Computing Gutman Connection Index of Thorn Graphs

Chemical structural formula can be represented by chemical graphs in which atoms are considered as vertices and bonds between them are considered as edges. A topological index is a real value that is numerically obtained from a chemical graph to predict its various physical and chemical properties. Thorn graphs are obtained by attaching pendant vertices to the different vertices of a graph under certain conditions. In this paper, a numerical relation between the Gutman connection (GC) index of a graph and its thorn graph is established. Moreover, the obtained result is also illustrated by computing the GC index for the particular families of the thorn graphs such as thorn paths, thorn rods, thorn stars, and thorn rings.

Evidential Identification of New Target based on Residual

Both incompleteness of frame of discernment and interference of data will lead to conflict evidence and wrong fusion. However how to identify new target that is out of frame of discernment is important but difficult when it is possible that data are interfered. In this paper, evidential identification based on residual is proposed to identify new target that is out of frame of discernment when it is possible that data are interfered. Through finding the numerical relation in different attributes, regress equations are established among various attributes in frame of discernment. And then collected data will be adjusted according to three mean value. Finally according to weighted residual it is able to decide whether the target requested to identify is new target. Numerical examples are used to verify this method.

A Parallel Dual Matrix Method for Blind Signal Separation

A parallel dual matrix method that considers all cases of numerical relations between a mixing matrix and a separating matrix is proposed in this letter. Different constrained terms are used to construct cost function for every subalgorithm. These constrained terms reflect numerical relation. Therefore, a number of undesired solutions are excluded, the search region is reduced, and the convergence efficiency of the algorithm is ultimately improved. Moreover, any parallel subalgorithm is proven to converge to a desired separating matrix only if its cost function converges to zero. Computer simulations indicate that the algorithm efficiently performs blind signal separation.

Optimization Design of a Piezoelectric Transduction Silicon Resonant Pressure Sensor

This paper presents about the optimization design of Silicon resonant pressure sensor. The new idea is the Silicon circular resonator was used as the sensing resonator. This sensor is Lead-Zinconate-Titanate (PZT) driven and the resonant frequency shift also detected by PZT. This micro resonant pressure sensor works on the principle of resonant shift caused by the change of internal stress due to applied of the external pressure. First, we analyze the numerical relation of circular resonator. Then, Finite element analysis (FEA) has been examined for optimization for the size of Si circular diaphragm, size of the PZT patches and placement of the PZT was analyzed. And the fabrication process also presented in this paper. The pressure range is 0~0.1Mpa. The resonant frequency is about 102.29 kHz and the linearity of the output frequencies shift is so good under Silicon diaphragm small deflection limited.

The Active Bijection between Regions and Simplices in Supersolvable Arrangements of Hyperplanes

Comparing two expressions of the Tutte polynomial of an ordered oriented matroid yields a remarkable numerical relation between the numbers of reorientations and bases with given activities. A natural activity preserving reorientation-to-basis mapping compatible with this relation is described in a series of papers by the present authors. This mapping, equivalent to a bijection between regions and no broken circuit subsets, provides a bijective version of several enumerative results due to Stanley, Winder, Zaslavsky, and Las Vergnas, expressing the number of acyclic orientations in graphs, or the number of regions in real arrangements of hyperplanes or pseudohyperplanes (i.e. oriented matroids), as evaluations of the Tutte polynomial. In the present paper, we consider in detail the supersolvable case – a notion introduced by Stanley – in the context of arrangements of hyperplanes. For linear orderings compatible with the supersolvable structure, special properties are available, yielding constructions significantly simpler than those in the general case. As an application, we completely carry out the computation of the active bijection for the Coxeter arrangements $A_n$ and $B_n$. It turns out that in both cases the active bijection is closely related to a classical bijection between permutations and increasing trees.