On orthogonal systems of functions
Extension of Hilbert method of linear functional equations to orthogonal systems of functions
FUNCTIONAL INTEGRATION↗
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Increasing software testability with standard access and control interfaces
Testing is the most common method of determining whether a software system satisfies its requirements. Traditionally, testing starts with the detailed examination of individual functions or methods, progresses through the integration of functions or methods into subsystems, and ends with testing the functionality and behavior of the completely integrated system. At each stage of testing, the amount of functionality and behavior of the artifact being tested is increasingly limited. One reason for this is that it becomes impossible to test all paths through the system within a reasonable amount of time. However, another reason for this progressive decrease of test coverage has to do with increasingly limited control of and visibility into the state of the artifact being tested. During unit test, it is rather simple to control the inputs of individual functions or methods or view their internal state - modem development environments provide adequate facilities for doing so. However, these facilities do not scale up to the testing of partially or completely integrated systems. Control of and visibility into the system's state is then limited to the input and output facilities provided by the software itself as well as the hardware on which the software is hosted during the test. These facilities are usually insufficient to precisely control the state of individual components or sets of components of the system; they are also inadequate to the task of displaying on demand the state of specific components. We describe an approach to improving the testability of complex software systems with software constructs modeled after the hardware JTAG bus, used to provide visibility and controllability in testing digital circuits.
Tamir, Yuval↗
Transfer of training as a function of stimulus and response integration of paired associates.
Transfer of training as function of stimulus and response integration of paired associates
LEARNING↗
IDEAS and App Development Internship in Hardware and Software Design
In this report, I will discuss the tasks and projects I have completed while working as an electrical engineering intern during the spring semester of 2016 at NASA Kennedy Space Center. In the field of software development, I completed tasks for the G-O Caching Mobile App and the Asbestos Management Information System (AMIS) Web App. The G-O Caching Mobile App was written in HTML, CSS, and JavaScript on the Cordova framework, while the AMIS Web App is written in HTML, CSS, JavaScript, and C# on the AngularJS framework. My goals and objectives on these two projects were to produce an app with an eye-catching and intuitive User Interface (UI), which will attract more employees to participate; to produce a fully-tested, fully functional app which supports workforce engagement and exploration; to produce a fully-tested, fully functional web app that assists technicians working in asbestos management. I also worked in hardware development on the Integrated Display and Environmental Awareness System (IDEAS) wearable technology project. My tasks on this project were focused in PCB design and camera integration. My goals and objectives for this project were to successfully integrate fully functioning custom hardware extenders on the wearable technology headset to minimize the size of hardware on the smart glasses headset for maximum user comfort; to successfully integrate fully functioning camera onto the headset. By the end of this semester, I was able to successfully develop four extender boards to minimize hardware on the headset, and assisted in integrating a fully-functioning camera into the system.
CSS↗
Quadrature, Interpolation and Observability
Methods of interpolation and quadrature have been used for over 300 years. Improvements in the techniques have been made by many, most notably by Gauss, whose technique applied to polynomials is referred to as Gaussian Quadrature. Stieltjes extended Gauss's method to certain non-polynomial functions as early as 1884. Conditions that guarantee the existence of quadrature formulas for certain collections of functions were studied by Tchebycheff, and his work was extended by others. Today, a class of functions which satisfies these conditions is called a Tchebycheff System. This thesis contains the definition of a Tchebycheff System, along with the theorems, proofs, and definitions necessary to guarantee the existence of quadrature formulas for such systems. Solutions of discretely observable linear control systems are of particular interest, and observability with respect to a given output function is defined. The output function is written as a linear combination of a collection of orthonormal functions. Orthonormal functions are defined, and their properties are discussed. The technique for evaluating the coefficients in the output function involves evaluating the definite integral of functions which can be shown to form a Tchebycheff system. Therefore, quadrature formulas for these integrals exist, and in many cases are known. The technique given is useful in cases where the method of direct calculation is unstable. The condition number of a matrix is defined and shown to be an indication of the the degree to which perturbations in data affect the accuracy of the solution. In special cases, the number of data points required for direct calculation is the same as the number required by the method presented in this thesis. But the method is shown to require more data points in other cases. A lower bound for the number of data points required is given.
Hodges, Lucille McDaniel↗
Accelerometer method and apparatus for integral display and control functions
Vibration analysis has been used for years to provide a determination of the proper functioning of different types of machinery, including rotating machinery and rocket engines. A determination of a malfunction, if detected at a relatively early stage in its development, will allow changes in operating mode or a sequenced shutdown of the machinery prior to a total failure. Such preventative measures result in less extensive and/or less expensive repairs, and can also prevent a sometimes catastrophic failure of equipment. Standard vibration analyzers are generally rather complex, expensive, and of limited portability. They also usually result in displays and controls being located remotely from the machinery being monitored. Consequently, a need exists for improvements in accelerometer electronic display and control functions which are more suitable for operation directly on machines and which are not so expensive and complex. The invention includes methods and apparatus for detecting mechanical vibrations and outputting a signal in response thereto. The apparatus includes an accelerometer package having integral display and control functions. The accelerometer package is suitable for mounting upon the machinery to be monitored. Display circuitry provides signals to a bar graph display which may be used to monitor machine condition over a period of time. Control switches may be set which correspond to elements in the bar graph to provide an alert if vibration signals increase over the selected trip point. The circuitry is shock mounted within the accelerometer housing. The method provides for outputting a broadband analog accelerometer signal, integrating this signal to produce a velocity signal, integrating and calibrating the velocity signal before application to a display driver, and selecting a trip point at which a digitally compatible output signal is generated. The benefits of a vibration recording and monitoring system with controls and displays readily mountable on the machinery being monitored and having capabilities described will be appreciated by those working in the art.
Bozeman, Richard J., Jr.↗
Functional Analysis for an Integrated Capability of Arrival/Departure/Surface Management with Tactical Runway Management
The runway is a critical resource of any air transport system. It is used for arrivals, departures, and for taxiing aircraft and is universally acknowledged as a constraining factor to capacity for both surface and airspace operations. It follows that investigation of the effective use of runways, both in terms of selection and assignment as well as the timing and sequencing of the traffic is paramount to the efficient traffic flows. Both the German Aerospace Center (DLR) and NASA have developed concepts and tools to improve atomic aspects of coordinated arrival/departure/surface management operations and runway configuration management. In December 2012, NASA entered into a Collaborative Agreement with DLR. Four collaborative work areas were identified, one of which is called "Runway Management." As part of collaborative research in the "Runway Management" area, which is conducted with the DLR Institute of Flight Guidance, located in Braunschweig, the goal is to develop an integrated system comprised of the three DLR tools - arrival, departure, and surface management (collectively referred to as A/D/S-MAN) - and NASA's tactical runway configuration management (TRCM) tool. To achieve this goal, it is critical to prepare a concept of operations (ConOps) detailing how the NASA runway management and DLR arrival, departure, and surface management tools will function together to the benefit of each. To assist with the preparation of the ConOps, the integrated NASA and DLR tools are assessed through a functional analysis method described in this report. The report first provides the highlevel operational environments for air traffic management (ATM) in Germany and in the U.S., and the descriptions of the DLR's A/D/S-MAN and NASA's TRCM tools at the level of details necessary to compliment the purpose of the study. Functional analyses of each tool and a completed functional analysis of an integrated system design are presented next in the report. Future efforts to fully develop the ConOps will include: developing scenarios to fully test environmental, procedural, and data availability assumptions; executing the analysis by a walk-through of the integrated system using these scenarios; defining the appropriate role of operators in terms of their monitoring requirements and decision authority; executing the analysis by a walk-through of the integrated system with operator involvement; characterizing the environmental, system data requirements, and operator role assumptions for the ConOps.
Phojanamongkolkij, Nipa↗
An integral transform with a Whittaker function kernel Interim report, 20 Jun. - 19 Aug. 1968
Integral transformation with Whittaker kernel functions
Wimp, J.↗
A THEORETICAL PHOTOMETRIC FUNCTION FOR THE LUNAR SURFACE
Differential and integral brightness functions determined by the formulation of the observed photometric properties of the lunar surface
LUNAR SURFACE↗
Scattering phase shift in quantum mechanics on quantum computers
Here, we investigate the feasibility of extracting infinite volume scattering phase shift on quantum computers in a simple one-dimensional quantum mechanical model, using the formalism established in the work by Guo and Gasparian [Phys. Rev. D 108, 074504 (2023)] that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral. The system is first discretized in a finite box with periodic boundary conditions, and the formalism in real time is verified by employing a contact interaction potential with exact solutions. Quantum circuits are then designed and constructed to implement the formalism on current quantum computing architectures. To overcome the fast oscillatory behavior of the integrated correlation functions in real-time simulation, different methods of postdata analysis are proposed and discussed. Test results on IBM hardware show that good agreement can be achieved with two qubits, but complete failure ensues with three qubits due to two-qubit gate operation errors and thermal relaxation errors.
Guo, Peng [Dakota State Univ., Madison, SD (United↗
Sensory integration for neuroprostheses: from functional benefits to neural correlates
In the field of sensory neuroprostheses, one ultimate goal is for individuals to perceive artificial somatosensory information and use the prosthesis with high complexity that resembles an intact system. To this end, research has shown that stimulation elicited somatosensory information improves prosthesis perception and task performance. While studies strive to achieve sensory integration, a crucial phenomenon that entails naturalistic interaction with the environment, this topic has not been commensurately reviewed. Therefore, here we present a perspective for understanding sensory integration in neuroprostheses. First, we review the engineering aspects and functional outcomes in sensory neuroprosthesis studies. In this context, we summarize studies that have suggested sensory integration. We focus on how they have used stimulation-elicited percepts to maximize and improve the reliability of somatosensory information. Next, we review studies that have suggested multisensory integration. These works have demonstrated that congruent and simultaneous multisensory inputs provided cognitive benefits such that an individual experiences a greater sense of authority over prosthesis movements (i.e., agency) and perceives the prosthesis as part of their own (i.e., ownership). Thereafter, we present the theoretical and neuroscience framework of sensory integration. We investigate how behavioral models and neural recordings have been applied in the context of sensory integration. Sensory integration models developed from intact-limb individuals have led the way to sensory neuroprosthesis studies to demonstrate multisensory integration. Neural recordings have been used to show how multisensory inputs are processed across cortical areas. Lastly, we discuss some ongoing research and challenges in achieving and understanding sensory integration in sensory neuroprostheses. Here, resolving these challenges would help to develop future strategies to improve the sensory feedback of a neuroprosthetic system.
60 APPLIED LIFE SCIENCES↗
An LSI variable function register.
Large Scale Integration /LSI/ variable function register developed using MOS technology
Lesniewski, R. J.↗
Symbolic integration of a class of algebraic functions
An algorithm is presented for the symbolic integration of a class of algebraic functions. This class consists of functions made up of rational expressions of an integration variable x and square roots of polynomials, trigonometric and hyperbolic functions of x. The algorithm is shown to consist of the following components:(1) the reduction of input integrands to conical form; (2) intermediate internal representations of integrals; (3) classification of outputs; and (4) reduction and simplification of outputs to well-known functions.
Ng, E. W.↗
Fourier transforms, generalized functions and two classes of integral equations. I.
Fundamental space phi and Fourier transformed function space psi
Pao, Y.-P.↗
On stochastic extremum problems - calculus.
Lagrange multiplier technique for determining stationary points /of functions/ or stationary functions /of integrals/ of expected value of random functions with certain random constraints
LAGRANGE MULTIPLIER↗
Assurance Technology Challenges of Advanced Space Systems
The initiative to explore space and extend a human presence across our solar system to revisit the moon and Mars post enormous technological challenges to the nation's space agency and aerospace industry. Key areas of technology development needs to enable the endeavor include advanced materials, structures and mechanisms; micro/nano sensors and detectors; power generation, storage and management; advanced thermal and cryogenic control; guidance, navigation and control; command and data handling; advanced propulsion; advanced communication; on-board processing; advanced information technology systems; modular and reconfigurable systems; precision formation flying; solar sails; distributed observing systems; space robotics; and etc. Quality assurance concerns such as functional performance, structural integrity, radiation tolerance, health monitoring, diagnosis, maintenance, calibration, and initialization can affect the performance of systems and subsystems. It is thus imperative to employ innovative nondestructive evaluation methodologies to ensure quality and integrity of advanced space systems. Advancements in integrated multi-functional sensor systems, autonomous inspection approaches, distributed embedded sensors, roaming inspectors, and shape adaptive sensors are sought. Concepts in computational models for signal processing and data interpretation to establish quantitative characterization and event determination are also of interest. Prospective evaluation technologies include ultrasonics, laser ultrasonics, optics and fiber optics, shearography, video optics and metrology, thermography, electromagnetics, acoustic emission, x-ray, data management, biomimetics, and nano-scale sensing approaches for structural health monitoring.
Chern, E. James↗
The Effects of Spaceflight and Head Down Tilt Bed Rest on Neurocognitive Performance: Extent, Longevity, and Neural Bases
Spaceflight effects on gait, balance, & manual motor control have been well studied; some evidence for cognitive deficits. Rodent cortical motor & sensory systems show neural structural alterations with spaceflight. specific Aims: Aim 1-Identify changes in brain structure, function, and network integrity as a function of head down tilt bed rest and spaceflight, and characterize their time course. Aim 2-Specify relationships between structural and functional brain changes and performance and characterize their time course.
Seidler, Rachael D.↗
The Effects of Spaceflight on Neurocognitive Performance: Extent, Longevity, and Neural Bases
Spaceflight effects on gait, balance, & manual motor control have been well studied; some evidence for cognitive deficits. Rodent cortical motor & sensory systems show neural structural alterations with spaceflight. We found extensive changes in behavior, brain structure & brain function following 70 days of HDBR. Specific Aim: Aim 1-Identify changes in brain structure, function, and network integrity as a function of spaceflight and characterize their time course. Aim 2-Specify relationships between structural and functional brain changes and performance and characterize their time course.
Seidler, Rachael D.↗