Signless Laplacian spectral radii of graphs with given chromatic number

AbstractLet G be a simple graph with vertices v1,v2,…,vn, of degrees Δ=d1⩾d2⩾⋯⩾dn=δ, respectively. Let A be the (0,1)-adjacency matrix of G and D be the diagonal matrix diag(d1,d2,…,dn). Q(G)=D+A is called the signless Laplacian of G. The largest eigenvalue of Q(G) is called the signless Laplacian spectral radius or Q-spectral radius of G. Denote by χ(G) the chromatic number for a graph G. In this paper, for graphs with order n, the extremal graphs with both the given chromatic number and the maximal Q-spectral radius are characterized, the extremal graphs with both the given chromatic number χ≠4,5,6,7 and the minimal Q-spectral radius are characterized as well

On the Effective Continuum Method for Modeling MultiphaseFlow, Multicomponent Transport and Heat Transfer in FracturedRock

Flow and transport through fractured porous media occurs in many subsurface systems and has received considerable attention in recent years due to the importance in the areas of underground natural resource recovery, waste storage, and environmental remediation scheme. Among the methods of handling fracture/matrix flow and transport through geological media, the effective continuum method (ECM) has been widely used, and misused in some cases, because of its simplicity in terms of data requirements and computational efficiency. This paper presents a rigorous, generalized effective continuum formulation, which has been implemented into the TOUGH2 code (Pruess, 1991) for modeling multiphase, multicomponent, non-isothermal flow and transport in fractured rocks. Also included in the paper are discussions of the conditions under which the ECM approach applies and the procedures for evaluating the effective parameters for both flow and transport simulations. Three application examples, one multiphase flow, one heat flow and one chemical transport problem, are given to demonstrate the usefulness of the ECM method

Automated Raman cytology system for cancer diagnostics

Raman spectroscopy is a promising optical diagnostic tool that can be applied to un-stained cells in order to detect changes in molecular composition. The data collected can be described as a chemical fingerprint of the sample under investigation. Thus it is very popular in the recent times to use Raman spectroscopy in cytology to increase diagnostic sensitivity and specificity for early stage cancer. In this thesis, I introduce an automated Raman cytology system for cancer diagnostics which integrates all the hardware and software in Micro-manager and operates them in a specific order. An autofocus algorithm for unstained cells and a three-dimensional morphology recovery algorithm are also investigated and contributed to the final automated system.With increasing usage of Raman cytology systems, automation is a solution to limit data variabilities which is a major problem at the moment. In addition, a higher throughput of cellular analysis and a reduction in manpower could be expected from the proposed automation system