For a given topological type of normal surface singularity, there are various types complex structures which realize it. We interested in the following problem: Find maximum geometric genus and condition for that maximal ideal cycle coincides with undamental on minimal good resolution. In this paper, we study weighted homogeneous singularities homeomorphic to Brieskorn complete intersection fro...

this article addresses an efficient and novel method for singularity-free path planning and obstacle avoidance of parallel manipulator based on neural networks. a modified 4-5-6-7 interpolating polynomial is used to plan a trajectory for a spherical parallel manipulator. the polynomial function which is smooth and continuous in displacement, velocity, acceleration and jerk is used to find a pat...

We prove the “End Curve Theorem” which states that a normal surface singularity (X, o) with rational homology sphere link Σ is a splice-quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An “end-curve function” is an analytic function (X, o) → (C, 0) whose zero set intersects Σ in the knot given by a meridian curve of the exceptional curve ...

Linear discriminant analysis (LDA) is a classical approach for dimensionality reduction. It aims to maximize between-class scatter and minimize within-class scatter, thus maximize the class discriminant. However, for undersampled problems where the data dimensionality is larger than the sample size, all scatter matrices are singular and the classical LDA encounters computational difficulty. Rec...

Stability aspects of redundancy resolution both in velocity and acceleration level have been investigated for a method which augments the weighted least norm solution by weighted residual of the current joint rate and preferred pose rate in null space. While doing this the first and second order inverse kinematics solutions with redundancy have been re-casted as a feedback control problem, with...

Contourlet transform is an effective solution to solve two or more dimensional singularity and has good direction and anisotropy. Against the shortage of ability of describing the spatial distribution characteristic of object’s edge information, this paper proposed a new image retrieval algorithm based on Contourlet transform, which blocks the indexed image and decomposes each sub-block images ...

We generalize existing Jacobi–Gauss–Lobatto collocation methods for variable-order fractional differential equations using a singular approximation basis in terms of weighted Jacobi polynomials of the form (1 ± x)μP a,b j (x), where μ > −1. In order to derive the differentiation matrices of the variable-order fractional derivatives, we develop a three-term recurrence relation for both integrals...

by Simin Hu An important application of microarray research is to develop cancer diagnostic and prognostic tools based on tumor genetic profiles. For easy interpretation, such studies aim to identify a small fraction of genes to build molecular predictors of clinical outcomes from at least thousands of genes thus require methodologies that can model high dimensional covariates and accomplish va...