A Lower Bound on the Ground State Energy of Dilute Bose Gas

Consider an N-Boson system interacting via a two-body repulsive short-range potential $V$ in a three dimensional box $\Lambda$ of side length $L$. We take the limit $N, L \to \infty$ while keeping the density $\rho = N / L^3$ fixed and small. We prove a new lower bound for its ground state energy per particle $$\frac{E(N, \Lambda)}{N} \geq 4 \pi a \rho [ 1 - O(\rho^{1/3} |\log \rho|^3) ],$$ as $\rho \to 0$, where $a$ is the scattering length of $V$.Comment: 26 pages, AMS LaTe

Noiseless coding for the magnetometer

Future unmanned space missions will continue to seek a full understanding of magnetic fields throughout the solar system. Severely constrained data rates during certain portions of these missions could limit the possible science return. This publication investigates the application of universal noiseless coding techniques to more efficiently represent magnetometer data without any loss in data integrity. Performance results indicated that compression factors of 2:1 to 6:1 can be expected. Feasibility for general deep space application was demonstrated by implementing a microprocessor breadboard coder/decoder using the Intel 8086 processor. The Comet Rendezvous Asteroid Flyby mission will incorporate these techniques in a buffer feedback, rate-controlled configuration. The characteristics of this system are discussed

THE ADJUSTMENT OF LEG STIFFNESS DURING DYNAMIC EXERCISE AND DOWNWARD STEPPING FOR ELDERLY

The purpose of the present study was to evaluate the ability of leg stiffness regulation during downward stepping and maximal Counter-Movement-Jump (CMJ) for the elderly. Ten healthy aged people (age: 68.6±5 years; height: 165.3±4.4cm; mass: 61.7±9.3kg) and 10 students (age: 24.3±2years; height: 171.5±4.6cm; mass: 65.9±8kg) volunteered as subjects. Kistler force platform (1200Hz) and Peak high-speed camera (120Hz) were used synchronously to record the ground reaction force and the kinematic parameters of the subjects performing CMJ and stepping down from different heights. The results revealed that the elderly group has a smaller joint range of motion and greater leg stiffness than the young group during stepping down. The force and the leg stiffness during CMJ were significantly smaller for the elderly. The leg stiffness during downward stepping is independent of dynamic leg stiffness during CMJ. With aging, the adjustment ability of leg stiffness for maximal dynamic voluntary contraction was decreased

Gas Chromatography-High Resolution Tandem Mass Spectrometry Using a GC-APPI-LIT Orbitrap for Complex Volatile Compounds Analysis

A new approach of volatile compounds analysis is proposed using a linear ion trap Orbitrap mass spectrometer coupled with gas chromatography through an atmospheric pressure photoionization interface. In the proposed GC-HRMS/MS approach, direct chemical composition analysis is made for the precursor ions in high resolution MS spectra and the structural identifications were made through the database search of high quality MS/MS spectra. Successful analysis of a complex perfume sample was demonstrated and compared with GC-EI-Q and GC-EI-TOF. The current approach is complementary to conventional GC-EI-MS analysis and can identify low abundance co-eluting compounds. Toluene co-sprayed as a dopant through API probe significantly enhanced ionization of certain compounds and reduced oxidation during the ionization

Connections between Reachability and Time Optimality

This paper presents the concept of an equivalence relation between the set of optimal control problems. By leveraging this concept, we show that the boundary of the reachability set can be constructed by the solutions of time optimal problems. Alongside, a more generalized equivalence theorem is presented together. The findings facilitate the use of solution structures from a certain class of optimal control problems to address problems in corresponding equivalent classes. As a byproduct, we state and prove the construction methods of the reachability sets of three-dimensional curves with prescribed curvature bound. The findings are twofold: Firstly, we prove that any boundary point of the reachability set, with the terminal direction taken into account, can be accessed via curves of H, CSC, CCC, or their respective subsegments, where H denotes a helicoidal arc, C a circular arc with maximum curvature, and S a straight segment. Secondly, we show that any boundary point of the reachability set, without considering the terminal direction, can be accessed by curves of CC, CS, or their respective subsegments. These findings extend the developments presented in literature regarding planar curves, or Dubins car dynamics, into spatial curves in $\mathbb{R}^3$. For higher dimensions, we confirm that the problem of identifying the reachability set of curvature bounded paths subsumes the well-known Markov-Dubins problem. These advancements in understanding the reachability of curvature bounded paths in $\mathbb{R}^3$ hold significant practical implications, particularly in the contexts of mission planning problems and time optimal guidance.Comment: Submitted to Automatic