On the Derivative of the Generalized Inverse of a Matrix
A general expression is given for the derivative of the C sub 4 - inverse of a differentiable matrix A whenever that derivative, as well as the derivative of A, exists.
Decell, H. P., Jr.↗
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Improved spatial uniformity of beam-plane interaction by means of inverse rastering
An analysis is presented that shows the desirability and feasibility of conducting irradiations of large test objects by beams of penetrating radiation, by the method of moving the test object back and forth through the beam, rather than by sweeping the beam across the object. An extension of this method of inverse rastering allows the generation of composite beams with any desired intensity-vs-energy spectrum, obviating the need to determine equivalent damage factors for every energy in the spectrum.
Miller, C. G.↗
Population inversion calculations using near resonant charge exchange as a pumping mechanism.
A theoretical study is conducted to investigate the possibility of obtaining inversions in a plasma of metals such as Mg, Ca, Sr, or Ba by charge exchange with inert gas ions. The gases considered include He, Ne, Xe, Ar, or N. The analysis uses rate equations to calculate the density of the various ion levels and an energy equation to calculate the electron temperature. Both charge exchange and electron collisional excitation of the various ion levels are considered.
Chubb, D. L.↗
On the computation of the generalized inverse by classical minimization.
An alternative method for deriving the generalized inverse of an arbitrary rectangular matrix with real or complex coefficients is described. The method applies a classical minimization procedure without iteration processes and is readily applicable in digital computer programming.
Voith, R. P.↗
Eigenproblem solution by a combined Sturm sequence and inverse iteration technique.
Description of an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = lambda Bq with band symmetric A and B, B being also positive-definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures. The program may be conveniently utilized for the efficient solution of practical engineering problems, involving free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.
Gupta, K. K.↗
Eigenvalue algorithm based on a combined sturm sequence and inverse iteration technique (EASI)
Desired roots are first isolated by Sturm sequence procedure. Then special variant of inverse iteration technique is applied for individual determination of each root along with its vector. Program was written in FORTRAN V for UNIVAC 1100-series computers.
Gupta, K. K.↗
Eleven-years inversion of the green corona emission
A cross correlation analysis of coronal green line intensity (5303A) and interplanetary magnetic field polarity for the period 1947-1970 shows that the coronal features are organized in a constant pattern with respect to the 4-sector structure through the solar cycle. A sudden inversion of the coronal pattern with respect to the sector structure takes place at the solar minima. The high emission regions of the green corona are located near the solar magnetic sector boundaries having polarities (-,+), (+,-), (-,+) during cycles 18, 19, 20 respectively in the Northern Hemisphere, and (+,-), (-,+), (+,-) in the Southern Hemisphere.
Antonucci, E.↗
An inversion in the atmosphere of Titan
A very detailed greenhouse model derives a methane to hydrogen ratio of unity and a minimum surface pressure of 0.4 atm. Based on a surface gravity g = 140 cm sec/2, the minimum CH4 abundance is 30-40 km-A and the minimum H2 abundance varies from 15 to 85 km-A. A model of the atmosphere of Titan is proposed which seems to be consistent with observations and requires a much smaller CH4 abundance (of the order or 2 km-atm). Although no H2 is required, the presence of some H2 is readily accommodated. In this model, a temperature inversion exists in the atmosphere due to absorption of blue and ultraviolet solar radiation by small particles. The absorbed radiation is re-radiated by the dust and by molecules having long wavelength bands such as CH4 7.7 micrometer and ethane at 12.2 micrometer. The brightness temperature at 20 micrometer is primarily due to re-radiation by the dust.
Danielson, R. E.↗
A technique for increasing the accuracy of the numerical inversion of the Laplace transform with applications
A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.
Berger, B. S.↗
Eleven-years inversion of the green corona emission
Study of the correlation between the green coronal emission and the polarity pattern of the interplanetary magnetic field for the years 1947-1970. Polarity data of the interplanetary magnetic field inferred from high latitude geomagnetic observations and synoptic tables of the intensity of the green corona emission line (5303 A) are used in the analysis. The analysis results indicate that the coronal features are organized in a constant pattern with respect to the 4-sector structure through the solar cycle. A sudden inversion of the coronal pattern with respect to the sector structure takes place at the solar minima.
Antonucci, E.↗
Partial-fraction expansion and inverse Laplace transform of a rational function with real coefficients
This paper presents a technique for the partial-fraction expansion of functions which are ratios of polynomials with real coefficients. The expansion coefficients are determined by writing the polynomials as Taylor's series and obtaining the Laurent series expansion of the function. The general formula for the inverse Laplace transform is also derived.
Chang, F.-C.↗
Inversion layer solar cell fabrication and evaluation
Inversion layer solar cells have been fabricated by etching through the diffused layer on p-type silicon wafers in a comb-like contact pattern. The charge separation comes from an induced p-n junction at the surface. This inverted surface is caused by a layer of transparent material applied to the surface that either contains free positive ions or that creates donor states at the interface. Cells have increased from 3 ma Isc to 100 ma by application of sodium silicate. The action is unstable, however, and decays with time.
Call, R. L.↗
Development of inverse inviscid transonic solution methods
A numerical method suitable for the analysis and/or design of supercritical transonic airfoils is reported. In order to achieve accuracy, the method utilizes the full inviscid potential flow equations; and in order to remain simple it solves the problem in a stretched Cartesian grid system. The resulting computer program has several advantages over others of its type -- its use in either the direct analysis mode in which the airfoil shape is prescribed and the flow field and surface pressures are determined, or in the inverse mode in which the surface pressures are given and the airfoil shape and flow field are computed. Other advantages of the program include its use in a design program, the rotated finite difference scheme and its determination of the airfoil shape simultaneously with the flow field relaxation solution.
Carlson, L. A.↗
Inversion layer solar cell fabrication and evaluation
Inversion layer solar cells were fabricated by etching through the diffused layer on p-type silicon wafers in a comb-like contact pattern. The charge separation comes from an induced p-n junction at the surface. The inverted surface is caused by a layer of transparent material applied to the surface that either contains free positive ions or that creates donor states at the interface. Cells are increased from 3 ma I sub sc to 100 ma by application of sodium silicate. The action is unstable, however, and decays. Non-mesa contaminated oxide cells were fabricated with short circuit currents of over 100 ma measured in the sun. Cells of this type have demonstrated stability.
Call, R. L.↗
On the convergence of certain finite-difference schemes by an inverse-matrix method
The inverse-matrix method of analyzing the convergence of the solution of a given system of finite-difference equations to the solution of the corresponding system of partial-differential equations is discussed and generalized. The convergence properties of a time- and space-centered differencing of the diffusion equation are analyzed as well as a staggered grid differencing of the Cauchy-Riemann equations. These two schemes are significant since they serve as simplified model algorithms for two recently developed methods used to calculate nonlinear aerodynamic flows.
Steger, J. L.↗
Inverse solutions for laminar boundary-layer flows with separation and reattachment
Numerical solutions of the laminar, incompressible boundary layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified; the pressure is deduced from the solution. A vorticity-stream-function formulation of the boundary layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite difference equations, in which the flow direction is taken into account, are obtained by several global iteration schemes which are stable and have unconditional diagonal dominance. Results are compared with Klineberg and Steger's separated boundary layer calculations, and with Briley's solution of Navier-Stokes equations for a separated region. In addition, an approximate technique is presented in which the streamwise convection of vorticity is set equal to zero in the reversed flow region; such a technique results in a quick forward marching procedure for separated flows.
Carter, J. E.↗
An inverse problem design method for branched and unbranched axially symmetrical ducts
This paper concerns the potential flow design of axially symmetrical ducts of both circular and annular cross section with or without wall suction or blowing slots. The objective of the work was to develop a method by which such ducts could be designed with directly prescribed wall pressure variation. Previous axially symmetrical design methods applied only to circular cross sectional ducts and required that the pressure distribution be prescribed along the duct centerline and not along the duct wall. The present method uses an inverse problem approach which extends the method of Stanitz to the axially symmetrical case, and an approximation is used to account for the stagnation point in branched duct designs. Two examples of successful designs of diffusers with suction slots are presented.
Nelson, C. D.↗
Inverse atmospheric radiative transfer problems - A nonlinear minimization search method of solution
The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.
Fymat, A. L.↗