The Dirac operator on untrapped surfaces

We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for constant mean curvature surfaces in Minkowski space.Comment: 16 page

Optimal eigenvalues estimate for the Dirac operator on domains with boundary

We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the \MIT bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.Comment: 10 page

Optimal eigenvalue estimate for the Dirac-Witten operator on bounded domains with smooth boundary

Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and chiral conditions). This result is a generalisation of Friedrich's inequality for the usual Dirac operator. The limiting cases are also investigated.Comment: 2007, 18 pages, submitted 02 June 200

Rigidity of compact Riemannian spin Manifolds with Boundary

In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake \cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy

On a spin conformal invariant on manifolds with boundary

On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of the Dirac operator under the chiral bag boundary condition. More precisely, we show that we can derive a spinorial analogue of Aubin's inequality.Comment: 26 page

A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

Performance Evaluation of Mutual Funds in Pakistan

In Pakistan Mutual Funds were introduced in 1962, when the public offering of National Investment (Unit) Trust (NIT) was introduced which is an open-end mutual fund. In 1966 another fund that is Investment Corporation of Pakistan (ICP) was establishment. ICP subsequently offered a series of closed-end mutual funds. Up to early 1990s, twenty six (26) closed-end ICP mutual funds had been floated by Investment Corporation of Pakistan. After considering the option of restructuring the corporation, government decided to wind up ICP in June, 2000. In 2002, the Government started Privatisation of the Investment Corporation of Pakistan. 25 Out of 26 closed-end funds of ICP were split into two lots. There had been a competitive bidding for the privatisation of funds. Management Right of Lot-A comprising 12 funds was acquired by ABAMCO Limited. Out of these 12, the first 9 funds were merged into a single closed-end fund and that was named as ABAMCO Capital Fund, except 4th ICP mutual fund as the certificate holders of the 4th ICP fund had not approved the scheme of arrangement of Amalgamation into ABAMCO capital fund in their extra ordinary general meeting held on December 20, 2003. The fund has therefore been reorganised as a separate closedend trust and named as ABAMCO Growth Fund. Rest of the three funds were merged into another single and named as ABAMCO Stock Market Fund. So far as the Lot-B is concerned, it comprised of 13 ICP funds, for all of these thirteen funds, the Management Right was acquired by PICIC Asset Management Company Limited. All of these thirteen funds were merged into a single closed-end fund which was named as “PICIC Investment Fund”. Later on the 26th fund of ICP (ICP-SEMF) was also acquired by PICIC Asset Management Company Limited

Developing a framework to enhance building handover practices in public sector construction projects in the Kingdom of Saudi Arabia

Many public sector construction projects in the Kingdom of Saudi Arabia (KSA) aremarred by communication and coordination problems, with owners having to pay a highprice for schedule delays and cost overruns. The process by which building informationis conveyed to owners lacks standardisation, a holistic approach, and consistency. Thisoften results in KSA public sector owners receiving building information in a variety offormats, resulting in buildings operating at sub-optimal levels and relevant building databeing unavailable at required times to support decision-making and optimal operationsand maintenance. Existing systems of data management within KSA public sectorprojects cannot match the demand of operations and maintenance, as buildings arebecoming more complex, in terms of space management, energy demand management,and addressing environmental concerns, due to the functional requirements of moderninfrastructure. This research focuses on investigating key technology and processrelatedchallenges in order to ensure smoother transition of information from projectdesign and construction to maintenance and operation phases of a building’s lifecycle.This research aims to develop a framework to enhance data management in buildinghandover practices of public sector construction projects in the KSA. This frameworkhelps improve the operation and maintenance of buildings by establishing a relationshipbetween the project design and construction team, and the operations and projectmaintenance team. The research identifies key data requirements for effective buildinghandover from a Saudi client perspective.In order to achieve the research aim, an empirically based systems analysis of a singledetailed case study organization of Al Madinah Al Munawwarah, RegionalMunicipality in KSA was carried out. Substantial fieldwork was undertaken using bothqualitative and quantitative methods to match specific research questions. Thequestionnaire survey provides a wider view of building handover practices in the KSA,while the qualitative study provided an in-depth understanding of the state-of-the-art inpractice. Many tools were used to collect the data, including semi-structured interviewssupplemented by survey questionnaires together with documentation review. Theimplementation of more than one method to collect the data was used in order to achieve data triangulation, to explore implementation of data management in buildinghandover practices, and to provide a more an in-depth understanding.The finding of this research concludes some unique factors that affect theimplementation of actual building handover practices within the public sectorconstruction industry in KSA. These factors include: high manager turnover; lack ofknowledge and experience; lack of use of technology; lack of training; lack ofcommunication during project data at the Handover Stage; unclear responsibilities.However, the finding indicates that it is important for all managers in public sectorconstruction to understand that the handover is started already at the beginning of theproject. Furthermore, early handovers must be reviewed and strengthened during thefinal project handover.Also, the research findings confirmed that the lack of communication was possiblybecause of the fact that the project team is big and multi-cultural. Thus, the individualswere afraid to ask any questions as they assumed others would think that they were tooinexperienced to understand some technical specifications. Hence, it is highly critical todefine and use a clear communication procedure. Every manager is responsible forcommunicating internally and externally about status and issues. These findings willstrengthen the existing literature on effective data handover at project completion stageand will narrow the gap in knowledge in KSA studies in particular and to Arab studiesin general. Therefore, significant recommendations to the policy, practitioners, andresearchers, within both the public and private sector projects, are made to aid andimprove construction industry practices.This research provides specific original findings, which include an in depthunderstanding of factors that affect the facilitation of data management in buildinghandover practices of construction projects in the KSA via a case study conductedwithin the KSA public sector construction context. This research is the first study inKSA regarding issues that affect data management in building handover practices ofconstruction projects in the KSA. It is also the first academic study of the Al MadinahAl Munawwarah, Regional Municipality in KSA