The A-like matrices for a hypercube

Let $D$ denote a positive integer and let $Q_D$ denote the graph of the $D$-dimensional hypercube. Let $X$ denote the vertex set of $Q_D$ and let A \in \MX denote the adjacency matrix of $Q_D$. A matrix B \in \MX is called $A$-{\em like} whenever both (i) $BA = AB$; (ii) for all $x,y \in X$ that are not equal or adjacent, the $(x,y)$-entry of $B$ is zero. Let \Al denote the subspace of \MX consisting of the $A$-like elements. We decompose \Al into the direct sum of its symmetric part and antisymmetric part. We give a basis for each part. The dimensions of the symmetric part and antisymmetric part are $D+1$ and ${D \choose 2}$, respectively

Wind tunnel results of advanced high speed propellers in the takeoff, climb and landing operating regimes

Low speed wind tunnel performance tests of two advanced propellers were completed. The 62.2 cm diameter adjustable pitch models were tested at Mach numbers typical of takeoff, initial climbout, and landing speeds in the 10 by 10 ft Supersonic Wind Tunnel. Both models had eight blades and a cruise design point operating condition of 0.80 Mach number, 10.668 km S.A. altitude, 243.8 m/s tip speed and a high power loading of 301 kW sq m. No adverse or unusual low speed operating conditions were found during the test with either the straight blade SR-2 or the 45 deg swept SR-3 propellers. The 45 deg swept propeller efficiency exceeded the straight blade efficiency by 4 to 5%. Typical net efficiencies of the straight and 45 deg swept propeller at a Mach 0.20 takeoff condition were 50.2 and 54.9% respectively. At a Mach 0.34 climb condition, the efficiencies were 53.7 and 59.1%. Reverse thrust data indicates that these propellers are capable of producing more reverse thrust at Mach 0.20 than a high bypass turbofan engine at Mach 0.20

Noise of the SR-6 propeller model at 2 deg and 4 deg angles of attack

The noise generated by supersonic-tip-speed propellers creates a cabin noise problem for future airplanes powered by these propellers. Noise of a number of propeller models were measured in the NASA Lewis 8- by 6-Foot Wind Tunnel with flow parallel to the propeller axis. In flight, as a result of the induced upwash from the airplane wing, the propeller is at an angle of attack with respect to the incoming flow. Therefore, the 10-blade SR-6 propeller was operated at angle of attack to determine its noise behavior. Higher blade passage tones were observed for the propeller operating at angle of attack in a 0.6 axial Mach number flow. The noise increase was not symmetrical, with one wall of the wind tunnel showing a larger noise increase than the other wall. No noise increase was observed at angle of attack in a 0.8 axial Mach number flow. For this propeller the dominance of thickness noise, which does not increase with angle of attack, explains the lack of noise increase at the higher 0.8 Mach number

Neurotrophic keratitis in a patient with disseminated lymphangiomatosis.

INTRODUCTION: Neurotrophic keratitis, a degenerative corneal disease caused by trigeminal nerve impairment, has many etiologies and remains very difficult to treat. METHODS: Case report of a 23-year-old male with a right corneal ulcer that failed to improve despite broad-spectrum antimicrobials. RESULTS: Prior diagnosis of disseminated lymphangiomatosis with a lesion in the right petrous apex effacing Meckel's (trigeminal) cave in conjunction with a history of nonhealing corneal abrasions suggested a neurotrophic etiology. Drawstring temporary tarsorrhaphy, in addition to antibiotics and autologous serum, lead to successful clearing of the infection and resolution of the corneal ulcer. Visual acuity improved from light perception (LP) at the peak of infection to 20/40 six weeks after treatment. CONCLUSIONS: To our knowledge, we report the first case of neurotrophic keratitis in a patient with disseminated lymphangiomatosis that caused a mass effect in Meckel's (trigeminal) cave leading to compression of the trigeminal nerve. The antibiotic-resistant corneal ulcer was successfully treated with drawstring tarsorrhaphy, confirming the utility of this therapeutic measure in treating neurotrophic keratitis