Local duality for 2-dimensional local ring

We prove a local duality for some schemes associated to a 2-dimensional complete local ring whose residue field is an n-dimensional local field in the sense of Kato-Parshin. Our results generalize the Saito works in the case n = 0 and are applied to study the Bloch-Ogus complex for such rings in various cases.     

Polynomial approximation of bilinear Diffie–Hellman maps

The problem of computing bilinear Diffie–Hellman maps is considered. It is shown that the problem of computing the map is equivalent to computing a diagonal version of it. Various lower bounds on the degree of any polynomial that interpolates this diagonal version of the map are found that shows that such an interpolation will involve a polynomial of large degree, relative to the size of the set on which it interpolates.     

On the characterization of spherical curves in 3-dimensional Sasakian spaces

In this paper, we give the spherical characterization of a regular curve in 3-dimensional Sasakian space. Furthermore the differential equation which expresses the mentioned characterization is solved.     

A characterization of helical polynomial curves of any degree

We give a full characterization of helical polynomial curves of any degree and a simple way to construct them. Existing results about Hermite interpolation are revisited. A simple method to select the best quintic interpolant among all possible solutions is suggested.      

Global Geometry of 3-Body Motions with Vanishing Angular Momentum Ⅰ

Following Jacobi's geometrization of Lagrange's least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor (U h), where U and h are the potential function and the total energy, respectively.In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M* ～- S2 (1/2).In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve (which only records the change of shape) in the case of h ≠ 0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover,these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonicity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.     

Analytic invariant curves for a planar mapping

This paper is concerned with the existence of analytic invariant curves for a planar mapping. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained. In this paper, we discuss not only the general case, but also the critical cases as well, in particular, the case where β is a unit root is discussed.     

Limit cycles and invariant parabola in a kukles system of degree three

In this article,the authors consider a class of Kukles planar polynomial differential system of degree three having an invariant parabola.For this class of second-order differential systems,it is shown that for certain values of the parameters the invariant parabola coexists with a center.For other values it can coexist with one,two or three small amplitude limit cycles which are constructed by Hopf bifurcation.This result gives an answer for the question given in[4],about the existence of limit cycles for such class of system.     

Monitoring process variability using auxiliary information

In this study a Shewhart type control chart namely V _r chart is proposed for improved monitoring of process variability (targeting large shifts) of a quality characteristic of interest Y. The proposed control chart is based on regression type estimator of variance using a single auxiliary variable X. It is assumed that (Y, X) follow a bivariate normal distribution. The design structure of V _r chart is developed and its comparison is made with the well-known Shewhart control chart namely S ² chart used for the same purpose. Using power curves as a performance measure it is observed that V _r chart outperforms the S ² chart for detecting moderate to large shifts, which is main target of Shewhart type control charts, in process variability under certain conditions on ρ _yx . These efficiency conditions on ρ _yx are also obtained for V _r chart in this study.     

Usefulness of Hysteresis Curves for Studying Temperature Effects on Ises Responses

Abstract

A procedure for study of the effects of the temperature on the response of ion-selective electrodes in which isothermal hysteresis cum determined at several concentrations are used for obtaining the temperature variation parameters (isothermal slope and potential coefficients and isopotential points) is proposed. The procedure was tested against the classic procedure in which calibration curves are obtained at different temperatures. 'All -solid-state' Ag₂S and Ag₂S/Agl electrodes with sensors applied to silver- and copper-loaded epoxy supports (and commercial electrodes, for comparison) were used for this purpose. The values of the temperature parameters obtained by the two procedures (in the raw 10–60°C) are compared. This comparison show that the present procedure yields acceptable values of temperature parameters for cases like the studied where the hysteresis is not very produced.     

Theoretical spectroscopic studies of InI and InI+

Relativistic configuration interaction calculations are carried out to study the electronic structure and spectroscopic properties of InI and InI⁺. Potential energy curves of the ground and a number of low‐lying states are constructed. Spectroscopic parameters of the bound states of both species are computed and compared with the experimental and other theoretical data. Effects of spin‐orbit coupling on the spectroscopic properties are studied. Because of the presence of the heavy atoms the effect is large. The spin‐orbit splitting of the ground state (X²Π) of InI⁺ is more than 8350 cm^?1. As a result of the strong spin‐orbit interaction between X²Π and A²Σ⁺ of InI⁺, the potential energy curve of A²Σ becomes repulsive. Radiative lifetimes for the spin‐forbidden transitions such as A³Π?X¹Σ and B³Π₁ ?X¹Σ of InI and spin‐allowed transitions such as B²Σ⁺?A²Σ⁺, C²Π?A²Σ⁺, and B²Σ⁺?X²Π are calculated. Vertical and adiabatic ionization energies of InI and the electric dipole moments of both the neutral and ionic species are estimated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010