Stitching Data: Recovering a Manifold’s Geometry from Geodesic Intersections

Let (M, g) be a Riemannian manifold with boundary. We show that knowledge of the length of each geodesic, and where pairwise intersections occur along the corresponding geodesics allows for recovery of the geometry of (M, g) (assuming (M, g) admits a Riemannian collar of a uniform radius). We call this knowledge the ‘stitching data’. We then pose a boundary measurement problem called the ‘delayed collision data problem’ and apply our result about the stitching data to recover the geometry from the collision data (with some reasonable geometric restrictions on the manifold).

Initial data problem for an equation related to a peridynamic model in a two-dimensional domain

В настоящей работе доказывается единственность и существование решения задачи Коши для интегро-дифференциального уравнения, связанного с перидинамической моделью механики твёрдого тела с двумя пространственными переменными. In this paper the uniqueness and existence of a solution of Cauchy problem for an integro-differential equation associated with a peridynamic model of solid mechanics in a two-dimensional domain are proved.

Establishing and maintaining property transactions data banks in Ghana through partnerships and participatory means

PurposeThe credibility of valuation is enhanced by the use of quality and reliable property market data. Nonetheless, the availability of quality and reliable market data remains a problem for valuers in Ghana, as current market data sources are tainted with issues of reliability. The purpose of this study is to examine the possibility of establishing property market data banks in Ghana, to help solve the market data problem faced by valuers.Design/methodology/approachThis study adopted a mixed-method approach consisting of the identification and review of literature, interviews with officials from the Lands Valuation Division of the Lands Commission and a questionnaire survey of property valuers.FindingsThe study finds that it is possible for property market data banks to be established, and in the absence of facilitating legislation, partnerships among various stakeholders are the best way of achieving this. The study identifies the lack of initiative and the lack of partnerships among the various stakeholders inter alia as the major factors limiting the establishment of property market data banks. The findings imply a need for stakeholders to take initiative to establish a property market data bank aimed at improving the quality and reliability of market data to enhance the valuation practice.Originality/valueThe study asserts the possibility of creating a property market data bank in Ghana, notwithstanding the limiting factors. The findings will provide a basis for relevant institutions and agencies to take cooperative action for the establishment of property market data banks, towards enhancing the valuation practice in Ghana as well as in other developing countries. The study will also prompt research into various tools and mechanisms to be adopted towards the establishment of property market data banks through participatory means.