A new weighted geometric inequality is established by Klamkin’s polar moment of inertia inequality and the inversion transformation, some interesting applications of this result are given, and some conjectures which verified by computer are also mentioned

We present a new algorithm in order to compute the multidimensional residue of a polynomial map based on a perturbation argument and the Generalized Transformation Law. Then we use it for studying some fundamental problems in Computer Aided Geometric Design.

Based on the ray transformation matrix formalism, we propose a simple method for the identification of the dynamic and geometric parts of the Gouy phase, acquired by an appropriate Gaussian-type beam while propagating through a first-order optical system.

On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a transformation group.

We present a framework for specifying spatiotemporal objects using spatial and temporal objects, and a parametric geometric transformation. We define a number of classes of spatiotemporal objects and summarize their closure properties under set-theoretic operations.

Bäcklund transformation for the Bullough-Dodd-Jiber-Shabat equation uxx−utt = e−e is found. The construction of integrable boundary condition for this equation together with the algebro-geometric solutions satisfying it are suggested.

We present a framework for specifying spatiotem-poral objects using spatial and temporal objects, and a geometric transformation. We deene a number of classes of spatiotemporal objects and study their closure properties.

This paper presents a content-based image retrieval technique based on interest points matching and geometric hashing. We estimate points with significant luminance variations as interest points. A small region around the interest point is located as an image patch. Low-level features are extracted to describe each image patch. To provide geometric invariant image matching, we index the image p...

We present an algebraic approach to geometric reasoning and learning. The purpose of this research is to avoid the usual difficulties in symbolic handling of geometric concepts. Our system GREW is grounded on a reasoning scheme that integrate the symbolic reasoning and algebraic reasoning of Wu's method. The basic principle of this scheme is to describe mathematical knowledge in terms of symbol...

Since they help to specify the shape of real objects, geometric constraint systems encountered in CAD domain are often invariant by isometries. But other transformation groups can be considered to improve the solving process. More precisely, using different transformation groups leads to a new approach of decomposition which generalize in some sense the classical approaches. This paper presents...