Dressing of resin-bonded superabrasive grinding wheels by means of acousto-optic Q-switched pulsed Nd:YAG laser

The preparation of the use of resin-bonded superabrasive grinding wheels remains a problem despite their availabilities on the market in the past years and possible technological advantages. In this paper, an acousto-optic Q-switched Nd:YAG pulsed laser is applied to dressing resin-bonded superabrasive wheels in orthogonal direction. The author proposes a systematical study on the mechanism of selective removal, crater ablated by single pulse and surface topography after dressing, and consequently presents a feasible method of selecting irradiation parameters and summarizes the dressing features and disciplines of dressing effects influenced by these parameters. Experiments results indicate the surface topography dressed by acousto-optic Q-switched YAG pulsed laser dressing is much superior to mechanical dressing and CW laser dressing.     

Representations of Knot Groups and Twisted Alexander Polynomials

We present a twisted version of the Alexander polynomial associated with a matrix representation of the knot group. Examples of two knots with the same Alexander module but different twisted Alexander polynomials are given.     

The route to MBxNyCz molecular wheels: II. Results using accurate functionals and basis sets

Applying ab initio quantum chemical methods, molecular wheels composed of metal and light atoms were investigated. High quality basis sets 6-31G*, TZPV, and cc-pVTZ as well as exchange and non-local correlation functionals B3LYP, BP86 and B3P86 were used. The ground-state energy and structures of cyclic planar and pyramidal clusters TiB_n (for n = 3–10) were computed. In addition, the relative stability and electronic structures of molecular wheels TiB_xN_yC_z (for x, y, z = 0–10) and MB_nC_10−n (for n = 2 to 5 and M = Sc to Zn) were determined. This paper sustains a follow-up study to the previous one of Boustani and Pandey [Solid State Sci. 14 (2012) 1591], in which the calculations were carried out at the HF-SCF/STO3G/6-31G level of theory to determine the initial stability and properties. The results show that there is a competition between the 2D planar and the 3D pyramidal TiB_n clusters (for n = 3–8). Different isomers of TiB₁₀ clusters were also studied and a structural transition of 3D-isomer into 2D-wheel is presented. Substitution boron in TiB₁₀ by carbon or/and nitrogen atoms enhances the stability and leads toward the most stable wheel TiB₃C₇. Furthermore, the computations show that Sc, Ti and V at the center of the molecular wheels are energetically favored over other transition metal atoms of the first row.     

Degeneracy from quadric cones for projective reconstruction from two views

Fundamental matrix encapsulates all the geometric information in two views, and it plays an important role in many applications of three-dimensional computer vision. However, some configurations have an inherent ambiguity, namely, degeneracy, and no matter how many matched image points are used, the fundamental matrix could not be determined uniquely. It is well-known that degeneracies occur when all the space points and both the camera centers belong to a ruled quadric. But it is not so well-known how great the degenerate degrees in different configurations are. In this paper, we discuss the degeneracies caused by a quadric cone and give the corresponding degenerate degrees. We parameterize all the points on a quadric cone by a twisted cubic lying on the cone, and obtain a parametric coefficient matrix of the equations for estimating the fundamental matrix. By analyzing the coefficient matrix, we get the rank of it, i.e. the degenerate degree of the given configuration. It gives a more intuitive degeneracy and the degenerate degrees of the configurations, and reveals the full picture of the degeneracies on a cone.     

两类特殊图的逆符号边控制数

设G=(V,E)是一个图,对于图G的一个函数f:E→{-1,1},如果对任意e∈E(G),均有Σe′∈N[e]f(e′)≤1,则称f为图G的一个逆符号边控制函数.图G的逆符号边控制数γ′s(G)=max{Σe∈E(G)f(e)|f为图G的一个逆符号边控制函数}.在逆符号边控制数定义基础上,得到了所有轮图和扇图的逆符号边控制数.     

A method for predicting the internal motion resistance of rubber-tracked undercarriages,Pt. 2. A research on the motion resistance of road wheels

In spite of an increasing number of rubber-tracked crawlers, the literature provides few guidelines and calculation models suitable for minimizing their internal motion resistance. This article presents a model where the internal resistance of double-flanged road wheels for rubber-tracked vehicles is calculated as a sum of the losses resulting from the indentation of the wheels into the track surface and friction of the wheels against the track guide lugs. The model allows for vertical and lateral load of the wheels, the non-uniform distribution of the wheel pressure on the track, and the relationship between the friction coefficient and normal reaction force in the interface between the wheel and track guide lugs. The model has been verified by experiments. According to the results of model computations and experiments discussed in the article, the internal losses of a given rubber-tracked undercarriage might be reduced if: the road wheels are covered with a material that exhibits low friction coefficient and mechanical hysteresis, the vehicle suspension system features oscillating bogie wheels, the undercarriage is fitted with the largest possible number of road wheels, and the vehicle weight is evenly distributed to all of the road wheels.     

On the twisted q-Euler numbers and polynomials associated with basic q-l-functions

One of the purposes of this paper is to construct the twisted q-Euler numbers by using p-adic invariant integral on Zp in the fermionic sense. Moreover, we consider the twisted Euler q-zeta functions and q-l-functions which interpolate the twisted q-Euler numbers and polynomials at a negative integer.     

Triangular Matrix Representations of Rings of Generalized Power Series

Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either （S,≤） satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]].     

Eigenvalue estimates for Dirac operators coupled to instantons

We prove a sharp lower bound for the first positive eigenvalue of Dirac operators coupled to instantons and discuss the limit case.