Three-dimensional subspace of l∞(5) with maximal projection constant

AbstractLet V be an n-dimensional real Banach space and let λ(V) denote its absolute projection constant. For any N∈N, N⩾n, defineλnN=sup{λ(V):dim(V)=n,V⊂l∞(N)} andλn=sup{λ(V):dim(V)=n}. A well-known Grünbaum conjecture (p. 465 in [B. Grünbaum, Projection constants, Trans. Amer. Math. Soc. 95 (1960) 451–465]) says thatλ2=4/3. In this paper we show thatλ35=5+427 and we determine a three-dimensional space V⊂l∞(5) satisfying λ35=λ(V). In particular, this shows that Proposition 3.1 from [H. König, N. Tomczak-Jaegermann, Norms of minimal projections, J. Funct. Anal. 119 (1994) 253–280] (see p. 259) is incorrect. Hence the proof of the Grünbaum conjecture given in [H. König, N. Tomczak-Jaegermann, Norms of minimal projections, J. Funct. Anal. 119 (1994) 253–280] which is based on Proposition 3.1 is incomplete

Low-noise, high-strength, spiral-bevel gears for helicopter transmissions

Improvements in spiral-bevel gear design were investigated to support the Army/NASA Advanced Rotorcraft Transmission program. Program objectives were to reduce weight by 25 percent, reduce noise by 10 dB, and increase life to 5000 hr mean-time-between-removal. To help meet these goals, advanced-design spiral-bevel gears were tested in an OH-58D helicopter transmission using the NASA 500-hp Helicopter Transmission Test Stand. Three different gear designs tested included: (1) the current design of the OH-58D transmission except gear material X-53 instead of AISI 9310; (2) a higher-strength design the same as the current but with a full fillet radius to reduce gear tooth bending stress (and thus, weight); and (3) a lower-noise design the same as the high-strength but with modified tooth geometry to reduce transmission error and noise. Noise, vibration, and tooth strain tests were performed and significant gear stress and noise reductions were achieved

Tooth Contact Shift in Loaded Spiral Bevel Gears

An analytical method is presented to predict the shifts of the contact ellipses of spiral bevel gear teeth under load. The contact ellipse shift is the motion of the tooth contact position from the ideal pitch point to its location under load. The shifts are due to the elastic motions of the gear and pinion supporting shafts and bearings. The calculations include the elastic deflections of the gear shafts and the deflections of the four shaft bearings. The method assumes that the surface curvature of each tooth is constant near the unloaded pitch point. Results from these calculations will help designers reduce transmission weight without seriously reducing transmission performance

Modular Acquisition and Stimulation System for Timestamp-Driven Neuroscience Experiments

Dedicated systems are fundamental for neuroscience experimental protocols that require timing determinism and synchronous stimuli generation. We developed a data acquisition and stimuli generator system for neuroscience research, optimized for recording timestamps from up to 6 spiking neurons and entirely specified in a high-level Hardware Description Language (HDL). Despite the logic complexity penalty of synthesizing from such a language, it was possible to implement our design in a low-cost small reconfigurable device. Under a modular framework, we explored two different memory arbitration schemes for our system, evaluating both their logic element usage and resilience to input activity bursts. One of them was designed with a decoupled and latency insensitive approach, allowing for easier code reuse, while the other adopted a centralized scheme, constructed specifically for our application. The usage of a high-level HDL allowed straightforward and stepwise code modifications to transform one architecture into the other. The achieved modularity is very useful for rapidly prototyping novel electronic instrumentation systems tailored to scientific research.Comment: Preprint submitted to ARC 2015. Extended: 16 pages, 10 figures. The final publication is available at link.springer.co

An investigation of the nature and reactivity of the carbonaceous species deposited on mordenite by reaction with methanol

An investigation of the nature of the carbonaceous species deposited upon mordenite by reaction with methanol has been undertaken. The nature of the species has been shown to be a strong function of both temperature and time on stream. Upon reaction at 300 degrees C a range of alkyl and aromatic species, consistent with the development of an active hydrocarbon pool, are evident and time on stream studies have shown that these are developed within 5 min. Upon reaction at 500 degrees C, a narrower range of hydrogen deficient aromatic species is evident. Thermal volatilisation analysis (TVA), not previously applied to the study of coked zeolites, is shown to be complementary to the more commonly applied C analysis, C-13 MAS NMR and TGA techniques

Six-week time series of eddy covariance CO2 flux at Mammoth Mountain, California: performance evaluation and role of meteorological forcing

CO{sub 2} and heat fluxes were measured over a six-week period (09/08/2006 to 10/24/2006) by the eddy covariance (EC) technique at the Horseshoe Lake tree kill (HLTK), Mammoth Mountain, CA, a site with complex terrain and high, spatially heterogeneous CO{sub 2} emission rates. EC CO{sub 2} fluxes ranged from 218 to 3500 g m{sup -2} d{sup -1} (mean = 1346 g m{sup -2} d{sup -1}). Using footprint modeling, EC CO{sub 2} fluxes were compared to CO{sub 2} fluxes measured by the chamber method on a grid repeatedly over a 10-day period. Half-hour EC CO{sub 2} fluxes were moderately correlated (R{sup 2} = 0.42) with chamber fluxes, whereas average-daily EC CO{sub 2} fluxes were well correlated (R{sup 2} = 0.70) with chamber measurements. Average daily EC CO{sub 2} fluxes were correlated with both average daily wind speed and atmospheric pressure; relationships were similar to those observed between chamber CO{sub 2} fluxes and the atmospheric parameters over a comparable time period. Energy balance closure was assessed by statistical regression of EC energy fluxes (sensible and latent heat) against available energy (net radiation, less soil heat flux). While incomplete (R{sup 2} = 0.77 for 1:1 line), the degree of energy balance closure fell within the range observed in many investigations conducted in contrasting ecosystems and climates. Results indicate that despite complexities presented by the HLTK, EC can be reliably used to monitor background variations in volcanic CO{sub 2} fluxes associated with meteorological forcing, and presumably changes related to deeply derived processes such as volcanic activity

Application of Face-Gear Drives in Helicopter Transmissions

The use of face gears in helicopter transmissions was explored. A light-weight, split torque transmission design utilizing face gears was described. Face-gear design and geometry were investigated. Topics included tooth generation, limiting inner and outer radii, tooth contact analysis, contact ratio, gear eccentricity, and structural stiffness. Design charts were developed to determine minimum and maximum face-gear inner and outer radii. Analytical study of transmission error showed face-gear drives were relatively insensitive to gear misalignment, but tooth contact was affected by misalignment. A method of localizing bearing contact to compensate for misalignment was explored. The proper choice of shaft support stiffness enabled good load sharing in the split torque transmission design. Face-gear experimental studies were also included and the feasibility of face gears in high-speed, high-load applications such as helicopter transmissions was demonstrated

Face-gear drives: Design, analysis, and testing for helicopter transmission applications

The use of face-gears in helicopter transmissions was explored. A light-weight, split-torque transmission design utilizing face-gears is described. Face-gear design and geometry were investigated. Topics included tooth generation, limiting inner and outer radii, tooth contact analysis, contact ratio, gear eccentricity, grinding, and structural stiffness. Design charts were developed to determine minimum and maximum face-gear inner and outer radii. An analytical study showed that the face-gear drive is relatively insensitive to gear misalignment with respect to transmission errors, but the tooth contact is affected by misalignment. A method of localizing the bearing contact to permit operation with misalignment was explored. Two new methods for grinding of the face-gear tooth surfaces were also investigated. The proper choice of shaft stiffness enabled good load sharing in the split-torque transmission design. Face-gear experimental studies were also conducted. These tests demonstrated the feasibility of face-gears in high-speed, high-load applications such as helicopter transmissions

Determination of Turboprop Reduction Gearbox System Fatigue Life and Reliability

Two computational models to determine the fatigue life and reliability of a commercial turboprop gearbox are compared with each other and with field data. These models are (1) Monte Carlo simulation of randomly selected lives of individual bearings and gears comprising the system and (2) two-parameter Weibull distribution function for bearings and gears comprising the system using strict-series system reliability to combine the calculated individual component lives in the gearbox. The Monte Carlo simulation included the virtual testing of 744,450 gearboxes. Two sets of field data were obtained from 64 gearboxes that were first-run to removal for cause, were refurbished and placed back in service, and then were second-run until removal for cause. A series of equations were empirically developed from the Monte Carlo simulation to determine the statistical variation in predicted life and Weibull slope as a function of the number of gearboxes failed. The resultant L(sub 10) life from the field data was 5,627 hr. From strict-series system reliability, the predicted L(sub 10) life was 774 hr. From the Monte Carlo simulation, the median value for the L(sub 10) gearbox lives equaled 757 hr. Half of the gearbox L(sub 10) lives will be less than this value and the other half more. The resultant L(sub 10) life of the second-run (refurbished) gearboxes was 1,334 hr. The apparent load-life exponent p for the roller bearings is 5.2. Were the bearing lives to be recalculated with a load-life exponent p equal to 5.2, the predicted L(sub 10) life of the gearbox would be equal to the actual life obtained in the field. The component failure distribution of the gearbox from the Monte Carlo simulation was nearly identical to that using the strict-series system reliability analysis, proving the compatibility of these methods