Graphs and Ideals generated by some 2-minors

Let G be a finite graph on [n] = {1,2,3,...,n}, X a 2 times n matrix of indeterminates over a field K, and S = K[X] a polynomial ring over K. In this paper, we study about ideals I_G of S generated by 2-minors [i,j] of X which correspond to edges {i,j} of G. In particular, we construct a Groebner basis of I_G as a set of paths of G and compute a primary decomposition.Comment: 14 pages, to appear in Communications in Algebr

Parity projection of QCD sum rules for the nucleon

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. First, we rederive the parity projected sum rules for baryons using forward correlation functions. Doing this, the method is generalized so that higher order operator product expansion (OPE) terms can be calculated unambiguously. We then apply this approach to the nucleon channel taking into account all known first order alpha_s corrections to the Wilson coefficients of the OPE. As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. Simultaneously, this phase rotation strongly suppresses the continuum contribution and improves the convergence of the OPE. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive and negative parity states.Comment: 17 pages, 6 figures, 3 tables; minor modifications, published versio

Three-dimensional shape measurement of a transparent object using a rangefinding approach

This paper describes a non-contact optical measuring approach by which to measure the three-dimensional (3D) shape of a transparent object such as a glass panel or an acrylic plate. In conventional approaches to obtain the 3D shape of a transparent object, contact-type sensors have been widely used. However, the measurement accuracy of contact-type sensors is susceptible to the influence of various factors. In this paper, we propose a novel triangulation-based rangefinding approach that can be applied to the 3D shape of a transparent object or to an opaque object. The rangefinder is based on the fact that the light projected onto the surface of a transparent object is in part reflected by the surface, though the majority of the projected light is transmitted through the surface. From the experimental results, the proposed rangefinding approach has the advantage that it can easily measure the 3D-shape of an object if the object reflects or transmits light, depending on its location. As a result, we conclude that the proposed approach has great potential for a wide range of industrial applications.</p