Singular values of the Rogers-Ramanujan continued fraction

Let z∊ C be imaginary quadratic in the upper half plane. Then the Rogers-Ramanujan continued fraction evaluated at q = e ^{2π iz} is contained in a class field of Q(z). Ramanujan showed that for certain values of z, one can write these continued fractions as nested radicals. We use the Shimura reciprocity law to obtain such nested radicals whenever z is imaginary quadratic. 2000 Mathematics Subject Classification Primary—11Y65; Secondary—11Y40     

Quotients of incidence geometries

We develop a theory for quotients of geometries and obtain sufficient conditions for the quotient of a geometry to be a geometry. These conditions are compared with earlier work on quotients, in particular by Pasini and Tits. We also explore geometric properties such as connectivity, firmness and transitivity conditions to determine when they are preserved under the quotienting operation. We show that the class of coset pregeometries, which contains all flag-transitive geometries, is closed under an appropriate quotienting operation.     

Electrical neuroimaging evidence that spatial frequency-based selective attention affects V1 activity as early as 40-60 ms in humans

Background  

Karns and Knight (2009) [1] demonstrated by using ERP and gamma band oscillatory responses that intermodal attention modulates visual processing at the latency of the early phase of the C1 response (62-72 ms) thought to be generated in the primary visual cortex. However, the timing of attentional modulation of visual cortex during object-based attention remains a controversial issue.     

Investigation of the conjectured nucleon deformation at low momentum transfer

We report new precise H(e,e(')p)pi(0) measurements at the Delta(1232) resonance at Q(2)=0.127 (GeV/c)(2) obtained at the MIT-Bates out-of-plane scattering facility which are particularly sensitive to the transverse electric amplitude (E2) of the gamma(*)N-->Delta transition. The new data have been analyzed together with those of earlier measurements to yield precise quadrupole to dipole amplitude ratios: Re(E(3/2)(1+)/M(3/2)(1+))=(-2.3+/-0.3(stat+syst)+/-0.6(model))% and Re(S(3/2)(1+)/M(3/2)(1+))=(-6.1+/-0.2(stat+syst)+/-0.5(model))% for M(3/2)(1+)=(41.4+/-0.3(stat+syst)+/-0.4(model))(10(-3)/m(pi(+))). The derived amplitudes give credence to the conjecture of deformation in hadrons favoring, at low Q2, the dominance of mesonic effects.     

Physics perspectives of the ALICE experiment at the large hadron collider

The large hadron collider (LHC) under construction at CERN will deliver ion beams up to centre of mass energies of the order of 5.5 TeV per nucleon, in case of lead. If compared to the available facilities for the study of nucleus-nucleus collisions (SpS and RHIC), this represents a huge step forward in terms of both volume and energy density that can be attained in nuclear interactions. ALICE (a large ion collider experiment) is the only detector specifically designed for the physics of nuclear collisions at LHC, even though it can also study high cross-section processes occurring in proton-proton collisions. The main goal of the experiment is to observe and study the phase transition from hadronic matter to deconfined partonic matter (quark gluon plasma —QGP). ALICE is conceived as a general-purpose detector and will address most of the phenomena related to the QGP formation at LHC energies: for this purpose, a large fraction of the hadrons, leptons and photons produced in each interaction will be measured and identified.     

Cyclobutane ring opening of allene-enone photoadducts by mercury (II) perchlorate

Cyclobutane ring opening of some allene-enone photoadducts by Hg(ClO₄)₂ in acetone gave diketones which led, in some cases, to bicyclic ketols through intramolecular aldol condensation.     

13C magnetic resonance studies of reduced proaporphine alkaloids

The natural abundance ¹³C magnetic resonance spectra of reduced proaporphines are reported, with complete assignments based on peak multiplicity and empirical calculations of chemical shifts. The chemical shift values of C-8, C-12 and C-7 are found to be strongly diagnostic of the spiro carbon configuration.     

Methods for the Fourier-series expansion of torsional energies

Several general procedures for the derivation and analysis of a Fourier-series expansion V(?) over computed torsional energies E(?_i) are formulated. STO-3G energy values in n-butane, 1-chloropropane, and 1,2-dichloroethane are used as test data for deriving V(?) with the numerical methods of interpolation and least squares. The accuracy of each derived V(?) is assessed on the basis of calculated conformational properties, mean and rms deviations, and an error curve, V(?)–V(?)_ref, where V(?)_ref represents a reference set of E(?_i). Results indicate that given the same number of expansion terms, interpolation and least squares yield functions of comparable accuracy; however, interpolation is a more efficient procedure for monitoring the accuracy of a function in regions of interest. In cases where there are too few input energies to achieve the desired accuracy, energy derivatives can be employed effectively for expanding the input set. In designing special-purpose functions, the error curve can be used meaningfully as a guide; an example for producing functions that are especially well behaved in regions for gauche conformations is provided. The present study continues to add systematics and rigor to the fitting of an internal rotation potential function from energy data.