Graded Betti numbers of path ideals of cycles and lines

We use purely combinatorial arguments to give a formula to compute all graded Betti numbers of path ideals of line graphs and cycles. As a consequence we can give new and short proofs for the known formulas of regularity and projective dimensions of path ideals of line graphs

On the resolution of path ideals of cycles

We give a formula to compute all the top degree graded Betti numbers of the path ideal of a cycle. Also we will find a criterion to determine when Betti numbers of this ideal are non zero and give a formula to compute its projective dimension and regularity

When is a Squarefree Monomial Ideal of Linear Type ?

In 1995 Villarreal gave a combinatorial description of the equations of Rees algebras of quadratic squarefree monomial ideals. His description was based on the concept of closed even walks in a graph. In this paper we will generalize his results for all squarefree monomial ideals by using a definition of even walks in a simplicial complex.Comment: 15 pages, 8 figures, To appear in Commutative Algebra and Noncommutative Algebraic Geometry and Representation Theor

Analysis of the quantum-classical Liouville equation in the mapping basis

The quantum-classical Liouville equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantum-classical Liouville equation consists of a Poisson bracket contribution and a more complex term. By transforming the evolution equation, term-by-term, back to the subsystem basis, the complex term (excess coupling term) is identified as being due to a fraction of the back reaction of the quantum subsystem on its environment. A simple approximation to quantum-classical Liouville dynamics in the mapping basis is obtained by retaining only the Poisson bracket contribution. This approximate mapping form of the quantum-classical Liouville equation can be simulated easily by Newtonian trajectories. We provide an analysis of the effects of neglecting the presence of the excess coupling term on the expectation values of various types of observables. Calculations are carried out on nonadiabatic population and quantum coherence dynamics for curve crossing models. For these observables, the effects of the excess coupling term enter indirectly in the computation and good estimates are obtained with the simplified propagation

Why do women like working in building conservation?

There is a perception that Building Conservation as a career is different from the mainstream, and it appears to be more attractive to women - at whatever level - than many other careers in the construction industry. Whilst recruitment and publicity can be targeted, the culture within the construction industry can be a barrier to entry for anyone that is &quot;different.&quot; As Clara Greed (1999) discovered in her research &quot;the traits, beliefs and lifestyle peculiar to the construction tribe&quot; can inhibit the entry to the industry of a number of groups outside the traditional pool. The growth of women in the workforce generally (some 50% according to Turrell et al, 2000) is nowhere near being matched within the construction industry as a whole - the Construction Industry Board placed it at around 8.6% in 2000 across all positions. The various UK industry and professional bodies are actively supporting the need to attract women, with the CITB saying they want a 10% year on year increase in participation, the RICS have their own Raising the Ratio working group and the RIBA have carried out research to find out &quot;why women leave architecture.&quot;Of course the whole of the industry is not unfriendly to women - there are a number of us who have been in the industry for many years and recognise it as a fulfilling and exciting career - a number of women work as surveyors working on historic buildings. The initiatives that are working towards change might have something to learn from Building Conservation - while the shortage of skills is just as severe in work with historc buildings - this area of work holds an attraction to women, not found elsewhere. This paper draws on research carried out to explore some of the reasons for this.The study involved sending a questionnaire to twenty women already working in Building Conservation (the response rate was over 100%) and arranging for questionnaires to be completed by school students (male and female) choosing university courses in one school (60 questionnaires sent out, with 35 returned at a response rate of 58%)The research showed that the majority women working in Building Conservation did not agree that men heavily dominated their sector of the industry, whereas within other areas of the construction industry men make up approximately 90% of the workforce. The research found that women often perceived the Construction Industry to be \u27cut-throat\u27, \u27egotistical\u27 and \u27financially beneficial\u27, whereas they thought Building Conservation required \u27patience\u27, \u27care\u27 and \u27attention to detail\u27.Of the women who took part in the research, 87% were working in Building Conservation because of a personal interest , and the main aspect of that attarction was history and architecture. The study examined attitudes of school students choosing careers and the research shows that when male and female sixth form students were told what Building Conservation was about and what it involved, 43% would consider a career in it and 49% would be interested in talking part in a work experience placement working with historic buildings. The shortage of people working in Building Conservation could be reduced if more people were educated about the profession in a way relevant to their skills and interests. In order to assist this action, the study examined ways to introduce Building Conservation careers to school girls and drew on the initiatives that the university is doing to promote careers in the built environment to schoolgirls.<br /

The internal features of high-growth firms in Finland

Abstract. It is evident that high-growth firms are getting attention from the researchers. But there is still a gap in defining high-growth firms as there is scattered data available for defining high-growth firms with respect to its characteristics. The purpose of this study is to find out the inner qualities of high growth firms that differentiate them from other firms due to which, it is called high-growth firms. Previous researches have mainly focused on high-growth firms with respect to job creation only. Also, researches have emphasized on the firm-specific features of high-growth firms such as size, age, and industry. As high growth firms play an important role to support economic growth and raise the employment level in the country so it is very important to further research on it due to which it stands out as compared to other companies in the entrepreneurial ecosystem. This research is a qualitative study. Data is gathered by semi-structured interviews. All the interviewees were personnel from Finnish high-growth firms and had several years of experience in their field. In this study, internal characteristics are highlight based on the contemporary literature such as the growth vision: the identified opportunities or needs: the strategic management, partnerships or the inter-organizational relations,innovation and R&D, capabilities, entrepreneurial teams: entrepreneur characteristics, and human resource management practices: human capital. From the finding of the research Finnish high-growth firms in the metropolitan area have similar internal features which help the firms to grow. Moreover, there are some features which are also positively correlated such as 1) entrepreneurial teams and entrepreneur characteristics, 2) entrepreneurial teams, human capital, and Strategic management, 3) human resource management practices and human capital, and 4) partnerships or inter-organizational relations, capabilities and identified opportunities. Hence, it is empirically proven that High-growth firms possess these characteristics and some are positively correlated to each other. Further, the findings of the study are similar to the extant literature. The limitations and future studies are also discussed