Vector Graphs Research Articles

Distinguishing labellings of group action on vector spaces and graphs

Suppose Γ is a group acting on a set X. A k-labeling of X is a mapping c : X → { 1 , 2 , … , k } . A labeling c of X is distinguishing (with respect to the action of Γ) if for any g ∈ Γ , g ≠ id X , there exists an element x ∈ X such that c ( x ) ≠ c ( g ( x ) ) . The distinguishing number, D Γ ( X ) , of the action of Γ on X is the minimum k for which there is a k-labeling which is distinguishing. This paper studies the distinguishing number of the linear group GL n ( K ) over a field K acting on the vector space K n and the distinguishing number of the automorphism group Aut ( G ) of a graph G acting on V ( G ) . The latter is called the distinguishing number of the graph G and is denoted by D ( G ) . We determine the value of D GL n ( K ) ( K n ) for all fields K and integers n. For the distinguishing number of graphs, we study the possible value of the distinguishing number of a graph in terms of its automorphism group, its maximum degree, and other structure properties. It is proved that if Aut ( G ) = S n and each orbit of Aut ( G ) has size less than ( n 2 ) , then D ( G ) = ⌈ n 1 / k ⌉ for some positive integer k. A Brooks type theorem for the distinguishing number is obtained: for any graph G, D ( G ) ⩽ Δ ( G ) , unless G is a complete graph, regular complete bipartite graph, or C 5 . We introduce the notion of uniquely distinguishable graphs and study the distinguishing number of disconnected graphs.

PIV experimental investigation of entrance configuration on flow maldistribution in plate-fin heat exchanger

Flow characteristics of flow field in the entrance of plate-fin heat exchanger have been investigated by means of particle image velocimetry (PIV). The velocity fields were measured using the two-frame cross-correlation technique. A series of velocity vector and streamline graphs of different cross-sections are achieved in the experiment. The experimental results indicate that performance of fluid maldistribution in conventional entrance configuration is very serious, while the improved entrance configuration with punched baffle can effectively improve the performance of fluid flow distribution in the entrance. Based on the analysis of the fluid flow maldistribution, a baffle with small holes is recommended to install in the entrance configuration in order to improve the performance of flow distribution. When the punched baffle is proper in length, the small holes is distributed in staggered arrangement, and the punched ratio gradually increases from central axis to the boundary along with the baffle length, the performance of flow distribution in plate-fin heat exchanger is effectively improved by the optimum design of the entrance configuration. The flow maldistribution parameter S in plate-fin heat exchanger has been reduced from 1.21 to 0.209 and the ratio of the maximum velocity to the minimum θ is reduced from 23.2 to 1.76 by installing the punched baffle. The results validate that PIV is well suitable to investigate complex flow pattern and the conclusion of this paper is of great significance in the optimum design of plate-fin heat exchanger.

Quantification of the curvature and shape of the interventricular septum.

The interventricular septum (IVS) occupies a unique position within the heart, lying between the left (LV) and right (RV) ventricular cavities. Changes in its normal geometry may signify not only abnormalities of the septal myocardium, but also abnormal pressure differences between the LV and RV. Flattening of the IVS has been noted with cross-sectional imaging in association with pulmonary hypertension, but the septal curvature and shape have not previously been measured in three dimensions. This paper describes a method to model the RV surface of the IVS from spatially registered cross-sectional images for measurements of curvature. A smoothing 2D spline surface is constructed through the RV septal surface at regular times during the cardiac cycle, and the principal curvatures, as well as the Gaussian and mean curvatures, shape index, and curvedness, are calculated. Vector and color surface maps and graphs of average curvature and shape indices are constructed. Consistent curvature patterns were observed in four normal subjects. This method of measuring septal geometry can provide potentially useful new information on the effects of RV disease. We examine the problem of describing septal motion, and describe a simple measure of septal curvature that may be of clinical value.

Three-dimensional vector graphing of the H reflex.

Comparison of latencies of the H reflex from side-to-side is considered a valid indicator of pathology, but amplitudes are too variable to allow similar comparison. Three pairs of electrodes were placed circumferentially and longitudinally along the calf to record the H reflex in three axes simultaneously. An H reflex with the greatest amplitude was produced by incrementally increasing submaximal stimulation to the tibial nerve. Three-dimensional vector graphs were constructed at three levels in each calf in ten normal individuals. Best fit curve Procrustes statistical analysis showed an average of 82.2 to 90.6% agreement of 3-D shape left-to-right with greater agreement at distal levels. Standard deviation ranged from 11.3% proximally to 8.2% distally. This represents much closer agreement than established norms for amplitude, which can vary from two to four times side-to-side. Three-dimensional vector analysis holds promise to further understanding of peripheral and central electrophysiologic phenomena.

Software Reviews : CoVis

CoVis is one of the first personal computer programs capable of making realtime animated scientific graphs of large data sets. Nine types of graphs are available: Nchannel; 2-D and 3-D snake graphs; contour, vector, and wireframe graphs; a point graph, and 2-D and 3-D programmable graphs. At this time, the capabilities of CoVis will most likely be utilized by physical and biological scientists. Social scientists have always been enamored with representations of data in graphs and charts, but until recently the computing power necessary to animate graphs has been out of reach of all but a few. Enter CoVis, a program designed to animate scientific graphs on a personal computer.