19,803 research outputs found
Jig protects transistors from heat while tinning leads
In tinning transistor leads, an aluminum jig is used to dip the leads into the molten tin. The jigs mass shunts excess heat given off by the molten tin before it reaches and damages the transistor body
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
Dynamic Aspects of Earnings Mobility
This paper proposes an econometric methodology to deal with life cycle earnings and mobility among discrete earnings classes. First, we use panel data on male log earnings to estimate an earnings function with permanent and serially correlated transitory components due to both measured and unmeasured variables. Assuming that the error components are normally distributed, we develop statements for the probability that an individual's earnings will fall into a particular but arbitrary time sequence of poverty states. Using these statements, we illustrate the implications of our earnings model for poverty dynamics and compare our approach to Markov chain models of income mobility.
Experimental study of acoustic loads on an upper-surface-blown STOL airplane configuration
Fluctuating pressure levels were measured on the flap and fuselage of an upper-surface-blown jet-flap airplane configuration in a wind tunnel. The model tested had turbofan engines with a bypass ratio of 3 and a thrust rating of 10 kN. Rectangular nozzles were mounted flush with the upper surface at 35 percent of the wing chord. Test parameters were flap deflection angle, jet impingement angle, angle of attack, free-stream velocity, spanwise location of the engine, and jet dynamic pressure. Load levels were high throughout the jet impingement region, with the highest levels (about 159 dB) occurring on the fuselage and near the knee of the flap. The magnitude of the forward-velocity effect appeared to depend upon the ratio of free-stream and jet velocities. Good agreement was obtained between fluctuating pressure spectra measured at jet dynamic pressures of 7 and 22 kPa when the spectra were scaled by nondimensional functions of dynamic pressure, velocity, and the empirical relationship between dynamic pressure and overall fluctuating pressure level
A dc to dc converter
The object of the invention is to provide an improved converter for converting one direct current voltage to another. A plurality of phased square wave voltages are provided from a ring counter through amplifiers to a like plurality of output transformers. Each of these transformers has two windings, and S(1) winding and an S(2) winding. The S(1) windings are connected in series, then the S(2) windings are connected in series, and finally, the two sets of windings are connected in series. One of six SCRs is connected between each two series connected windings to a positive output terminal and one of diodes is connected between each set of two windings of a zero output terminal. By virtue of this configuration, a quite high average direct current voltage is obtained, which varies between full voltage and two-thirds full voltage rather than from full voltage to zero. Further, its variation, ripple frequency, is reduced to one-sixth of that present in a single phase system. Application to raising battery voltage for an ion propulsion system is mentioned
On obtaining classical mechanics from quantum mechanics
Constructing a classical mechanical system associated with a given quantum
mechanical one, entails construction of a classical phase space and a
corresponding Hamiltonian function from the available quantum structures and a
notion of coarser observations. The Hilbert space of any quantum mechanical
system naturally has the structure of an infinite dimensional symplectic
manifold (`quantum phase space'). There is also a systematic, quotienting
procedure which imparts a bundle structure to the quantum phase space and
extracts a classical phase space as the base space. This works straight
forwardly when the Hilbert space carries weakly continuous representation of
the Heisenberg group and recovers the linear classical phase space
. We report on how the procedure also allows
extraction of non-linear classical phase spaces and illustrate it for Hilbert
spaces being finite dimensional (spin-j systems), infinite dimensional but
separable (particle on a circle) and infinite dimensional but non-separable
(Polymer quantization). To construct a corresponding classical dynamics, one
needs to choose a suitable section and identify an effective Hamiltonian. The
effective dynamics mirrors the quantum dynamics provided the section satisfies
conditions of semiclassicality and tangentiality.Comment: revtex4, 24 pages, no figures. In the version 2 certain technical
errors in section I-B are corrected, the part on WKB (and section II-B) is
removed, discussion of dynamics and semiclassicality is extended and
references are added. Accepted for publication on Classical and Quantum
Gravit
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