Showing papers on "Tangent published in 1971"
TL;DR: The results show that there is no detectable variation in the properties for all specimen orientations tangent to the surface of the skull, and these data provide a basis for selecting candidate materials for a physical head model.
242 citations
Journal Article•
TL;DR: In this paper, the authors calculate the limb radiance as a function of tangent height and the vertical distribution of temperature and the pressure at one level, using an iterative technique.
Abstract: The calculation of limb radiance as a function of tangent height is shown to require information about the vertical distribution of temperature and the pressure at one level. Conversely, given the limb radiance curve and the pressure corresponding to one tangent point, it is possible to determine the temperature profile as a function of height relative to the given level, using an iterative technique. Results of inverting synthesized realistic data are presented. The data include the effects of water vapor and ozone contamination of the carbon dioxide signal, instrument field of view, and random and systematic noise for real atmospheres having small-scale vertical structure.
123 citations
TL;DR: In this article, the vertical distribution of temperature and the pressure at one level is used to determine the temperature profile as a function of height relative to the given level, using an iterative technique.
Abstract: The calculation of limb radiance as a function of tangent height is shown to require the vertical distribution of temperature and the pressure at one level. Conversely, given the limb radiance curve and the pressure corresponding to one tangent point, it is possible to determine the temperature profile as a function of height relative to the given level, using an iterative technique. If the given pressure is incorrect, there will be systematic errors in the inferred temperatures. This feature may he used to determine the correct pressure by requiring that temperatures inferred from measurements in two spectral regions of differing opacities agree. Results of inverting synthesized realistic data are presented. The data include the effects of water vapor and ozone contamination of the carbon dioxide signal, instrument field of view, and random and systematic noise for real atmospheres having small-scale vertical structure. Results indicate that the temperature may be obtained from the tropopause to...
121 citations
01 Jan 1971
TL;DR: In this article, the authors explore singularities in interface problems, where two interface curves cross, where an interface curve meets the boundary, or where a boundary has a discontinuous tangent (a corner).
Abstract: Publisher Summary This chapter explores singularities in interface problems. It presents the interface problem for second-order elliptic partial differential equations in two independent variables. The behavior of the solution is determined at the singular points of the problem: where two interface curves cross, where an interface curve meets the boundary, or where an interface or boundary has a discontinuous tangent (a corner). The chapter presents the application of these two dimensional results to analogous problems in three dimensions. The methods presented in the chapter are similar to those used by Birman and Skvorcov in studying the effect of a corner on the solution of an elliptic boundary value problem. The chapter also discusses a few results on higher dimensional corners. It presents a density theorem in two dimensions.
88 citations
TL;DR: In this article, the authors considered the linear inviscid reflexion of internal/inertial waves from smooth bumpy surfaces where a characteristic (or ray) is tangent to the surface at some point.
Abstract: This paper considers the linear inviscid reflexion of internal/inertial waves from smooth bumpy surfaces where a characteristic (or ray) is tangent to the surface at some point. There are two principal cases. When a characteristic associated with the incident wave is tangent to the surface we have diffraction; when the tangential characteristic is associated with a reflected wave we have split reflexion, a phenomenon which has no counterpart in classical non-dispersive wave theory. In both these cases the problem of determining the wave field may be reduced to a set of coupled integral equations with two unknown functions. These equations are solved for the simplest topography for each case, and the properties of the wave fields for more general topographies are discussed. For both split reflexion and diffraction, the fluid velocity has an inverse-square-root singularity on the tangential characteristic, and the energy density has a corresponding logarithmic singularity. The diffracted wave field penetrates into the shadow region a distance which is of the order of the incident wavelength. Possibilities for instability and mixing are discussed.
34 citations
TL;DR: In this paper, the secant or Muller's method is used to solve equation solving problems with alternate function and derivative values, where the derivative is simpler to obtain than the function itself.
Abstract: Equation-solving methods that utilize alternate function and derivative values are developed. The procedures are similar to the secant or to Muller's method, and are especially competitive when the derivative is simpler to obtain than the function itself. Related hybrid methods are also found to be attractive.
30 citations
TL;DR: In this paper, a functional representation of nonlinear stress-strain curves is used for finite element analyses to predict load-displacement behavior of a model test footing resting on a cohesive soil.
Abstract: Cubic spline functions are utilized for functional representation of nonlinear stress-strain curves, and are found to provide satisfactory approximations to stress, strain, and moduli required for nonlinear stress-deformation analyses of geologic media. Stresses, strains and moduli from spline and hyperbolic representations are compared. The spline approximation is used in finite element analyses to predict load-displacement behavior of a model test footing resting on a cohesive soil. Comparisons are also obtained between load-displacement curves computed from the spline and the hyperbolic representations, and the experimental curve. Spline approximation provides good correlation over complete range of deformation history. Effects of the magnitude of initial tangent stiffness on the load-deformation behavior are briefly studied.
17 citations
Book•
01 Jan 1971TL;DR: In this paper, a generalization of the maximal contact exponent at a singular point of a singular plane curve with a non-singular curve through that point was presented, and the invariant appeared as the inclination of a compact face of the Newton polygon.
Abstract: This text is the redaction of lectures given in 1971-72 by Monique Lejeune-Jalabert and Bernard Teissier at the Centre de Mathematiques de l'Ecole Polytechnique. The redaction is due to Le Dung Trang and Jean-Jacques Risler. The aim was to give a complete proof of the continuity of maximal contact along the strata of a Samuel stratification in complex analytic geometry. This result is a part of Hironaka's strategy to prove resolution of singularities in complex analytic geometry. The main ingredients are generalizations of the concept of normal cone of a singular space along a subspace and of the concept of Newton polygon, In particular, we study a generalization of the maximal contact exponent at a singular point of a singular plane curve with a non singular curve through that point. For plane curves, this invariant appears as the inclination of a compact face of the Newton polygon in suitable coordinates, and also as a " critical tropism " for a family of weighted tangent cones.
9 citations
7 citations
TL;DR: In this paper, the program described here has been used successfully to choose starting sets for 12 crystal structures (5 previously undetermined) and the number of sets of phases to be calculated was not greater than 32 for any structure.
Abstract: The program described here has been used successfully to choose starting sets for 12 crystal structures (5 previously undetermined). The number of sets of phases to be calculated was not greater than 32 for any structure.
2 citations
Abstract: An informal account of the ideas and techniques involved in « lifting » an ∞2 correspondence between algebraic surfaces into a correspondence between their tangent direction bundles.
TL;DR: A new computational treatment of integrals of the form ∫ g( x) expf (x) dx is described, which involves approximating to f(x) between mesh points by a line whose slope is the average of that of the tangent at the higher point and that ofThe chord joining the two points.
Abstract: A new computational treatment of integrals of the form ∫ g(x) expf (x) dx is described. This involves approximating to f(x) between mesh points by a line whose slope is the average of that of the tangent at the higher point and that of the chord joining the two points. The resulting errors are compared with those given by the trapezium rule, and the new method is shown to be greatly superior for most practical applications.
TL;DR: In this article, the authors obtained the number of singular points on one coupler curve of planar four-link crank-and-rocker mechanism and derived the conditions for syntheses.
Abstract: Four-link coupler curve is discontinuous at the change point, and is separable into two or four curves by reversing the driven link about the fixed link Nevertheless, in former algebraic analysis of singular points, it was not able to distinguish between the singular points on one curve and those on two curves For practical uses of mechanisms it is required to analyze the singular points on one curve and to synthesize a mechanism having such singular points In the present paper, the authors first obtain the number of singular points on one coupler curve of planar four-link crank-and-rocker mechanism, and derive the conditions for syntheses Second, calculating the inclinations of tangents at the singular points, they synthesize the mechanisms satisfying the number and the positions of singular points and the inclinations of tangents at the singular points As a result, it became possible to apply the coupler curve to automatic assembling and conveying machines
01 Jan 1971
TL;DR: In this article, a method for computing generalized stress-strain relationships (mament-thrustcurvature relationships) for metal column sections in biaxial bending is described.
Abstract: A method for computing generalized stress-strain relationships (mament-thrust-curvature relationships) for metal column sections in biaxial bending is described. The analytical formulation of the force-deformation equations in terms of the rate of change leads to a linear relationship between these quantities. Solutions. are obtained by the tangent stiffness method and a,digital computer. The method is found to be extremely powerful and efficient for com-, puter solution.
01 Aug 1971
TL;DR: In this article, an expression for computing the reference coordinates in a plane tangent to the earth spheroid is derived which requires less numerical effort than the standard procedure, and an approximation of geocentric latitude is used in the program.
Abstract: : Methods are investigated which apply to the conversion of latitude, longitude and height to cartesian coordinates in a plane tangent to the earth's surface in connection with onboard missile targeting. The criterion for the usefullness of the method is the error in the north and east coordinate with reference to Clarke's spheroid 1866. This error is determined as a function of vector length and azimuth for the spherical earth model referenced to the mean geodetic latitude at White Sands Missile Range using a program prepared for a programmable electronic desk calculator. An approximation of geocentric latitude is used in the program. It is explained how the error inherent to the spherical earth model can be reduced applying a certain correction. An expression for computing the reference coordinates in a plane tangent to the earth spheroid is derived which requires less numerical effort than the standard procedure.
01 Jan 1971
TL;DR: In this article, the authors proposed a method for estimating the shock locations and surface pressure coefficients in the vertical plane of symmetry in nonanalytic shapes such as wing-body combinations by tangent wedge and tangent circular cone methods.
Abstract: require that the body be a simple analytic shape. Approximate pressure distributions have been computed for more general (nonanalytic) shapes such as wing-body combinations by tangent wedge and tangent circular cone methods and by Newtonian theory. The present method for estimating the shock locations and surface pressure coefficients in the vertical plane of symmetry