the representation involves smoothing with gaussians at different scales, extracting the critical points from the smoothed curves, and using dynamic programming to construct a list of critical points which best approximate the curve for each length of list possible. We propose to examine the tradeoff between the error of the approximation and length of the lists to find natural scales.

On the validity and practical applicability of derivative analyticity relations

Abstract: We examine derivative analyticity relations (DAR), which were originally proposed by Bronzan as an alternative to dispersion relations and in which the dispersion integral is replaced by a tangent series of derivatives. We characterize the class of functions satisfying DAR, and show that outside this class the dispersion integral represents a Borel‐like sum of tangent series. We point out difficulties connected with the application of DAR.

Circuit arrangement for generating an electric velocity signal

Abstract: The circuit arrangement processes two input signals which are periodically variable as a function of the position of a moving part and particularly of the angle of rotation of a rotating part and which are phase-shifted by approximately 90° with respect to each other and have a sinusoidal or sine wave-like characteristic. In an inverting circuit, inverted input signals are generated. A curve change-over switch assembles from the input signals and the inverted input signals two sequences of similar signals sections which are divided in a divider circuit which forms quotient signals which represent the variation of the tangent function. The y signals are then converted in a tangent/arc tangent converter by forming the arc tangent function into an at least approximately sawtooth-shaped voltage signal which consists of path-proportional path signals. These path signals are differentiated with respect to time in a differentiating circuit and finally the step positions of the differentiating operation are removed from the signals in a circuit. The result analog output signal is a voltage u which is proportional to the speed of the moving part and which can be supplied as actual speed of rotation to a servo control loop.

Apparatus for generating an electrical speed signal

Abstract: The circuit processes the two input signals (v, w) vary periodically depending on the position of a movable element, in particular the angle of rotation of a rotating element, phase-shifted by approximately 90 ° and having a shape sinusoidal or quasi-sinusoidal. inverse input signals (V, W) are formed by means of an inverter circuit (1). A curve switch (2) outputs from the input signals and the inverse input signals two successions of identical signal segments (x1, x2) which are divided by a divider (5) outputting the quotients signals (y) represents the tangent function. The signals are processed by a tangent arc tangent converter (7) into a signal at least approximately formed sawtooth signal (z) proportional to the displacement. These displacement signals are differentiated with respect to time (t) by a differentiator (8), the points of discontinuity resulting from differentiation being finally removed by an ad hoc circuit (9). The resulting analog output signal is a voltage u proportional to the speed of the movable portion usable as voltage actual value of the speed in a servo loop control.

Method for error compensation in three-dimensional measuring and/or marking-out instruments

Abstract: A method for computerised error compensation of three-D measuring instruments is proposed, in which the deflection of the columns in two vertical, mutually perpendicular planes is measured by means of electronic spirit-levels and fed to a computer. The errors are determined from this in terms of angular tangent functions as a function of the transverse arm overhang length and the vertical distance thereof from the plane surface of the table per coordinate to a measurement point, and are logically combined by computer with the measured value for the purpose of correction. All errors are thereby taken into consideration, including temperature influences, errors in the drive system and other external effects on the instrument.

Use of surface deflection for pavement design and evaluation

Abstract: Most current mechanistic pavement design methods are based on strain calculated at the bottom of the asphalt layer and the top of the subgrade. Because the only part of a pavement that is reasonably accessible when construction has been completed is the surface, it is virtually impossible to verify for a design that the parameters have actually been met. The ability of the engineer to check the design will therefore be greatly enhanced if a parameter based on surface deflection can be used. The development of just such a parameter, which has been called the tangent slope, is reported. This parameter is the slope of the tangent drawn from the point of maximum deflection of the pavement to graze its surface. A sensitivity analysis is reported in which the tangent slope is compared with several other parameters based on surface deflection as well as the conventional asphalt and subgrade strains. The calibration by back analysis of the tangent slope against current practice is presented so that is can be used as a design parameter, although its principal use may be as a tool for the structural evaluation of existing pavements and for validating designs.

Concentrated Edge Loads on Hyperboloidal Shells

Abstract: The work presented in this paper shows that hyperboloid shells can be inexpensively analyzed under the action of concentrated loads using an axisymmetric program From the point of view of behavior, the numerical analyses pointed out that a negative curvature shell under the action of a concentrated load tangent to the meridian develops important bending moments and out of plane shears as a condition for the distribution of the concentrated load throughout the shell It also exhibits a tendency of the stresses to propagate along the straight line generatrices as in the membrane theory; but the numerical results of the membrane theory can be misleading Under a self‐equilibrating harmonic load tangent to the meridian this shell shows a rapid damping of the stresses away from the edge when the harmonic number is high (usually as n⩾5) The increase in the ratio h/R and the decrease in the foundation stiffness are two factors that reduce the membrane propagation and increase the bending moments

Rotation driving device of disk-like recording medium

Abstract: PURPOSE:To place on a turntable by an eccentric amount of several microns and easily even in case of a disk having no center hole by detecting an eccentric amount between the center of a disk placed on the turntable and the rotating center of the turntable, and adjusting a projecting amount of a positioning member which is made to press-contact with the outside face of the disk in accordance with its detecting output. CONSTITUTION:A disk 1 having no center hole is attracted on a turntable 2 by a vacuum attracting means. A positioning means 6 consists of a disk pressure part 7 in which a part contacting with the disk 1 is constituted of a roll, a slide part 8 for supporting its disk pressure part 7 so that it can move linearly in the radial direction of the disk 1, and a motor 9 for moving linearly the disk pressure part 7. Also, a laser 10 is provided as a means for detecting an eccentric amount of the disk 1, and the center of its beam 11 is adjusted so as to be a tangent of the outside circumference of the disk in case when the center of the turntable 2 coincides with the center of the disk 1.

Generic space curves and secants

Abstract: In this paper, we study the local structure of the secant mapping of a pair of disjoint curves. We show that for generic curves, the secant map and unit secant maps are locally stable. If we allow our curves to coincide, we can define anew unit secant map to be the natural unit tangent map near the diagonal. This is, for a generic curve, a locally stablemap away from the diagonal. Along the diagonal, it is locally stable as a ℤ 2 symmetric germ (the ℤ 2 symmetry originating with reflection in the diagonal).

Track curve lining method and apparatus

Abstract: A railroad track curve is plotted by measuring ordinates (58) at a fixed point (61) of a fixed length reference line that is moved to a series of incremental points spaced around the curve (59), and the ordinates (58) are stored in a data processor memory. The data processor calculates theoretical ordinates for an ideal curve which most closely fits the measured ordinates (58), and the track is shifted at the incremental points under control of the processor a distance and direction corresponding to the deviation between the measured and calculated ordinates. The system permits determination of transition points for simple and compound curves, and allows superelevation values to be selected and intermediate values calculated for smooth transition between tangent and constant curve track. The reference line may be established by a light beam (14), and the processor may be part of a self-propelled, on-track lining machine.

Measurement of dielectric tangent

Abstract: PURPOSE:To determine a dielectric tangent by a method wherein the minimum unbalanced voltage of a Schering bridge is integrated at each half cycle synchronizing the positive polarity of voltage across a non-inductive resistance and means are determined to remove the effect on the dielectric tangent due to an induced voltage CONSTITUTION:It is so arranged as to have a Schering bridge circuit 1 and a measuring circuit 4 comprising a synchronous integration circuit 2 and an averaging circuit 3 Minimum unbalanced voltage Vmin=VA-VL of a bridge corresponding to a dielectric tangent tandelta is cynchronized with a power source voltage V0 by means of the synchronous integration circuit 2 and averaged at each half cycle with the averaging circuit 3 In other words, the averaging is done only when the power source V0 is in the positive polarity to determine the mean at the first half cycle from 0 to pi and then, after the power source phase is shifted by 180 deg, only when the power source V0 is in positive polarity, it is done at determine the mean at the second half cycle from pi to 2pi The dielectric tangent tandelta is determined from the sum of the means and the ratio of the mean of voltages across a non-inductive resistance Thus, no non-inductive voltage is contained

Naturally reductive metrics on homogeneous systems

Abstract: We show that naturally reductive (indefinite) metrics on homogeneous systems are determined by nondegenerate invariant forms of their tangent Lie triple algebras. By using this we obtain the decomposition theorem of homogeneous systems. Furthermore, we show that a naturally reductive Riemannian homogeneous space is irreducible if and only if its tangent Lie triple algebra is simple.

Characterization And Evaluation Of Automatic Target Recognizer Performance

Abstract: SummaryThe operating curve provides a means to characterize and compare ATR designs. Moreimportantly, it can be used to determine performance measures for ATR evaluation. Shootingscore and exchange ratio are quantitatively related to operating curves.Operating curves deserve further study, including: 1 How to handle multiclass classification problems 2 How to generate operating curves for a complex ATR design with piecewise decisionboundaries 346 / SPIE Vol 504 Applications of Digital Image Processing VII (1984) whereP TT = 1 - TFP = 1 - p FF FTThe risk relates to the operating curve, since it is a function of Pprp and P«pp.The same procedure explained in the previous section is used to find the optimum operating point. That is, the slope of the tangent at the optimum operating point is equal to -£o.The computation of the threshold value involves both a priori probabilities and cost functions in terms of the Bayes criterion for minimum risk: (C21 - c ) P(C ) - ^I ^ (12)\-L * I

The Numerical Bückling of a Visco-elastic Rod

Abstract: We consider the deformation of a thin, inextensible rod under axial thrust P. The rod has pinned ends and is assumed to deform in a plane with one end free to move horizontally. It is of unit length and if xe[0,1] denotes the material points in the initial undeformed configuration then u(x) denotes the angle between the tangent to the rod at x and the horizontal.

The precise determination of Maxwell sets for cuspoid catastrophes

Abstract: Given a polynomial in a single variable, we can find algebraic conditions on the coefficients corresponding to geometrically apparent features of its graph. For example, in elementary catastrophe theory, a bifurcation set in the coefficient space corresponds to a flat point of inflection on the curve. In this paper we establish algebraic conditions for the polynomial to have a pair of minima that have a common horizontal tangent. This condition is exactly that required by the Maxwell convention of catastrophe theory. The first step is a proof of a result giving a factorization of the discriminant of the discriminant of a polynomial. The proof given is a direct algebraic factorization. This result provides a condition for equal critical values. To narrow down to the cases in which the equal values are both minima, a method of using a combination of Sturm sequences has been devised. The paper thus provides complete rigorous algorithm for the determination of an algebraic expression for the Maxwell set of a ...

Boundary Value Problems

Abstract: In the previous chapters, we studied various kinds of questions concerning the initial value problem. We now propose to investigate other types of problems, in which the desired solution depends either on the values that it assumes at various points in its domain or on geometrical conditions (e.g., intersecting two given curves or being tangent to two lines), or on periodic conditions. Before studying such problems, we will discuss certain notions and results about continuous mappings on Euclidean spaces.

Zur Kennzeichnung von Quadriken unter den Kegelschnittflächen

Abstract: A surface, generated by a one-parameter family of conics in projective 3-space, such that the tangent planes along a generating conic form a quadric cone, is called a surface of Blutel [1]. The surface is said to be of hyperbolic type, if the characteristic line of the plane of a generating conic intersects it in two different real points s1, s2. Formerly [5] it was shown that such a surface must be a quadric if it is unbranched along the curves, generated by s1, s2, these points not being stationary. In the present paper analogous results are established in the remaining cases when one or both points s1, s2 are fixed.

Heat transfer element of heat exchanger

Abstract: PURPOSE:To increase the coefficient of heat transfer of the heat transfer element and to prevent the element from being damaged by a method wherein the corrugated intermediated section of the heat transfer element is formed to have such a cross- sectional configuration that the pitch is in the order of 10-16mm., the height of each corrugation is in the order of 3-10mm. and the tangent line passing through the intermediate part between the top or the bottom of the corrugation intersects the tangent line at the top or the bottom of the corrugation. CONSTITUTION:The corrugated intermediate section 4 of the heat transfer element is formed to have such a cross-sectional configuration that the pitch is in the order of 10-16mm., the height of each corrugation is in the order of 3-10mm. and the tangent line M passing through an arbitrary point of the intermediate part between the top (a) and the bottom (b) of the corrugation intersects the tangent line N at the top (a) or the bottom (b) of the corrugation. As a result, the pitch becomes small and the surface area of heat transfer per unit volume increases so that the coefficient of heat transfer of the heat transfer element increases. Further, as the corrugated intermediate section of the element has substantially no horizontal section, the element hardly vibrates even when it is subjected to a strong washing force and there is no fear of its being damaged.

Tangent Planes with Infinitesimals

Abstract: (1984). Tangent Planes with Infinitesimals. The American Mathematical Monthly: Vol. 91, No. 7, pp. 433-435.

The Tangent Method

Abstract: The present chapter contains a general approach to the construction of algorithms for optimum problems, both static and dynamic. The reader will certainly notice a resemblance to the classical Newton method (tangent method), but there is an essential difference: we are looking for constrained extrema of functions or functionals by means of solving unconstrained problems. The functions involved are well-known mathematical objects and they play an important role in dynamic programming [21]. Again we shall pay a lot of attention to significant mechanical analogies.

Machine for machining the outlines of planar or curved components

Abstract: The invention relates to a machine for machining the outlines of planar or curved components. It is characterised in that, in order to be positioned with respect to the tangent to the curve, the feeler 23 bears on the outline of the template at two points 24, 25 which are close together. Application to the special machine industry.