28,634 research outputs found

    Orbit decomposition of Jordan matrix algebras of order three under the automorphism groups

    Get PDF
    The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification, explicitly, in terms of the cross product of H. Freudenthal and the characteristic polynomial.Comment: v2, 32 pages, presentation improved, minor errors corrected, and the title changed as appeared in J. Math. Sci. Univ. Toky

    Quantitative and qualitative characteristics of greenery in suburban residential districts of Metro Manila

    Get PDF
    This case study was conducted to better understand the present situation of urban greenery in Marikina City, in the suburbs of metropolitan Manila, a typical large Asian city. A vegetation survey was conducted in residential districts of Marikina City, and the quantitative and qualitative characteristics of trees were analyzed. Lot size had some influence on the quantity of greenery in residential lots. In smaller lots, however, quantity did not increase in proportion to lot size. It appears, then, that the land-use controls for individual lots did not function effectively. Quantitative differences of greenery were related to qualitative differences, depending on the year or period of development of the residential area. In the newly developed residential lots, the greenery is comprised mostly of ornamental trees. Under the present circumstances, there is no assurance of sustaining the desired quantity of greenery in smaller residential lots. From these results, we proposed that regulations on lot size/coverage and promotion of tree planting involving local residents are needed to sustain urban greenery in residential districts

    Polynomial Relations for q-Characters via the ODE/IM Correspondence

    Full text link
    Let Uq(b)U_q(\mathfrak{b}) be the Borel subalgebra of a quantum affine algebra of type Xn(1)X^{(1)}_n (X=A,B,C,DX=A,B,C,D). Guided by the ODE/IM correspondence in quantum integrable models, we propose conjectural polynomial relations among the qq-characters of certain representations of Uq(b)U_q(\mathfrak{b})

    Freeness of adjoint linear systems on threefolds with terminal Gorenstein singularities or some quotient singularities

    Get PDF
    We generalize the result of Kawamata concerning the strong version of Fujita's freeness conjecture for smooth 3-folds to some singular cases, namely, Gorenstein terminal singularities and quotient singularities of type 1/r(1,1,1) and of type 1/r(1,1,-1). We generalize furthermore the result of that to projective threefolds with only canonical singularities for canonical and not terminal singularities. It turns out that the estimates in the first three cases are better than the one for the smooth case, which it is not in the fourth case. We also give explicit examples which show the estimate in the fourth case is necessarily worse than the one for the smooth case.Comment: 21 pages, Late

    Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach

    Full text link
    We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard symmetric stable distribution with the characteristic exponent α\alpha estimated from the data. We treat α\alpha as an unknown parameter, but for theoretical simplicity we also consider the case that α\alpha is fixed. For estimation of parameters and the standardization of data we use maximum likelihood estimator (MLE) and an equivariant integrated squared error estimator (EISE) which minimizes the weighted integral. We derive the asymptotic covariance function of the characteristic function process with parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of the covariance function are numerically evaluated and asymptotic distribution of the test statistic is obtained using complex integration. Simulation studies show that the asymptotic distribution of the test statistics is very accurate. We also present a formula of the asymptotic covariance function of the characteristic function process with parameters estimated by an efficient estimator for general distributions

    Some remarks on A_1^{(1)} soliton cellular automata

    Full text link
    In this short note, we describe the A_1^{(1)} soliton cellular automata as an evolution of a poset. This allows us to explain the conservation laws for the A_1^{(1)} soliton cellular automata, one given by Torii, Takahashi and Satsuma, and the other given by Fukuda, Okado and Yamada, in terms of the stack permutations of states in a very natural manner. As a biproduct, we can prove a conjectured formula relating these laws.Comment: 10 pages, LaTeX2

    Connections and the Second Main Theorem for Holomorphic Curves

    Full text link
    By means of CC^\infty-connections we will prove a general second main theorem and some special ones for holomorphic curves. The method gives a geometric proof of H. Cartan's second main theorem in 1933. By applying the same method, we will prove some second main theorems in the case of the product space (\pone)^2 of the Riemann sphere.Comment: 21 page

    Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions

    Full text link
    We present a theoretical foundation for the Index theorem in naive and minimally doubled lattice fermions by studying the spectral flow of a Hermitean version of Dirac operators. We utilize the point splitting method to implement flavored mass terms, which play an important role in constructing proper Hermitean operators. We show the spectral flow correctly detects the index of the would-be zero modes which is determined by gauge field topology. Using the flavored mass terms, we present new types of overlap fermions from the naive fermion kernels, with a number of flavors that depends on the choice of the mass terms. We succeed to obtain a single-flavor naive overlap fermion which maintains hypercubic symmetry.Comment: 27 pages, 17 figures; references added, version accepted in JHE

    Local Manipulation of Nuclear Spin in a Semiconductor Quantum Well

    Get PDF
    The shaping of nuclear spin polarization profiles and the induction of nuclear resonances are demonstrated within a parabolic quantum well using an externally applied gate voltage. Voltage control of the electron and hole wave functions results in nanometer-scale sheets of polarized nuclei positioned along the growth direction of the well. RF voltages across the gates induce resonant spin transitions of selected isotopes. This depolarizing effect depends strongly on the separation of electrons and holes, suggesting that a highly localized mechanism accounts for the observed behavior.Comment: 18 pages, 4 figure

    Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk via braid groups

    Full text link
    Recently Gambaudo and Ghys proved that there exist infinitely many quasi-morphisms on the group DiffΩ(D2,D2){\rm Diff}_\Omega^\infty (D^2, \partial D^2) of area-preserving diffeomorphisms of the 2-disk D2D^2. For the proof, they constructed a homomorphism from the space of quasi-morphisms on the braid group to the space of quasi-morphisms on DiffΩ(D2,D2){\rm Diff}_\Omega^\infty (D^2, \partial D^2). In this paper, we study the homomorphism and prove its injectivity.Comment: 8pages. The title of the paper has been changed, to appear in Proc. Amer. Math. So
    corecore