On the unimodality of independence polynomials of some graphs

In this paper we study unimodality problems for the independence polynomial of a graph, including unimodality, log-concavity and reality of zeros. We establish recurrence relations and give factorizations of independence polynomials for certain classes of graphs. As applications we settle some unimodality conjectures and problems.Comment: 17 pages, to appear in European Journal of Combinatoric

Novel applications of pulse pre-pump Brillouin Optical Time Domain Analysis for behavior evaluation of structures under thermal and mechanical loading

This study aims to: (1) develop an analytical model for the strain transfer effect of distributed fiber optic sensors in a uniform or non-uniform stress field; (2) develop a measurement approach to monitor strains in concrete and detect damage (e.g. crack and delamination) in bonded and unbonded concrete overlays; (3) characterize the strain and temperature sensitivities of distributed fiber optic sensors at elevated temperatures; (4) develop a thermal annealing approach to enhance the thermal stability and temperature sensitivity of the distributed sensors; and (5) apply the distributed sensors to assess structural behaviors of concrete and steel structures exposed to fire. The pulse pre-pump Brillouin Optical Time Domain Analysis (PPP-BOTDA) was employed to measure strain and temperature distributions along a fused silica single-mode optical fiber. Strain distributions in concrete were measured from the distributed fiber optic sensors embedded in bonded and unbonded concrete overlays. Peaks of the strain distributions represent the effect of concrete cracks and delamination. The strain sensitivity coefficient of distributed sensors was reduced from 0.054 MHz/µε to 0.042 MHz/µε when temperature increased from 22 ⁰C to 750 ⁰C. The temperature sensitivity coefficient of distributed sensors was reduced from 1.349x10-3 GHz/⁰C to 0.419x10-3 GHz/⁰C when temperature increased from 22 ⁰C to 1000 ⁰C. The distributed sensors embedded in concrete beams measured non-uniform temperature distributions with local peaks representing a sudden increase of temperature through concrete cracks. Temperature distributions measured from the distributed sensors attached on steel beams enabled an enhanced thermo-mechanical analysis to understand the structural behaviors of steel beams subjected to fire --Abstract, page iii

Three Dimensional Imaging of the Nucleon and Semi-Inclusive High Energy Reactions

We present a short overview on the studies of transverse momentum dependent parton distribution functions of the nucleon. The aim of such studies is to provide a three dimensional imagining of the nucleon and a comprehensive description of semi-inclusive high energy reactions. By comparing with the theoretical framework that we have for the inclusive deep inelastic lepton-nucleon scattering and the one-dimensional imaging of the nucleon, we summarize what we need to do in order to construct such a comprehensive theoretical framework for semi-inclusive processes in terms of three dimensional gauge invariant parton distributions. After that, we present an overview of what we have already achieved with emphasize on the theoretical framework for semi-inclusive reactions in leading order perturbative QCD but with leading and higher twist contributions. We summarize in particular the results for the differential cross section and the azimuthal spin asymmetries in terms of the gauge invariant transverse momentum dependent parton distribution functions. We also briefly summarize the available experimental results on semi-inclusive reactions and parameterizations of transverse momentum dependent parton distributions extracted from them and make an outlook for the future studies.Comment: 20 pages, 7 figure