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A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.
A general class of even/odd transforms is presented that includes the Karhunen-Loeve transform, the discrete cosine transform, the Walsh-Hadamard transform, and other familiar transforms. The more complex even/odd transforms can be computed by combining a simpler even/odd transform with a sparse matrix multiplication. A theoretical performance measure is computed for some even/odd transforms, and two image compression experiments are reported.
According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.
The disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them. The improved method is based on introducing a new integration step length Delta(omega) = pi/mT for trapezoidal-rule approximation of the Bromwich integral, in which a new parameter, m, is introduced for controlling the accuracy of the numerical integration. Naturally, this method leads to multiple sets of complex FFT computations. A new inversion formula is derived such that N equally spaced samples of the inverse Laplace transform function can be obtained by (m/2) + 1 sets of N-point complex FFT computations or by m sets of real fast Hartley transform (FHT) computations.
The CRISPR (Clustered, Regularly Interspaced, Short Palindromic Repeats)/Cas9 system has revolutionized genome editing by providing unprecedented DNA-targeting specificity. Here we demonstrate that this system can be also applied in vitro to fundamental cloning steps to facilitate efficient plasmid selection for transformation and selective gene insertion into plasmid vectors by cleaving unwanted plasmid byproducts with a single-guide RNA (sgRNA)-Cas9 nuclease complex. Using fluorescent and chromogenic proteins as reporters, we demonstrate that CRISPR/Cas9 cleavage excludes multiple plasmids as well as unwanted ligation byproducts resulting in an unprecedented increase in the transformation success rate from approximately 20% to nearly 100%. Thus, this CRISPR/Cas9-Assisted Transformation-Efficient Reaction (CRATER) protocol is a novel, inexpensive, and convenient application to conventional molecular cloning to achieve near-perfect selective transformation.
The Transformational Concept of Operations (CONOPS) provides a long-term, sustainable vision for future U.S. space transportation infrastructure and operations. This vision presents an interagency concept, developed cooperatively by the Department of Defense (DoD), the Federal Aviation Administration (FAA), and the National Aeronautics and Space Administration (NASA) for the upgrade, integration, and improved operation of major infrastructure elements of the nation s space access systems. The interagency vision described in the Transformational CONOPS would transform today s space launch infrastructure into a shared system that supports worldwide operations for a variety of users. The system concept is sufficiently flexible and adaptable to support new types of missions for exploration, commercial enterprise, and national security, as well as to endure further into the future when space transportation technology may be sufficiently advanced to enable routine public space travel as part of the global transportation system. The vision for future space transportation operations is based on a system-of-systems architecture that integrates the major elements of the future space transportation system - transportation nodes (spaceports), flight vehicles and payloads, tracking and communications assets, and flight traffic coordination centers - into a transportation network that concurrently accommodates multiple types of mission operators, payloads, and vehicle fleets. This system concept also establishes a common framework for defining a detailed CONOPS for the major elements of the future space transportation system. The resulting set of four CONOPS (see Figure 1 below) describes the common vision for a shared future space transportation system (FSTS) infrastructure from a variety of perspectives.
Gauge transformations of third kind and operator gauge transformations of first and second kinds, relating electron and photon propagators to quantum electrodynamical vertex function
Algorithm for inverse Laplace transformation of irrational transfer function via fast Fourier transform
Overview of how NASA OSMA and R&M are leveraging the agency’s Digital Transformation (DT) initiative to transform its own delivery of services and products in support of NASA mission. Focus is on R&M related activities.
NASA has a long history of serving the Nation and the world, by reaching for new heights and revealing the unknown for the benefit of all humankind. To ensure the agency will deliver on its mission in a hyper-connected, technology-enabled, globally-partnered, and rapidly-changing world, NASA launched a Digital Transformation initiative in late 2020 to modernize the way it works, the experience of its workforce and the agility of its workplace. At the core of its workplace transformation strategy, NASA is on a journey to leverage smart operational technologies, weaving together IoT, AI, intelligent automation, extended reality, and digital twins to build a network of reliable, adaptable and sustainable “Smart Centers” to execute its mission… on planet Earth and beyond. Come hear NASA’s digital strategy, the exciting progress being made, lessons learned from their journey, and how the AIMST community can enable NASA and its partners to serve humanity in a digital future.
A set of equations which transform position and angular orientation of the centroid of the payload platform of a six-degree-of-freedom motion simulator into extensions of the simulator's actuators has been derived and is based on a geometrical representation of the system. An iterative scheme, Newton-Raphson's method, has been successfully used in a real time environment in the calculation of the position and angular orientation of the centroid of the payload platform when the magnitude of the actuator extensions is known. Sufficient accuracy is obtained by using only one Newton-Raphson iteration per integration step of the real time environment.
A spectrometric imager and a thermal imager, which achieve multiplexing by the use of binary optical encoding masks, were developed. The masks are based on orthogonal, pseudorandom digital codes derived from Hadamard matrices. Spatial and/or spectral data is obtained in the form of a Hadamard transform of the spatial and/or spectral scene; computer algorithms are then used to decode the data and reconstruct images of the original scene. The hardware, algorithms and processing/display facility are described. A number of spatial and spatial/spectral images are presented. The achievement of a signal-to-noise improvement due to the signal multiplexing was also demonstrated. An analysis of the results indicates both the situations for which the multiplex advantage may be gained, and the limitations of the technique. A number of potential applications of the spectrometric imager are discussed.
A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.
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The "final frontier" is not what is used to be. Advancements in systems capabilities, easier access to orbit, a rapidly expanding spacefaring community saddled with imagination, and innovative approaches to mitigate chronic fiscal constraints are all converging to create novel spaceflight systems and mission architectures. Persons content to apply yesterday's thought to today's challenges stand the risk of finding themselves following instead of leading. The Dellingr 6U CubeSat project ongoing at NASA Goddard Space Flight Center is demonstrating that while there is great potential to achieve compelling science, new systems and processes are required to fully leverage the cost and schedule efficiencies small satellites can yield. In addition, realizing the potential of these platforms in environments more challenging than benign low earth orbit requires spacecraft systems designed for reliable or resilient operation, and reliable components and subsystems.
Many non-intrusive combustion diagnosis methods generate line-of-sight projections of a flame field. To reconstruct the spatial field of the measured properties, these projections need to be deconvoluted. When the spatial field is axisymmetric, commonly used deconvolution method include the Abel transforms, the onion peeling method and the two-dimensional Fourier transform method and its derivatives such as the filtered back projection methods. This paper proposes a new approach for performing the Abel transform method is developed, which possesses the exactness of the Abel transform and the flexibility of incorporating various filters in the reconstruction process. The Abel transform is an exact method and the simplest among these commonly used methods. It is evinced in this paper that all the exact reconstruction methods for axisymmetric distributions must be equivalent to the Abel transform because of its uniqueness and exactness. Detailed proof is presented to show that the two dimensional Fourier methods when applied to axisymmetric cases is identical to the Abel transform. Discrepancies among various reconstruction method stem from the different approximations made to perform numerical calculations. An equation relating the spectrum of a set of projection date to that of the corresponding spatial distribution is obtained, which shows that the spectrum of the projection is equal to the Abel transform of the spectrum of the corresponding spatial distribution. From the equation, if either the projection or the distribution is bandwidth limited, the other is also bandwidth limited, and both have the same bandwidth. If the two are not bandwidth limited, the Abel transform has a bias against low wave number components in most practical cases. This explains why the Abel transform and all exact deconvolution methods are sensitive to high wave number noises. The filtered Abel transform is based on the fact that the Abel transform of filtered projection data is equal to an integral transform of the original projection data with the kernel function being the Abel transform of the filtering function. The kernel function is independent of the projection data and can be obtained separately when the filtering function is selected. Users can select the best filtering function for a particular set of experimental data. When the kernal function is obtained, it can be used repeatedly to a number of projection data sets (rovs) from the same experiment. When an entire flame image that contains a large number of projection lines needs to be processed, the new approach significantly reduces computational effort in comparison with the conventional approach in which each projection data set is deconvoluted separately. Computer codes have been developed to perform the filter Abel transform for an entire flame field. Measured soot volume fraction data of a jet diffusion flame are processed as an example.
In a high-speed signal transmission system that uses transformer coupling, there is a need to provide increased transmitted signal strength without adding active components. This invention uses additional transformers to achieve the needed gain. The prior art uses stronger drivers (which require an IC redesign and a higher power supply voltage), or the addition of another active component (which can decrease reliability, increase power consumption, reduce the beneficial effect of serializer/deserializer preemphasis or deemphasis, and/or interfere with fault containment mechanisms), or uses a different transformer winding ratio (which requires redesign of the transformer and may not be feasible with high-speed signals that require a 1:1 winding ratio). This invention achieves the required gain by connecting the secondaries of multiple transformers in series. The primaries of these transformers are currently either connected in parallel or are connected to multiple drivers. There is also a need to split a receive signal to multiple destinations with minimal signal loss. Additional transformers can achieve the split. The prior art uses impedance-matching series resistors that cause a loss of signal. Instead of causing a loss, most instantiations of this invention would actually provide gain. Multiple transformers are used instead of multiple windings on a single transformer because multiple windings on the same transformer would require a redesign of the transformer, and may not be feasible with high-speed transformers that usually require a bifilar winding with a 1:1 ratio. This invention creates the split by connecting the primaries of multiple transformers in series. The secondary of each transformer is connected to one of the intended destinations without the use of impedance-matching series resistors.
The analysis and design of co-axial winding transformers is presented. The design equations are derived and the different design approaches are discussed. One of the most important features of co-axial winding transformers is the fact that the leakage inductance is well controlled and can be made low. This is not the case in conventional winding transformers. In addition, the power density of co-axial winding transformers is higher than conventional ones. Hence, using co-axial winding transformers in a certain converter topology improves the power density of the converter. The design methodology used in meeting the proposed specifications of the co-axial winding transformer specifications are presented and discussed. The final transformer design was constructed in the lab. Co-axial winding transformers proved to be a good choice for high power density and high frequency applications. They have a more predictable performance compared with conventional transformers. In addition, the leakage inductance of the transformer can be controlled easily to suit a specific application. For space applications, one major concern is the extraction of heat from power apparatus to prevent excessive heating and hence damaging of these units. Because of the vacuum environment, the only way to extract heat is by using a cold plate. One advantage of co-axial winding transformers is that the surface area available to extract heat from is very large compared to conventional transformers. This stems from the unique structure of the co-axial transformer where the whole core surface area is exposed and can be utilized for cooling effectively. This is a crucial issue here since most of the losses are core losses.