On the relation between hyperrings and fuzzy rings

We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings and explicitly characterize the essential image --- it fails to be essentially surjective in a very minor way. This embedding provides an identification of Baker's theory of matroids over hyperfields with Dress's theory of matroids over fuzzy rings (provided one restricts to those fuzzy rings in the essential image). The embedding functor extends from hyperfields to hyperrings, and we study this extension in detail. We also analyze the relation between hyperfields and Baker's partial demifields

Characterizing Block Graphs in Terms of their Vertex-Induced Partitions

Given a finite connected simple graph $G=(V,E)$ with vertex set $V$ and edge set $E\subseteq \binom{V}{2}$, we will show that $1.$ the (necessarily unique) smallest block graph with vertex set $V$ whose edge set contains $E$ is uniquely determined by the $V$-indexed family ${\bf P}_G:=\big(\pi_0(G^{(v)})\big)_{v \in V}$ of the various partitions $\pi_0(G^{(v)})$ of the set $V$ into the set of connected components of the graph $G^{(v)}:=(V,\{e\in E: v\notin e\})$, $2.$ the edge set of this block graph coincides with set of all $2$-subsets $\{u,v\}$ of $V$ for which $u$ and $v$ are, for all $w\in V-\{u,v\}$, contained in the same connected component of $G^{(w)}$, $3.$ and an arbitrary $V$-indexed family ${\bf P}p=({\bf p}_v)_{v \in V}$ of partitions $\pi_v$ of the set $V$ is of the form ${\bf P}p={\bf P}p_G$ for some connected simple graph $G=(V,E)$ with vertex set $V$ as above if and only if, for any two distinct elements $u,v\in V$, the union of the set in ${\bf p}_v$ that contains $u$ and the set in ${\bf p}_u$ that contains $v$ coincides with the set $V$, and $\{v\}\in {\bf p}_v$ holds for all $v \in V$. As well as being of inherent interest to the theory of block graphs, these facts are also useful in the analysis of compatible decompositions and block realizations of finite metric spaces

Operating envelope charts for the Langley 0.3-meter transonic cryogenic wind tunnel

To take full advantage of the unique Reynolds number capabilities of the 0.3-meter Transonic Cryogenic Tunnel (0.3-m TCT) at the NASA Langley Research Center, it was designed to accommodate test sections other than the original, octagonal, three-dimensional test section. A 20- by 60-cm two-dimensional test section was installed in 1976 and was extensively used, primarily for airfoil testing, through the fall of 1984. The tunnel was inactive during 1985 so that a new test section and improved high speed diffuser could be installed in the tunnel circuit. The new test section has solid adaptive top and bottom walls to reduce or eliminate wall interference for two-dimensional testing. The test section is 33- by 33-cm in cross section at the entrance and is 142 cm long. In the planning and running of past airfoil tests in the 0.3-m TCT, the use of operating envelope charts have proven very useful. These charts give the variation of total temperature and pressure with Mach number and Reynolds number. The operating total temperature range of the 0.3-m TCT is from about 78 K to 327 K with total pressures ranging from about 17.5 psia to 88 psia. This report presents the operating envelope charts for the 0.3-m TCT with the adaptive wall tes t section installed. They were all generated based on a 1-foot chord model. The Mach numbers vary from 0.1 to 0.95

Characterizing block graphs in terms of their vertex-induced partitions

Block graphs are a generalization of trees that arise in areas such as metric graph theory, molecular graphs, and phylogenetics. Given a finite connected simple graph $G=(V,E)$ with vertex set $V$ and edge set $E\subseteq \binom{V}{2}$, we will show that the (necessarily unique) smallest block graph with vertex set $V$ whose edge set contains $E$ is uniquely determined by the $V$-indexed family \Pp_G =\big(\pi_v)_{v \in V} of the partitions $\pi_v$ of the set $V$ into the set of connected components of the graph $(V,\{e\in E: v\notin e\})$. Moreover, we show that an arbitrary $V$-indexed family \Pp=(\p_v)_{v \in V} of partitions \p_v of the set $V$ is of the form \Pp=\Pp_G for some connected simple graph $G=(V,E)$ with vertex set $V$ as above if and only if, for any two distinct elements $u,v\in V$, the union of the set in \p_v that contains $u$ and the set in \p_u that contains $v$ coincides with the set $V$, and \{v\}\in \p_v holds for all $v \in V$. As well as being of inherent interest to the theory of block graphs,these facts are also useful in the analysis of compatible decompositions of finite metric spaces

Computer program for calculating flow parameters and power requirements for cryogenic wind tunnels

A computer program has been written that performs the flow parameter calculations for cryogenic wind tunnels which use nitrogen as a test gas. The flow parameters calculated include static pressure, static temperature, compressibility factor, ratio of specific heats, dynamic viscosity, total and static density, velocity, dynamic pressure, mass-flow rate, and Reynolds number. Simplifying assumptions have been made so that the calculations of Reynolds number, as well as the other flow parameters can be made on relatively small desktop digital computers. The program, which also includes various power calculations, has been developed to the point where it has become a very useful tool for the users and possible future designers of fan-driven continuous-flow cryogenic wind tunnels

Drag measurements on a laminar flow body of revolution in Langley's 13 inch magnetic suspension and balance system

Low-speed wind tunnel drag force measurements were taken on a laminar flow body of revolution free of support interference. This body was tested at zero incidence in the NASA Langley 13 inch Magnetic Suspension and Balance System (MSBS). The primary objective of these tests was to substantiate the drag force measuring capabilities of the 13 inch MSBS. A secondary objective was to obtain support interference free drag measurements on an axisymmetric body of interest. Both objectives were met. The drag force calibrations and wind-on repeatability data provide a means of assessing the drag force measuring capabilities of the 13 inch MSBS. The measured drag coefficients for this body are of interest to researchers actively involved in designing minimum drag fuselage shapes. Additional investigations included: the effects of fixing transition; the effects of fins installed in the tail; surface flow visualizations using both liquid crystals and oil flow; and base pressure measurements using a one-channel telemetry system. Two drag prediction codes were used to assess their usefulness in estimating overall body drag. These theoretical results did not compare well with the measured values because of the following: incorrect or non-existent modeling of a laminar separation bubble on the body and incorrect of non-existent estimates of base pressure drag

High Reynolds number tests of the CAST 10-2/DOA 2 airfoil in the Langley 0.3-meter transonic cryogenic tunnel, phase 1

A wind tunnel investigation of an advanced technology airfoil, the CAST 10-2/DOA 2, was conducted in the Langley 0.3 meter Transonic Cryogenic Tunnel (0.3 m TCT). This was the first of a series of tests conducted in a cooperative National Aeronautics and Space Administration (NASA) and the Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt e. V. (DFVLR) airfoil research program. Test temperature was varied from 280 K to 100 K to pressures from slightly above 1 to 5.8 atmospheres. Mach number was varied from 0.60 to 0.80, and the Reynolds number (based on airfoil chord) was varied from 4 x 10 to the 8th power to 45 x 10 to the 6th power. This report presents the experimental aerodynamic data obtained for the airfoil and includes descriptions of the airfoil model, the 0.3 m TCT, the test instrumentation, and the testing procedures

Экранное трубчатое многопараметровое вихретоковое устройство

Рассмотрено экранное трубчатое многопараметровое устройство, с помощью которого определяются четыре параметра ферромагнитной трубы: относительная магнитная проницаемость µrt, удельное электрическое сопротивление Pt, температура трубы t и коэффициент затухания магнитного поля в трубчатом изделии ht.The screen tubular mnogoparametrovoe device is considered, which four parameters of ferromagnetic pipe are determined by: relative permeance µrt, specific electric resistance Pt, temperature of pipe of t and coefficient of fading of the magnetic field in tubular good of ht

k-Spectra of weakly-c-Balanced Words

A word $u$ is a scattered factor of $w$ if $u$ can be obtained from $w$ by deleting some of its letters. That is, there exist the (potentially empty) words $u_1,u_2,..., u_n$, and $v_0,v_1,..,v_n$ such that $u = u_1u_2...u_n$ and $w = v_0u_1v_1u_2v_2...u_nv_n$. We consider the set of length-$k$ scattered factors of a given word w, called here $k$-spectrum and denoted \ScatFact_k(w). We prove a series of properties of the sets \ScatFact_k(w) for binary strictly balanced and, respectively, $c$-balanced words $w$, i.e., words over a two-letter alphabet where the number of occurrences of each letter is the same, or, respectively, one letter has $c$-more occurrences than the other. In particular, we consider the question which cardinalities n= |\ScatFact_k(w)| are obtainable, for a positive integer $k$, when $w$ is either a strictly balanced binary word of length $2k$, or a $c$-balanced binary word of length $2k-c$. We also consider the problem of reconstructing words from their $k$-spectra