Investigation of Surface Micro Waviness in Single Point Diamond Fly Cutting

Single point diamond fly cutting is widely used in the manufacture of large-aperture ultra-precision optical elements. However,some micro waviness( amplitude about 30 nm,wavelength about 15 mm) along the cutting direction which will decrease the quality of the optical elements can always be found in the processed surface,and the axial vibration of the spindle caused by the cut-in process is speculated as the immediate cause of this waviness. In this paper,the analytical method of dynamic mesh is applied for simulating the dynamic behavior of the vertical spindle. The consequence is then exerted to the fly cutter and the processed surface profile is simulated. The wavelength of the simulation result coincides well with the experimental result which proves the importance of the cut-in process during the single point diamond fly cutting.

Power Generation Expansion Planning Using an Interior Point with Cutting Plane （IP/CP） Method

The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point with cutting plane （IP/CP） method is proposed to solve the mixed-integer optimization problem of the electrical power generation expansion planning. The IP/CP method could improve the overall efficiency of the solution and reduce the computational time. Proposed method is combined with the Bender＇s decomposition technique in order to decompose the generation expansion problem into a master investment problem and a slave operational problem. The numerical example is presented to compare with the effectiveness of the proposed algorithm.

Theoretical study on separation density of gravity beneficiation

Separation density is one of the most concerned operating parameters in gravity beneficiation.Although equal-errors cut point or distribution density is usually used as practical separation density in gravity beneficiation, the gravity separating process complexly affected by many kinds of factors is actually carried out at a fluctuant density; namely, the practical separation density is essentially a random variable.The studied results show that the equal-errors cut point is the mathematical expectation of this random variable, and the distribution density corresponds to the highest separation efficiency in the gravity separation process.This shows that the distribution density is the best working point of the gravity separation equipment under a particular operating condition.Therefore,in order to fully develop the function of the gravity separation equipment, the distribution density should be close to the theoretical separation density unlimitedly in the range of minimum fluctuation.

Realization of Fixed Point Sets

Let f: X→X be a selfmap of a compact connected polyhedron, and A a nonempty closed subset of X. In this paper, we shall deal with the question whether or not there is a map g: X→X homotopic to f such that the fixed point set Fixg of g equals A. We introduce a necessary condition for the existence of such a map g. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.

Cheeger's cut, maxcut and the spectral theory of1-Laplacian on graphs

This is primarily an expository paper surveying up-to-date known results on the spectral theory of1-Laplacian on graphs and its applications to the Cheeger cut, maxcut and multi-cut problems. The structure of eigenspace, nodal domains, multiplicities of eigenvalues, and algorithms for graph cuts are collected.