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All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

On the Laplace transform for distributions

A new characterization of the Laplace transform for Schwartz distributions is developed, using sequences of linear transformations on the space of distributions. The standard theorems on analyticity, uniqueness and invertibility of the transform are proved, using the new characterization as the definition of the Laplace transform. It is shown that this sequential definition is equivalent to Schwartz's extension of the ordinary Laplace transform to distributions which he obtained from the Fourier transform.

Price, D. B.↗
NASA NTRS1975

The transformation of aerodynamic stability derivatives by symbolic mathematical computation

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

Howard, J. C.↗
NASA NTRS1982

Discrete Fourier transforms of nonuniformly spaced data

Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.

Swan, P. R.↗
NASA NTRS1983

Development of a rotary power transformer and inverter drive for spacecraft

Many future satellites and spacecraft with spun and despun configurations will require the transfer of power across rotating interfaces in lieu of slip-rings and/or flexures. This is particularly true of spacecraft that have to demonstrate a long life expectancy. The rotary transformer has the desirable characteristics of high reliability and low noise, which qualify it as a potential replacement for slip rings. Development of a rotary power transformer follows the successful completion of a task to develop rotary signal-level transformers for the Galileo Spacecraft Project. The physical configuration of a rotary power transformer has a significant effect on its magnetic and electrical characteristics and therefore impacts the design of the dc/ac inverter driver. Important characteristics addressed during this development effort include: operating frequency, efficiency, transformer gap size, leakage inductance, and leakage flux. A breadboard inverter and rotary transformer were designed, fabricated and tested.

Mclyman, W. T.↗
NASA NTRS1984

Use of the TM tasseled cap transform for interpretation of spectral contrasts in an urban scene

Investigations are being conducted with the objective to develop automated numerical image analysis procedures. In this context, an examination is performed of physically-based multispectral data transforms as a means to incorporate a priori knowledge of land radiance properties in the analysis process. A physically-based transform of TM observations was developed. This transform extends the Landsat MSS Tasseled Cap transform reported by Kauth and Thomas (1976) to TM data observations. The present study has the aim to examine the utility of the TM Tasseled Cap transform as applied to TM data from an urban landscape. The analysis conducted is based on 512 x 512 subset of the Washington, DC November 2, 1982 TM scene, centered on Springfield, VA. It appears that the TM tasseled cap transformation provides a good means to explain land physical attributes of the Washington scene. This result provides a suggestion regarding a direction by which a priori knowledge of landscape spectral patterns may be incorporated into numerical image analysis.

Goward, S. N.↗
NASA NTRS1986

Mechanisms and depths of atlantic transform earthquakes

Mechanisms and depths of 40 earthquakes on major transforms along the Mid-Atlantic Ridge are studied in order to identify events that deviate from the transform-parallel strike-slip motion. Long and short period waves and Rayleigh wave spectral amplitudes are used to analyze focal mechanisms, depths, source time functions, and seismic moments of earthquakes. The relationship between centroid depths and transform thermal structures is examined. The data reveal that transform earthquake centroid depths occur above the predicted 400 C isotherms and the oceanic intraplate depths extend to the 750 C isotherm. Slip rates inferred from seismic moment releases are compared to those predicted by plate motions and good correlation is detected. The difference in the centroid depths of transform and interplate seismicity indicates transforms are either weaker or higher temperatures than expected.

Engeln, J. F.↗
NASA NTRS1986

Optimal block cosine transform image coding for noisy channels

The two dimensional block transform coding scheme based on the discrete cosine transform was studied extensively for image coding applications. While this scheme has proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. A method is presented for the joint source channel coding optimization of a scheme based on the 2-D block cosine transform when the output of the encoder is to be transmitted via a memoryless design of the quantizers used for encoding the transform coefficients. This algorithm produces a set of locally optimum quantizers and the corresponding binary code assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, an algorithm was used based on the steepest descent method, which under certain convexity conditions on the performance of the channel optimized quantizers, yields the optimal bit allocation. Comprehensive simulation results for the performance of this locally optimum system over noisy channels were obtained and appropriate comparisons against a reference system designed for no channel error were rendered.

Vaishampayan, V.↗
NASA NTRS1989

Data compression properties of the Hartley transform

The data compression performance of the Hartley transform on a Markov-1 signal is theoretically compared to that of the Fourier transform. Covariance distribution and residue correlation measurements have been computed for the Hartley, Fourier, and cosine transforms. The Hartley transform achieves better coding performance than the Fourier transform, but is inferior to the cosine transform.

Yeh, Pen-Shu↗
NASA NTRS1988

A kinematic model of ridge-transform geometry evolution

A simple kinematic model is used to study the effects of various parameters on the evolution of zero-offset transforms and very-long-offset transforms. Consideration is given to the effects of initial configuration, degree of asymmetry, and degree of bias in asymmetry on the generation of these ridge transform geometries and on the possible steady-state nature of the transform length spectra. Of the parameters tests, only lack of 'memory' of zero-offset transforms affects transform length distribution.

Stoddard, Paul R.↗
NASA NTRS1991

A two-dimensional time domain near zone to far zone transformation

In a previous paper, a time domain transformation useful for extrapolating 3-D near zone finite difference time domain (FDTD) results to the far zone was presented. In this paper, the corresponding 2-D transform is outlined. While the 3-D transformation produced a physically observable far zone time domain field, this is not convenient to do directly in 2-D, since a convolution would be required. However, a representative 2-D far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required it can be obtained by inverse Fourier transform of the final frequency domain result.

Luebbers, Raymond J.↗
NASA NTRS1991

A two-dimensional time domain near zone to far zone transformation

A time domain transformation useful for extrapolating three dimensional near zone finite difference time domain (FDTD) results to the far zone was presented. Here, the corresponding two dimensional transform is outlined. While the three dimensional transformation produced a physically observable far zone time domain field, this is not convenient to do directly in two dimensions, since a convolution would be required. However, a representative two dimensional far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required, it can be obtained by inverse Fourier transform of the final frequency domain result.

Luebbers, Raymond J.↗
NASA NTRS1995

Neoplastic transformation of human cells

The goal of this project was to gain a better understanding of the cellular mechanisms of cancer induction by ionizing radiation as a risk assessment for workers subjected to high LET irradiation such as that found in space. The following ions were used for irradiation: Iron, Argon, Neon, and Lanthanum. Two tests were performed: growth in low serum and growth in agar were used as indicators of cell transformation. The specific aims of this project were to: (1) compare the effectiveness of various ions on degree of transformation of a single dose of the same RBE; (2) determine if successive irradiations with the same ion (Ge 600 MeV/u) increases the degree of transformation; (3) test if clones with the greatest degree of transformation produce tumors in nude mice; and (4) construct a cell hybrid of a transformed and control (non-transformed) clone. The cells used for this work are human mammary epithelial cells with an extended lifespan and selected for growth in MEM + 10% serum.

Goth-Goldstein, Regine↗
NASA NTRS2004

Transformations in Air Transportation Systems For the 21st Century

Globally, our transportation systems face increasingly discomforting realities: certain of the legacy air and ground infrastructures of the 20th century will not satisfy our 21st century mobility needs. The consequence of inaction is diminished quality of life and economic opportunity for those nations unable to transform from the 20th to 21st century systems. Clearly, new thinking is required regarding business models that cater to consumers value of time, airspace architectures that enable those new business models, and technology strategies for innovating at the system-of-networks level. This lecture proposes a structured way of thinking about transformation from the legacy systems of the 20th century toward new systems for the 21st century. The comparison and contrast between the legacy systems of the 20th century and the transformed systems of the 21st century provides insights into the structure of transformation of air transportation. Where the legacy systems tend to be analog (versus digital), centralized (versus distributed), and scheduled (versus on-demand) for example, transformed 21st century systems become capable of scalability through technological, business, and policy innovations. Where air mobility in our legacy systems of the 20th century brought economic opportunity and quality of life to large service markets, transformed air mobility of the 21st century becomes more equitable available to ever-thinner and widely distributed populations. Several technological developments in the traditional aircraft disciplines as well as in communication, navigation, surveillance and information systems create new foundations for 21st thinking about air transportation. One of the technological developments of importance arises from complexity science and modern network theory. Scale-free (i.e., scalable) networks represent a promising concept space for modeling airspace system architectures, and for assessing network performance in terms of robustness, resilience, and other metrics. The lecture offers an air transportation system topology and a scale-free network linkage graphic as framework for transportation system innovation. Successful outcomes of innovation in air transportation could lay the foundations for new paradigms for aircraft and their operating capabilities, air transportation system topologies, and airspace architectures and procedural concepts. These new paradigms could support scalable alternatives for the expansion of future air mobility to more consumers in more parts of the world.

Holmes, Bruce J.↗
NASA NTRS2017

Structure in the 3D Galaxy Distribution: III. Fourier Transforming the Universe: Phase and Power Spectra

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Galactic clusters↗
NASA NTRSDate not supplied

Space Transformation -- Localizing the Remote and Connecting the Isolated

In motivating the Space Transformation theme for this year’s 4S symposium, the organizers provided the following context, “Transformation of economies are driven by a change in values and accelerated by new technologies.” These words rang particularly true when I read them at the beginning of the holiday season. Like so many others, I was in the early phases of my Christmas shopping procrastination campaign, and I’d just been reflecting on how Amazon Prime was the transformational tool I’d been waiting for. Basic limiting principles of time and space, supply and demand, were all but erased by the Amazon Prime phenomenon. Coupled with emerging 3D printing and other adaptive manufacturing technologies, a transformation from deliberate planning to “think it … have it” had occurred, empowering me to procrastinate longer than I’d ever dreamed possible. The organizers went on to ponder, “Will space transformation also affect society?”, just as our team at the Air Force Research Lab’s (AFRL) Center for Rapid Innovation (CRI) were working alongside partners within our larger Integrated Capabilities Directorate, NASA’s Flight Opportunities and Small Spacecraft Technology programs, and DARPA’s Luna-10 program to develop technologies and execute demonstration missions that leverage the space domain to genuinely connect even the most remote and austere domains on the timeline of need. Picking apart the miracle that is Amazon prime, where does the model fail, and why? More relevantly to the theme of this year’s symposium, how can the space domain be used to overcome its limitations and minimize its weaknesses? Perhaps it is best assessed in the context of Use Cases. What are the Amazon delivery cost, schedule, and cargo limiters to the Amundsen-Scott South Pole Research Station, or the Lunar South Pole Research Station? This paper will explore enabling infrastructure that allows Amazon prime to thrive and assess the transformational enabling technologies that would be necessary to extend that miracle to the truly remote or the truly austere. Localizing the Remote • First, it will evaluate the ability of the on-going AFRL Rocket Cargo and Space Initiatives Ringside Seats systems, coupled with Astrobotic’s Xodiak and Xogdor capabilities, developed to support the NASA Flight Opportunities Program (FOP), to supply orbital/suborbital delivery to both improved and austere sites on the Earth and Moon. • Then, it will add the surface terminal distribution leg, with an examination of Lunar Outpost’s Mobile Autonomous Prospecting Platform (MAPP), equipped with Mobile Autonomous Robotic Swarm (MARS) software, and Intuitive Machine’s Hopper, developed with support of AFRL and NASA’s Commercial Lunar Payload Services (CLPS) program. Connecting the Isolated From there, it will focus on the destination, asking what implied destination services are required to support highly assured autonomous delivery. • Specifically, it will highlight Astrobotic’s Skymage mesh-networked publish and subscribe communication and navigation service, as well as AFRL’s on-going developments of radioisotope and reactor nuclear-sourced thermoelectric power generation and distribution systems under development under the Joint Emergent Technology Supplying On-orbit Nuclear Power (JETSON) program by Lockheed Martin, Westinghouse, Intuitive Machines, and Zeno Power, to provide the power service to locations well off the grid. • Finally, the paper will connect to the “human machine”. What connects the remote or in-situ human consumer to the remote domain? What connects the diverse international government and commercial services to each other? The former will focus on AFRL’s OraCloud feeding their Space Defense Control and Characterization System (SDCCS) and Lunar Station’s MoonHacker systems, while the latter will focus on the BlueHalo/Tensor LunX Technology Platform for the Cislunar Commodity Marketplace. In 1984, Krafft Ehricke famously remarked that, “If God wanted man to become a spacefaring species, He would have given man a Moon.” This paper is not about the Moon, but is about humans as a spacefaring species, shedding the pesky land/air limitations of the Amazon Prime model … so that we can all live a procrastinator’s “think it … have it” existence.

Charles Finley↗
NASA NTRS1996

DNA damage and repair in oncogenic transformation by heavy ion radiation

Energetic heavy ions are present in galactic cosmic rays and solar particle events. One of the most important late effects in risk assessment is carcinogenesis. We have studied the carcinogenic effects of heavy ions at the cellular and molecular levels and have obtained quantitative data on dose-response curves and on the repair of oncogenic lesions for heavy particles with various charges and energies. Studies with repair inhibitors and restriction endonucleases indicated that for oncogenic transformation DNA is the primary target. Results from heavy ion experiments showed that the cross section increased with LET and reached a maximum value of about 0.02 micrometer2 at about 500 keV/micrometer. This limited size of cross section suggests that only a fraction of cellular genomic DNA is important in radiogenic transformation. Free radical scavengers, such as DMSO, do not give any effect on induction of oncogenic transformation by 600 MeV/u iron particles, suggesting most oncogenic damage induced by high-LET heavy ions is through direct action. Repair studies with stationary phase cells showed that the amount of reparable oncogenic lesions decreased with an increase of LET and that heavy ions with LET greater than 200 keV/micrometer produced only irreparable oncogenic damage. An enhancement effect for oncogenic transformation was observed in cells irradiated by low-dose-rate argon ions (400 MeV/u; 120 keV/micrometer). Chromosomal aberrations, such as translocation and deletion, but not sister chromatid exchange, are essential for heavy-ion-induced oncogenic transformation. The basic mechanism(s) of misrepair of DNA damage, which form oncogenic lesions, is unknown.

NASA Discipline Number 45-10↗
NASA NTRS1997

Initiation of oncogenic transformation in human mammary epithelial cells by charged particles

Experimental studies have shown that high linear-energy transfer (LET) charged particles can be more effective than x-rays and gamma-rays in inducing oncogenic transformation in cultured cells and tumors in animals. Based on these results, experiments were designed and performed with an immortal human mammary epithelial cell line (H184B5), and several clones transformed by heavy ions were obtained. Cell fusion experiments were subsequently done, and results indicate that the transforming gene(s) is recessive. Chromosome analysis with fluorescence in situ hybridization (FISH) techniques also showed additional translocations in transformed human mammary epithelial cells. In addition, studies with these cell lines indicate that heavy ions can effectively induce deletion, break, and dicentrics. Deletion of tumor suppressor gene(s) and/or formation of translocation through DNA double strand breaks is a likely mechanism for the initiation of oncogenic transformation in human mammary epithelial cells.

NASA Discipline Radiation Health↗
NASA NTRS2023

NASA Langley Transformation Plan

NASA Langley Research Center has a strong history of creating impactful contributions to NASA’s mission and the Nation, working across NASA’s mission directorate portfolio. NASA Langley develops and delivers innovative solutions and technologies across a diversified portfolio that includes aeronautics, space technology and exploration, and science. As NASA Langley enters its 106th year, the Center is working in changing environment driven by the global pace of technology advancement and increased global connectivity. It is within this global context that NASA Langley leadership has recognized the need to intentionally invest in modernization efforts and established the Langley Transformation Initiative. This document outlines the Langley Transformation Initiative vision and goals. Current transformation challenges are described, and a strategy is outlined for how to the Transformation Initiative plans to advance towards the transformation vision.

Transformation↗