A TWO-DIMENSIONAL RIEMANNIAN MANIFOLD WITH TWO ONE-DIMENSIONAL DISTRIBUTIONS

one and two dimensional ultrasonic vibration tool

this research is carried out to design and manufacturing of lathe vibration tool and their tests. firstly, one-dimensional vibration tool is designed and made of the bending vibration mode. one-dimensional vibration tool with half piezoelectric rings is considered to excite the bending mode of tool. structure of vibration tool is designed in abaqus software about 20 khz and then is made with re...

One - dimensional versus two - dimensional dynamics Sebastian

On two-dimensional Cayley graphs

A subset W of the vertices of a graph G is a resolving set for G when for each pair of distinct vertices u,v in V (G) there exists w in W such that d(u,w)≠d(v,w). The cardinality of a minimum resolving set for G is the metric dimension of G. This concept has applications in many diverse areas including network discovery, robot navigation, image processing, combinatorial search and optimization....

Constructing Two-Dimensional Multi-Wavelet for Solving Two-Dimensional Fredholm Integral Equations

In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

Two-dimensional bin packing with one-dimensional resource augmentation

The 2-dimensional Bin Packing problem is a generalization of the classical Bin Packing problems and is defined as follows: Given a collection of rectangles specified by their width and height, the goal is to pack these into minimum number of square bins of unit size. Recently, the problem was proved to be APX-hard even in the asymptotic case, i.e. when the optimum solutions requires a large num...