An exact formula for the measure dimensions associated with a class of piecewise linear maps

An exact formula for the various measure dimensions of attractors associated with contracting similitudes is given. An example is constructed showing that for more general affine maps the various measure dimensions are not always equal.Communicated by Michael F. Barnsley.     

Frequency discrimination near the spectral edge of simultaneous and forward maskers

The effects of the presence of an amplitude discontinuity in the spectrum of a noise masker on frequency discrimination performance were examined. First, detection thresholds as a function of masker level were obtained for pure-tone signals masked by either simultaneous or forward white and low-pass maskers. Then frequency discrimination thresholds were obtained using four masker levels that were chosen to yield predetermined masked thresholds, with signal levels corresponding to each of three sensation levels above these masked thresholds. The principal results indicate that frequency discrimination is poorer in simultaneous low-pass noise than in simultaneous white noise, and that this difference in performance increases with increasing sensation level and with increasing masker level. These results are inconsistent with an explanation based on the pitches generated at spectral edges ("edge pitch"), pitch shifts, or disruption of phase-locking information, but are generally consistent with an explanation based on lateral suppression. It is proposed that a release from suppression may occur in filtered noise backgrounds at high noise levels and at high sensation levels. The reduced suppression may result in poorer frequency discrimination due, in part, to reduced signal detectability.     

Insights into dolphin sonar discrimination capabilities from human listening experiments

A variety of dolphin sonar discrimination experiments have been conducted, yet little is known about the cues utilized by dolphins in making fine target discriminations. In order to gain insights on cues available to echolocating dolphins, sonar discrimination experiments were conducted with human subjects using the same targets employed in dolphin experiments. When digital recordings of echoes from targets ensonified with a dolphinlike signal were played back at a slower rate to human subjects, they could also make fine target discriminations under controlled laboratory conditions about as well as dolphins under less controlled conditions. Subjects reported that time-separation-pitch and duration cues were important. They also reported that low-amplitude echo components 32 dB below the maximum echo component were usable. The signal-to-noise ratio had to be greater than 10 dB above the detection threshold for simple discrimination and 30 dB for difficult discrimination. Except for two cases in which spectral cues in the form of "click pitch" were important, subjects indicated that time-domain rather than frequency-domain processing seemed to be more relevant in analyzing the echoes.     

The evaluation of Cauchy principal value integrals involving unknown poles

A method is described for the evaluation of a Cauchy principal value integral of the formf ₀ ^p f(t)dt, wheref is analytic in the interval [0,p] except at a simple pole at an unknown point in (0,p), with an unknown residue. The method is based on the trapezoidal rule.     

Windmill polynomials over fields of characteristic two

Chambers andSmeets [3] have designed a windmill arrangement of linear feedback shift registers (LFSRs) to generate pn-sequences overGF(2) with high speed. When the windmill hasv vanes, the associated minimal feedback polynomial (having degreen, relatively prime tov) can be taken to have the shapef ₁(x ^v )+x ⁿ f ₂(x ^–v ), where the polynomialsf ₁ andf ₂ have degree [n/v]. Their numerical evidence, whenv is divisible by 4, suggests that, surprisingly, there areno such windmill polynomials which are irreducible ifn±3 (mod 8), while about twice as many irreducible and primitive windmill polynomials as they expected occur ifn±1 (mod 8). A discussion of this behaviour is presented here with proofs. The brief explanation is that the Galois group of the underlying generic windmill polynomial overGF (4) is equal to the alternating groupA _n .     

Anticancer agent development: X-ray crystal structure and keto-enol tautomerism of dimethyl 1-hydroxy-6,7-methylenedioxy-4-(3′,4′,5′-trimethoxyphenyl-trans-3,4-dihydronaphthalene-2,3-dicarboxylate

Structural and conformational information obtained from the crystal structure and solution¹H nmr investigations of the title compound are compared. The 4-aryltetralone, C₂₄H₂₄O₁₀, crystallizes as a chloroform solvate in the monoclinic space group, P2₁/n, witha=12.519(4),b=17.938(6),c=12.534(9)Å,=111.90(5)°, and D_calc=1.51 g cm^–3 forZ=4. The data for this compound were collected at –150°C. Least-squares refinement of 2796 observed [F _o5(F _o)] reflections led to the final agreement index ofR=0.062. A threefold static disorder was observed for one of the carboxyl groups. The second carboxyl group participates in an intramolecular hydrogen bond and is thus ordered. The¹H nmr spectrum revealed the title compound to exist as a keto-enol tautomeric mixture in solution. Vicinal hydrogen coupling constant analysis proved reliable in ascertaining B-ring stereochemistry of 2,3-disubstituted-4-aryltetralones.     

On the Role of Mixed Strategies in Elementary Decision Analysis and Related Decision-Support-System Treatments

We first demonstrate that mixed strategies are relevant in decision analysis for a maximin decision-maker quite apart from any game-theory considerations. This rectifies the apparent misconception that results from MS/OR textbooks which discuss mixed strategies only in the game-theory setting. Next we show an example of an implementable mixed strategy, by which we mean a mixed decision strategy which does not require randomization for its implementation. This application is to portfolio construction.     

Spectral asymptotics for the Schrödinger operator with potential which steadies at infinity

We consider the discrete spectrum of the selfadjoint Schrödinger operatorA _h =–h ² +V defined inL ²(^m) with potentialV which steadies at infinity, i.e.V(x)=g+|x|^– f(1+o(1)) as |x| for>0 and some homogeneous functionsg andf of order zero. Let _h (),0, be the total multiplicity of the eigenvalues ofA _h smaller thanM–, M being the minimum value ofg over the unit sphereS ^m–1 (hence,M coincides with the lower bound of the essential spectrum ofA _h ). We study the asymptotic behaviour of ₁() as0, or of _h () ash0, the number0 being fixed. We find that these asymptotics depend essentially on the structure of the submanifold ofS ^m–1, where the functiong takes the valueM, and generically are nonclassical, i.e. even as a first approximation (2) ^m _h () differs from the volume of the set {(x, )^2m:h ²||²+V(x)<M–}.Partially supported by Contract No. 52 with the Ministry of Culture, Science and Education     

Combined CARS/LDA instrument for simultaneous temperature and velocity measurements

The performance of a combined CARS/LDA instrument capable of measuring temperature and two velocity components with a time coincidence of about 4 s is evaluated in a turbulent premixed propane-air Bunsen-burner flame. Measurements near the base of the flame exhibit negative axial correlations, indicative of normal gradient transport; those near the flame tip show strong positive axial correlations, indicative of transport counter to the temperature gradient. The radial correlations are positive both in the reaction zone and in the plume. An analysis of temperature data from measurements made (1) independent of and (2) coincidental with LDA measurements indicates that the CARS/LDA instrument provides a density-weighted velocity, temperature, and velocity temperature correlation due to the density variations in the flame.