Temporal Aperture Modulation

The two types of modulation techniques useful to X-ray imaging are reviewed. The use of optimum coded temporal aperature modulation is shown, in certain cases, to offer an advantage over a spatial aperture modulator. Example applications of a diffuse anisotropic X-ray background experiment and a wide field of view hard X-ray imager are discussed

A teaching experiment to foster the conceptual understanding of multiplication based on children's literature to facilitate dialogic learning

The importance of conceptual understanding as opposed to low-level procedural knowledge in mathematics has been well documented (Hiebert & Carpenter, 1992). Development of conceptual understanding of multiplication is fostered when students recognise the equal group structure that is common in all multiplicative problems (Mulligan & Mitchelmore, 1996). This paper reports on the theoretical development of a transformative teaching experiment based on conjecture-driven research design (Confrey & Lachance, 1999) that aims to enhance Year 3 students’ conceptual understanding of multiplication. The teaching experiment employs children’s literature as a motivational catalyst and mediational tool for students to explore and engage in multiplication activities and dialogue. The SOLO taxonomy (Biggs & Collis, 1989) is used to both frame the novel teaching and learning activities, as well as assess the level of students’ conceptual understanding of multiplication as displayed in the products derived from the experiment. Further, student’s group interactions will be analysed in order to investigate the social processes that may contribute positively to learning

Convexity of tableau sets for type A Demazure characters (key polynomials), parabolic Catalan numbers

This is the first of three papers that develop structures which are counted by a "parabolic" generalization of Catalan numbers. Fix a subset R of {1,..,n-1}. Consider the ordered partitions of {1,..,n} whose block sizes are determined by R. These are the "inverses" of (parabolic) multipermutations whose multiplicities are determined by R. The standard forms of the ordered partitions are refered to as "R-permutations". The notion of 312-avoidance is extended from permutations to R-permutations. Let lambda be a partition of N such that the set of column lengths in its shape is R or R union {n}. Fix an R-permutation pi. The type A Demazure character (key polynomial) in x_1, .., x_n that is indexed by lambda and pi can be described as the sum of the weight monomials for some of the semistandard Young tableau of shape lambda that are used to describe the Schur function indexed by lambda. Descriptions of these "Demazure" tableaux developed by the authors in earlier papers are used to prove that the set of these tableaux is convex in Z^N if and only if pi is R-312-avoiding if and only if the tableau set is the entire principal ideal generated by the key of pi. These papers were inspired by results of Reiner and Shimozono and by Postnikov and Stanley concerning coincidences between Demazure characters and flagged Schur functions. This convexity result is used in the next paper to deepen those results from the level of polynomials to the level of tableau sets. The R-parabolic Catalan number is defined to be the number of R-312-avoiding permutations. These special R-permutations are reformulated as "R-rightmost clump deleting" chains of subsets of {1,..,n} and as "gapless R-tuples"; the latter n-tuples arise in multiple contexts in these papers.Comment: 20 pp with 2 figs. Identical to v.3, except for the insertion of the publication data for the DMTCS journal (dates and volume/issue/number). This is one third of our "Parabolic Catalan numbers ..", arXiv:1612.06323v

Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials)

Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain semistandard tableaux of shape lambda. Let pi be an n-permutation. The type A Demazure character (key polynomial, Demazure polynomial) indexed by lambda and pi is another such polynomial generating function. Reiner and Shimozono and then Postnikov and Stanley studied coincidences between these two families of polynomials. Here their results are sharpened by the specification of unique representatives for the equivalence classes of indexes for both families of polynomials, extended by the consideration of more general beta, and deepened by proving that the polynomial coincidences also hold at the level of the underlying tableau sets. Let R be the set of lengths of columns in the shape of lambda that are less than n. Ordered set partitions of {1,..,n} with block sizes determined by R, called R-permutations, are used to describe the minimal length representatives for the parabolic quotient of the nth symmetric group specified by the set {1,..,n-1}\R. The notion of 312-avoidance is generalized from n-permutations to these set partitions. The R-parabolic Catalan number is defined to be the number of these. Every flagged Schur function arises as a Demazure polynomial. Those Demazure polynomials are precisely indexed by the R-312-avoiding R-permutations. Hence the number of flagged Schur functions that are distinct as polynomials is shown to be the R-parabolic Catalan number. The projecting and lifting processes that relate the notions of 312-avoidance and of R-312-avoidance are described with maps developed for other purposes.Comment: 27 pages, 2 figures. Identical to v.2, except for the insertion of the publication data for the DMTCS journal (dates and volume/issue/number). This is two-thirds of our preprint "Parabolic Catalan numbers count flagged Schur functions; Convexity of tableau sets for Demazure characters", arXiv:1612.06323v

Viewpoint : graphene is thin, but not infinitely so

Atomically thin graphene is considered a prototypical 2D material, but high-pressure experiments now reveal the 3D nature of its mechanical properties

Study of outgassing and decomposition of space shuttle heat protection tiles, fillers and adhesive

The purpose of this project was to determine the chemicals desorbing from the space shuttle heat protection tiles. The original protocol for this project involved direct insertion probe mass spectrometry (DIPMS) analysis of the outgassing products from the tiles. However, this method proved unsatisfactory due to the large number of compounds desorbing from the tiles. A purge and trap technique was then employed to collect and separate the chemicals desorbing from the tiles. The maximum temperature in this analysis was 180 C which is the gas chromatograph fused silica capillary column's temperature limit. The desorption was also carried out at atmospheric pressure with helium as the purge gas. A description of the modified protocol is given. All compounds are tentatively identified

Transient technique for measuring heat transfer coefficients on stator airfoils in a jet engine environment

A transient technique was used to measure heat transfer coefficients on stator airfoils in a high-temperature annular cascade at real engine conditions. The transient response of thin film thermocouples on the airfoil surface to step changes in the gas stream temperature was used to determine these coefficients. In addition, gardon gages and paired thermocouples were also utilized to measure heat flux on the airfoil pressure surface at steady state conditions. The tests were conducted at exit gas stream Reynolds numbers of one-half to 1.9 million based on true chord. The results from the transient technique show good comparison with the steady-state results in both trend and magnitude. In addition, comparison is made with the STAN5 boundary layer code and shows good comparison with the trends. However, the magnitude of the experimental data is consistently higher than the analysis

Combustor flame flashback

A stainless steel, two-dimensional (rectangular), center-dump, premixed-prevaporized combustor with quartz window sidewalls for visual access was designed, built, and used to study flashback. A parametric study revealed that the flashback equivalence ratio decreased slightly as the inlet air temperature increased. It also indicated that the average premixer velocity and premixer wall temperature were not governing parameters of flashback. The steady-state velocity balance concept as the flashback mechanism was not supported. From visual observation several stages of burning were identified. High speed photography verified upstream flame propagation with the leading edge of the flame front near the premixer wall. Combustion instabilities (spontaneous pressure oscillations) were discovered during combustion at the dump plane and during flashback. The pressure oscillation frequency ranged from 40 to 80 Hz. The peak-to-peak amplitude (up to 1.4 psi) increased as the fuel/air equivalence ratio was increased attaining a maximum value just before flashback. The amplitude suddenly decreased when the flame stabilized in the premixer. The pressure oscillations were large enough to cause a local flow reversal. A simple test using ceramic fiber tufts indicated flow reversals existed at the premixer exit during flickering. It is suspected that flashback occurs through the premixer wall boundary layer flow reversal caused by combustion instability. A theoretical analysis of periodic flow in the premixing channel has been made. The theory supports the flow reversal mechanism