Multiplicity Preserving Triangular Set Decomposition of Two Polynomials

In this paper, a multiplicity preserving triangular set decomposition algorithm is proposed for a system of two polynomials. The algorithm decomposes the variety defined by the polynomial system into unmixed components represented by triangular sets, which may have negative multiplicities. In the bivariate case, we give a complete algorithm to decompose the system into multiplicity preserving triangular sets with positive multiplicities. We also analyze the complexity of the algorithm in the bivariate case. We implement our algorithm and show the effectiveness of the method with extensive experiments.Comment: 18 page

Latest results on standard model Higgs boson at LEP

In this talk, the search results on standard model Higgs boson using LEP data collected at energies up to 209 GeV are reported. An excess of 2.9 sigma beyond the background expectation is found, consistent with the production of the Higgs boson with a mass near 115 GeV/c/sup 2/. (4 refs)

Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation

In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the roots of the equation system are represented as linear combinations of roots of several univariate polynomial equations. The main advantage of this representation is that the precision of the roots can be easily controlled. In fact, based on the linear univariate representation, we can give the exact precisions needed for roots of the univariate equations in order to obtain the roots of the equation system to a given precision. As a consequence, a root isolation algorithm for a zero-dimensional polynomial equation system can be easily derived from its linear univariate representation.Comment: 19 pages,2 figures; MM-Preprint of KLMM, Vol. 29, 92-111, Aug. 201

Electricity System Expansion Studies to Consider Uncertainties and Interactions in Restructured Markets

This dissertation concerns power system expansion planning under different market mechanisms. The thesis follows a three paper format, in which each paper emphasizes a different perspective. The first paper investigates the impact of market uncertainties on a long term centralized generation expansion planning problem. The problem is modeled as a two-stage stochastic program with uncertain fuel prices and demands, which are represented as probabilistic scenario paths in a multi-period tree. Two measurements, expected cost (EC) and Conditional Value-at-Risk (CVaR), are used to minimize, respectively, the total expected cost among scenarios and the risk of incurring high costs in unfavorable scenarios. We sample paths from the scenario tree to reduce the problem scale and determine the sufficient number of scenarios by computing confidence intervals on the objective values. The second paper studies an integrated electricity supply system including generation, transmission and fuel transportation with a restructured wholesale electricity market. This integrated system expansion problem is modeled as a bi-level program in which a centralized system expansion decision is made in the upper level and the operational decisions of multiple market participants are made in the lower level. The difficulty of solving a bi-level programming problem to global optimality is discussed and three problem relaxations obtained by reformulation are explored. The third paper solves a more realistic market-based generation and transmission expansion problem. It focuses on interactions among a centralized transmission expansion decision and decentralized generation expansion decisions. It allows each generator to make its own strategic investment and operational decisions both in response to a transmission expansion decision and in anticipation of a market price settled by an Independent System Operator (ISO) market clearing problem. The model poses a complicated tri-level structure including an equilibrium problem with equilibrium constraints (EPEC) sub-problem. A hybrid iterative algorithm is proposed to solve the problem efficiently and reliably

Long Term Power Generation Planning Under Uncertainty

Generation expansion planning concerns investment and operation decisions for different types of power plants over a multi-decade horizon under various uncertainties. The goal of this research is to improve decision-making under various long term uncertainties and assure a robust generation expansion plan with low cost and risk over all possible future scenarios. In a multi-year numerical case study, we present a procedure to deal with the long term uncertainties by first modeling them as a multidimensional stochastic process and then generating a scenario tree accordingly. Two-stage stochastic programming is applied to minimize the total expected cost, and robust optimization is further applied to reduce the cost variance. Results of experiments on a realistic case study are compared. An efficient frontier of the planning solutions that illustrates the tradeoff between the cost and risk is further shown and analyzed

What Factors Influence Customers’ Purchase Intentions in Travel-Related Social Commerce?

Social commerce significantly impacts the tourism and hospitality industry. Nonetheless, further empirical research investigating the factors that impact the purchase intentions of those who engage with travel-related social commerce. Combining the Uses and Gratification Theory (UGT) and TAM, the present study will investigate the relationships between purchases intentions and the following factors: perceived usefulness, perceived ease-of-use, entertainment, interaction and information seeking. During the research, four different models will be compared. The Ridge Model will be used to explain the effects of the aforementioned factors. The findings indicate that customers’ social commerce purchase intentions are positively impacted by all five factors

Factors associated with childhood depression in Saskatoon students: a multilevel analysis

Depression is a multi-factorial mental health problem that deeply impacts individuals’ emotions, behaviours and productivity. This study investigated links between depression and its determinants among children recruited from Saskatoon elementary schools. The overall goal of the study is to (i) determine the extent of mental health disparity and identify multilevel factors that are associated with depression (individual-level), and (ii) examine whether there is a depression discrepancy among Saskatoon elementary schools (school-level). Our study could provide theoretical bases for future interventions which reducing mental health disparities in Saskatoon school children. This is a cross-sectional study based on the Saskatoon Student Health Survey administered by Saskatoon Health Region in 2008/2009. It included 4200 students from 76 elementary schools. Data on self-reported mental health, physical activity, bullying experiences, and school refusal behaviours was collected. School-level material and social deprivation were also measured. A multilevel logistic model was used to analyze the data. A total of 3648 (86.9%) students responded to the questions on depression. Among them, 813 (22.3%) reported suffering from symptoms of depression. Most of the responders were between the ages of 11 and 13, 80% had a normal Body Mass Index (BMI), and a majority (78.2%) were Caucasian. Factors associated with depression were: female, student from single parent family, reporting a ‘good relationship’ with parents, over weight/obese, having experienced social or electronic bullying, having few friends, feeling like an outsider, skipped school, and being treated badly at school. In addition, students in schools deemed as representing moderate material deprivation were 2.04 times more likely to be depressed compared to schools deemed to represent low material deprivation (OR=2.04, 95% CI: 1.53-2.72, p<.0001). Our study revealed that disparities in depression exist between schools, and students’ school refusal behaviour was the main factors contributing to the disparity between schools. The study will increase awareness in Saskatoon Health Region and among stakeholders about mental health disparity and its complex determinants among children in Saskatoon