On computing elliptic integrals and functions.
Elliptic integral and function direct computation method using successive quadratic Landen and Gauss transformations
ELLIPTIC INTEGRAL↗
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A characterization of integral operators on the space of Borel measurable functions bounded with respect to a weight function.
Integral operators on space of Borel measurable functions bounded considering weight function, giving condition for infinite complex matrices, mapping analytic sequence spaces
Raphael, L. A.↗
NORMAL ELLIPTIC INTEGRALS OF THE FIRST AND SECOND KINDS
Transformation formulas and hypergeometric elliptical integral functions
ELLIPTIC FUNCTION↗
Medical Operations Support for ISS Operations - The Role of the BME Operations Team Leads
This slide presentation reviews the role of the biomedical flight controllers (BMEs), and BME Operations Team Leads (OTLs) in providing medical support for personnel on the International Space Station. This presentation will concentrate on role of the BME OTLs, who provide the integration function across the integration function across all Crew Health Care System (CHeCS) disciplines for operational products and medical procedures.
Janney, Rob↗
Toward extracting scattering phase shift from integrated correlation functions. III. Coupled channels
The formalism developed in the preceding papers that connects integrated correlation function of a trapped two-particle system to infinite volume scattering phase shift is further extended to coupled-channel systems in the present work. Using a trapped nonrelativistic two-channel system as an example, a new relation is derived that retains the same structure as in the single channel, and has explicit dependence on the phase shifts in both channels but not on the inelasticity. The relation is illustrated by a exactly solvable coupled-channel quantum mechanical model with contact interactions. It is further validated by path integral Monte Carlo simulation of a quasi-one-dimensional model that can admit general interaction potentials. In all cases, we found rapid convergence to the infinite volume limit as the trap size is increased, even at short times, making it potentially a good candidate to overcome signal-to-noise issues in Monte Carlo applications. Published by the American Physical Society 2025
Guo, Peng (ORCID:0000000265660881)↗
A single bout of exhaustive exercise affects integrated baroreflex function after 16 days of head-down tilt
We tested the hypothesis that one bout of maximal exercise performed 24 h before reambulation from 16 days of 6 degrees head-down tilt (HDT) could increase integrated baroreflex sensitivity. Isolated carotid-cardiac and integrated baroreflex function was assessed in seven subjects before and after two periods of HDT separated by 11 mo. On the last day of one HDT period, subjects performed a single bout of maximal cycle ergometry (exercise). Subjects did not exercise after the other HDT period (control). Carotid-cardiac baroreflex sensitivity was evaluated using a neck collar device. Integrated baroreflex function was assessed by recording heart rate (HR) and blood pressure (MAP) during a 15-s Valsalva maneuver (VM) at a controlled expiratory pressure of 30 mmHg. The ratio of change in HR to change in MAP (delta HR/ delta MAP) during phases II and IV of the VM was used as an index of cardiac baroreflex sensitivity. Baroreflex-mediated vasoconstriction was assessed by measuring the late phase II rise in MAP. Following HDT, carotid-cardiac baroreflex sensitivity was reduced (2.8 to 2.0 ms/mmHg; P = 0.05) as was delta HR/ delta MAP during phase II (-1.5 to -0.8 beats/mmHg; P = 0.002). After exercise, isolated carotid baroreflex activity and phase II delta HR/ delta MAP returned to pre-HDT levels but remained attenuated in the control condition. Phase IV delta HR/ delta MAP was not altered by HDT or exercise. The late phase II increase of MAP was 71% greater after exercise compared with control (7 vs. 2 mmHg; P = 0.041).(ABSTRACT TRUNCATED AT 250 WORDS).
Randomized Controlled Trial↗
Background-field Method and QCD Factorization
One method for deriving a factorization for QCD processes is to use successive integration over fields in the functional integral. In this approach, we separate the fields into two categories: dynamical fields with momenta above a relevant cutoff, and background fields with momenta below the cutoff. The dynamical fields are then integrated out in the background of the low-momentum background fields. This strategy works well at tree level, allowing us to quickly derive QCD factorization formulas at leading order. However, to extend the approach to higher loops, it is necessary to rigorously define the functional integral over dynamical fields in an arbitrary background field. This framework was carefully developed for the calculation of the effective action in a background field at the two-loop level in the classic paper by Abbott «The Background Field Method Beyond One Loop», Nucl. Phys. B 185 , 189 (1981). Building on this work, I specify the renormalized background-field Lagrangian and define the notion of the quantum average of an operator in a background field, consistent with the “separation of scales” scheme mentioned earlier. As examples, I discuss the evolution of the twist-2 gluon light-ray operator and the one-loop gluon propagator in a background field near the light cone.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The implementation of fail-operative functions in integrated digital avionics systems
System architectures which incorporate fail operative flight guidance functions within a total integrated avionics complex are described. It is shown that the mixture of flight critical and nonflight critical functions within a common computer complex is an efficient solution to the integration of navigation, guidance, flight control, display, and flight management. Interfacing subsystems retain autonomous capability to avoid vulnerability to total avionics system shutdown as a result of only a few failures.
Osoer, S. S.↗
Elliptic Functions and Integrals with Real Modulus in Fluid Mechanics
Advantage of the elliptic functions and of the more general functions of Schwarz for fluid mechanics. Flows outside and inside polygons. Application to the calculation of an elbow diffuser for a wind tunnel. Properties of the elliptic integrals of the first kind and of the elliptic functions. Properties of the theta functions and decomposition of the elliptic functions into products of theta functions. Properties of the zeta functions. Decomposition of the elliptic functions into sums of zeta functions and calculations of the elliptic integrals. Applications to the calculation of wing profiles, of compressor profiles, and to the study of the vibrations of airplane wings and of compressor vanes. The manuscript of the present paper was checked by Mr. Eichelbrenner who corrected several imperfections and suggested numerous improvements to make reading of the paper easier. However, the limited subject does not permit filling in more than an incomplete knowledge of the properties of analytic functions.
Legendre, Robert↗
Two-integral distribution functions for axisymmetric galaxies
The new method presented for finding distribution functions, which depend only on the classical integrals of energy and angular momentum for stellar systems with known axisymmetric densities, is the analog for the axisymmetric case of Eddington's classical solution for the isotropic distribution function, depending only on energy, of a known spherical density. It is required that density be expressed as a function of the potential and of a radial coordinate. Our solution is also an integral which is derived directly from the density, and hence can be used with complicated densities. A numerical quadrature is generally required to evaluate this solution, but contour integrals can be computed accurately by numerical quadrature; this is preferable to an explicit evaluation if the latter is an infinite series, such as is obtained using Fricke's method. We give several examples, including some for which our distribution functions are new. Our method can be extended simply to the related problems of finding anisotropic distribution functions for spherical or disk systems.
Hunter, C.↗
Formation of functionally graded steel by laser powder bed fusion via in-situ carbon doping
Additive Manufacturing (AM) enables functional integration by combining multiple components into a single part to shorten assembly time, reduce weight, and improve performance. Laser Powder Bed Fusion (LPBF) is an important AM method due to excellent spatial resolution, surface finish, and material properties without the need for extensive post-processing. Functional integration could be enhanced by spatial tuning of properties, but LPBF cannot readily vary material composition. Here, this paper addresses a method to add spatial composition control by printing small quantities of dopants via liquid carrier prior to laser fusion. The impact of carbon black suspension added to select regions of a Stainless Steel 316 L powder bed on melt pool dimension, hardness, and porosity is reported. The distribution of the carbon between the doped and plain layers and the resulting spatial variation in hardness is measured. Optical microscopy and composition analysis show that the carbon dispersed uniformly within the layer of deposition and diffused as little as 50 μm in the build direction. Keyhole conditions dramatically increase the inter-layer transport of the dopant. The added carbon increased hardness by >50 %. Porosity increased in doped regions but remained below 1.5 % for the best processing parameters. These results demonstrate that the composition of LPBF parts could be controlled in 3-dimensions using a dopant that is soluble in the melt pool. Additional work will be required to evaluate different dopant materials and optimize processing conditions for full density, but microalloying with soluble dopants appears to be a plausible solution to enhance functional integration with LPBF.
36 MATERIALS SCIENCE↗
Path integrals, Liapunov functions, and quadratic minimization.
Nonlinear DC circuits analyzed by digital computer for application to path integrals and stability problems
SYSTEM STABILITY↗
A cost effective data management subsystem for the LST
The paper outlines the approach used in developing DMS (Data Management Subsystem) alternatives for the LST (Large Space Telescope) and in selecting the concept considered to be the most cost effective means of implementing the LST DMS requirements. Two candidate DMS concepts are discussed: a functionally integrated and a functionally separated one. For the single vehicle LST program, separation of the DMS functions best provides high reliability, operations flexibility, minimal interface complexity, and the least complex software development and verification task. The use of available hardware and NASA standard components is stressed.
Dougherty, J. A.↗
Exact triple integrals of beam functions
Definite triple integrals encountered in applying the Galerkin method to the problem of heat and mass transfer across rectangular enclosures are discussed. Rather than evaluating them numerically, the technique described by Reid and Harris (1958) was extended to obtain the exact solution of the integrals. In the process, four linear simultaneous equations with triple integrals as unknowns were obtained. These equations were then solved exactly to obtain the closed form solution. Since closed form representations of this type have been shown to be useful in solving nonlinear hydrodynamic problems by series expansion, the integrals are presented here in general form.
Jhaveri, B. S.↗
Is it possible to create a universe in the laboratory by quantum tunneling?
We explore the possibility that a new universe can be created by producing a small bubble of false vacuum. The initial bubble is small enough to be produced without an initial singularity, but classically it could not become a universe - instead it would reach a maximum radius and then collapse. We investigate the possibility that quantum effects allow the bubble to tunnel into a larger bubble, of the same mass, which would then classically evolve to become a new universe. The calculation of the tunneling amplitude is attempted, in lowest order semiclassical approximation (in the thin-wall limit), using both a canonical and a functional integral approach. The canonical approach is found to have flaws, attributable to our method of space-time slicing. The functional integral approach leads to a Euclidean interpolating solution that is not a manifold. To describe it, we define an object which we call a 'pseudomanifold', and give a prescription to define its action. We conjecture that the tunneling probability to produce a new universe can be approximated using this action, and we show that this leads to a plausible result.
Farhi, Edward↗
International Space Station Payload Operations Integration
The Payload Operations Integrator (POINT) plays an integral part in the Certification of Flight Readiness process for the Mission Operations Laboratory and the Payload Operations Integration Function that supports International Space Station Payload operations. The POINTs operate in support of the POIF Payload Operations Manager to bring together and integrate the Certification of Flight Readiness inputs from various MOL teams through maintaining an open work tracking log. The POINTs create monthly metrics for current and future payloads that the Payload Operations Integration Function supports. With these tools, the POINTs assemble the Certification of Flight Readiness package before a given flight, stating that the Mission Operations Laboratory is prepared to support it. I have prepared metrics for Increment 29/30, maintained the Open Work Tracking Logs for Flights ULF6 (STS-134) and ULF7 (STS-135), and submitted the Mission Operations Laboratory Certification of Flight Readiness package for Flight 44P to the Mission Operations Directorate (MOD/OZ).
Fanske, Elizabeth Anne↗
Quantum-Inspired Maximizer
A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).
Zak, Michail↗
Integrated Locomotor Function Tests for Countermeasure Evaluation
Following spaceflight crewmembers experience locomotor dysfunction due to inflight adaptive alterations in sensorimotor function. Countermeasures designed to mitigate these postflight gait alterations need to be assessed with a new generation of tests that evaluate the interaction of various sensorimotor sub-systems central to locomotor control. The goal of the present study was to develop new functional tests of locomotor control that could be used to test the efficacy of countermeasures. These tests were designed to simultaneously examine the function of multiple sensorimotor systems underlying the control of locomotion and be operationally relevant to the astronaut population. Traditionally, gaze stabilization has been studied almost exclusively in seated subjects performing target acquisition tasks requiring only the involvement of coordinated eye-head movements. However, activities like walking involve full-body movement and require coordination between lower limbs and the eye-head-trunk complex to achieve stabilized gaze during locomotion. Therefore the first goal of this study was to determine how the multiple, interdependent, full-body sensorimotor gaze stabilization subsystems are functionally coordinated during locomotion. In an earlier study we investigated how alteration in gaze tasking changes full-body locomotor control strategies. Subjects walked on a treadmill and either focused on a central point target or read numeral characters. We measured: temporal parameters of gait, full body sagittal plane segmental kinematics of the head, trunk, thigh, shank and foot, accelerations along the vertical axis at the head and the shank, and the vertical forces acting on the support surface. In comparison to the point target fixation condition, the results of the number reading task showed that compensatory head pitch movements increased, peak head acceleration was reduced and knee flexion at heel-strike was increased. In a more recent study we investigated the adaptive remodeling of the full-body gaze control systems following exposure to visual-vestibular conflict. Subjects walked on a treadmill before and after a 30- minute exposure to 0.5X minifying during which self-generated sinusoidal vertical head rotations were performed while seated. Following exposure to visual-vestibular conflict subjects showed a restriction in compensatory head movements, increased knee and ankle flexion after heel-strike and a decrease in the rate of body loading during the rapid weight transfer phase after the heel strike event. Taken together, results from both studies provide evidence that the full body contributes to gaze stabilization during locomotion, and that different functional elements are responsive to changes in visual task constraints and are subject to adaptive alterations following exposure to visual-vestibular conflict. This information provides the basis for the design of a new generation of integrative tests that incorporate the evaluation of multiple neural control systems relevant to astronaut operational performance.
Bloomberg, J. J.↗