Ordering the zeroes of Legendre functions Pvm(Z0) when considered as a function of v

AbstractIn the following, we will consider the problem of ordering the zeroes of the Legendre functions Pvm(Z0) when m is a nonnegative integer and 0 < z0 <1. Let v = vjm(z0) denote the jth positive root of Pvm(z0) = 0, where j = 1, 2, …. It is well known from the Sturm-Liouville theory that vjm(z0) < vjm + 1(z0) < vj + 1m(z0). We will show that vjm + 2(z0) < vj + 1m(z0). Using these and several other inequalities, we will also show that v10 < v11 < v12 < v20 < v13 < v21 < v14 < v22 < v 30 <v 15 for all 0<z0 <1. Moreover, this is the unique ordering of the first ten vjm(z0)′s for 0<z0<1

Paired Pulse Basis Functions for the Method of Moments EFIE Solution of Electromagnetic Problems Involving Arbitrarily-shaped, Three-dimensional Dielectric Scatterers

A pair of basis functions is presented for the surface integral, method of moment solution of scattering by arbitrarily-shaped, three-dimensional dielectric bodies. Equivalent surface currents are represented by orthogonal unit pulse vectors in conjunction with triangular patch modeling. The electric field integral equation is employed with closed geometries for dielectric bodies; the method may also be applied to conductors. Radar cross section results are shown for dielectric bodies having canonical spherical, cylindrical, and cubic shapes. Pulse basis function results are compared to results by other methods

Estimating the Collapse Pressure of an Inflatable Aerodynamic Decelerator

The collapse pressure of an inflatable membrane is the minimum differential pressure which will sustain a specific desired shape under an applied load. In this paper, we present a method for estimating the collapse pressure of a tension-cone inflatable aerodynamic decelerator (IAD) that is subject to a static aerodynamic load. The IAD surface is modeled as an elastic membrane. For a given aerodynamic load and sufficiently high torus differential pressure, the IAD assumes a stable axisymmetric equilibrium shape. When the torus pressure is reduced sufficiently, the symmetric equilibrium state becomes unstable and we define this instance to be the critical pressure Pcr. In this paper, we will compare our predicted critical torus pressure with the corresponding observed torus collapse pressure (OTCP) for fifteen tests that were conducted by the third author and his collaborators at the NASA Glenn Research Center 10x10 Supersonic Wind Tunnel in April 2008. One of the difficulties with these types of comparisons is establishing the instance of torus collapse and determining the OTCP from quantities measured during the experiment. In many cases, torus collapse is gradual and the OTCP is not well-defined. However, in eight of the fifteen wind tunnel tests where the OTCP is well-defined, we find that the average of the relative differences (Pcr - OTCP/Pcr) was 8.9%. For completeness, we will also discuss the seven tests where the observed torus collapse pressure is not well-defined

An Alternate Set of Basis Functions for the Electromagnetic Solution of Arbitrarily-Shaped, Three-Dimensional, Closed, Conducting Bodies Using Method of Moments

In this work, we present an alternate set of basis functions, each defined over a pair of planar triangular patches, for the method of moments solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped, closed, conducting surfaces. The present basis functions are point-wise orthogonal to the pulse basis functions previously defined. The prime motivation to develop the present set of basis functions is to utilize them for the electromagnetic solution of dielectric bodies using a surface integral equation formulation which involves both electric and magnetic cur- rents. However, in the present work, only the conducting body solution is presented and compared with other data

New Basis Functions for the Electromagnetic Solution of Arbitrarily-shaped, Three Dimensional Conducting Bodies Using Method of Moments

In this work, we present a new set of basis functions, de ned over a pair of planar triangular patches, for the solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped surfaces using the method of moments solution procedure. The basis functions are constant over the function subdomain and resemble pulse functions for one and two dimensional problems. Further, another set of basis functions, point-wise orthogonal to the first set, is also de ned over the same function space. The primary objective of developing these basis functions is to utilize them for the electromagnetic solution involving conducting, dielectric, and composite bodies. However, in the present work, only the conducting body solution is presented and compared with other data

The anatomical landmarks effective in the localisation of the median nerve during orthopaedic procedures

Background: The aim of this study was to create a safe zone for surgeons who perform procedures in the wrist to avoid iatrogenic damage to the median nerve (MN) by identifying anatomical landmarks using ultrasound (USG).Materials and methods: We measured the distances between the MN and two easily identifiable anatomical landmarks at the level of the proximal border of carpal ligament using USG.Results: A total of 57 volunteers (n = 114 upper limbs) were included in this study. Our main findings revealed that the distance from the flexor carpi radialis tendon to MN (FCR-MN) was 7.87 mm (95% confidence interval 7.37–8.37) and the distance from flexor carpi ulnaris tendon to MN (FCU-MN) was 19.09 mm (95% confidence interval 18.51–19.67).Conclusions: The tendons of FCR and FCU are easily identifiable landmarks that can be distinguished using simple palpation. Based on our USG findings, the area around FCR should be carefully navigated to avoid iatrogenic injury to the MN during surgical procedures around the carpal tunnel

The Nylon Scintillator Containment Vessels for the Borexino Solar Neutrino Experiment

Borexino is a solar neutrino experiment designed to observe the 0.86 MeV Be-7 neutrinos emitted in the pp cycle of the sun. Neutrinos will be detected by their elastic scattering on electrons in 100 tons of liquid scintillator. The neutrino event rate in the scintillator is expected to be low (~0.35 events per day per ton), and the signals will be at energies below 1.5 MeV, where background from natural radioactivity is prominent. Scintillation light produced by the recoil electrons is observed by an array of 2240 photomultiplier tubes. Because of the intrinsic radioactive contaminants in these PMTs, the liquid scintillator is shielded from them by a thick barrier of buffer fluid. A spherical vessel made of thin nylon film contains the scintillator, separating it from the surrounding buffer. The buffer region itself is divided into two concentric shells by a second nylon vessel in order to prevent inward diffusion of radon atoms. The radioactive background requirements for Borexino are challenging to meet, especially for the scintillator and these nylon vessels. Besides meeting requirements for low radioactivity, the nylon vessels must also satisfy requirements for mechanical, optical, and chemical properties. The present paper describes the research and development, construction, and installation of the nylon vessels for the Borexino experiment

Clefting in a Pumpkin Balloon

NASA\u27s development of a large payload, high altitude, long duration balloon, the Ultra Long Duration Balloon, centers on a pumpkin shape super-pressure design. Under certain circumstances, it has been observed that a pumpkin balloon may be unable to pressurize into the desired cyclically symmetric equilibrium configuration, settling into a distorted, undesired state instead. In this paper, we will use th concept of stability to classify equilibrium shapes of fully pressurized/fully deployed strained ball oons

An anatomical investigation of rare upper limb neuropathies due to the Struthers’ ligament or arcade: a meta-analysis

Background: The Struthers’ ligament (SL) is a fibrous band that originates fromthe supracondylar humeral process and inserts into the medial humeral epicondyle, potentially compressing both the median nerve and brachial artery. The controversial Struthers’ arcade (SA) is a musculotendinous band found in the distal end of the arm that might compress the ulnar nerve. This study aimed to evaluate the pooled prevalence estimate of the SL and SA, and their anatomical features. Materials and methods: A meticulous search of major electronic medical databases was carried out regarding both structures. Applicable articles (and all relevant references) were analysed. Data from the eligible articles was extracted and evaluated. The quality and the potential risk of bias in the included studies were assessed using the AQUA tool. Results: The arcade was reported in 13 studies (510 arms), whereas the ligament in 6 studies (513 arms). The overall pooled prevalence estimate of the ligament was 1.8%, and 52.6% for the arcade. Most frequently, the ulnar nerve was covered by a tendinous arcade (42.2%). In all cases, the ligament inserted into the medial humeral epicondyle, but had various origins. Only 1 study reported compression of the median nerve by the ligament, whilst another contradicted this view. Conclusions: Although the SL is rare, and the SA is a valid anatomical entity (though with a variable presentation), clinically meaningful neurovascular entrapments caused by these structures are infrequent. Nonetheless, a better understanding of each may be beneficial for the best patient outcomes