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Research Article Open Access

Governing the Filtration Process of Contractors to Insolvent Point in Construction Projects with Nmorcha (Threshold) Operator


There are recurrent literatures to show that contractors in the construction industry are going insolvent. As a crippling process, there are early signs leading to contractor’s insolvency. Conflicting literatures have documented causes of insolvency in construction project in an irregular calibration. This paper argues theoretically that those causes can be stabilized calibrated with a view to establishing a threshold point or the limiting point beyond which a contractor becomes insolvent. A conceptual theory was built on spherical harmonic polynomial for which a sector of the sphere representing an entire economic sphere was taken to represent the construction industry sector. The sectors’ investigation precipitated five (5) main causes of insolvency from five (5) significant unethical practices. These variables were subjected to an orthogonal 5 × 5 square matrix to derive a pseudodifferential operator matrix with Fredholm properties narrated in Athanasiadis et al. and Claeys’ boundary integral problems. The derived determinant was used to operate as Nmorcha operator (∇N) on the population variable that assumed a chaotic attribute under a normal distribution curve at the critical stressed boundary plane. The Nmorcha operator(∇N) as a determinant operand at the boundary point of the critical region fittered variables to the skew of accepted and reject domains. The filtration operation at the boundary point presented a value of e2i4 representing falsification of projects financial status (e2) arising from poor project cost control (i4). Beyond this point in the array of causes in the calibrated insolvency scale, the contractor becomes insolvent.

Definition of Terms

Nmorcha operator (∇N): A theoretical operator derived from the characteristics property of a sectorial polynomial (m=n) matrix of spherical harmonic function that operates filtration on functions with indeterminate or chaotic state!

Threshold operation: An operation performed on operand to obtain the value of a threshold function.

Threshold gate: A logic plane where a threshold operation is performed.

Threshold operator: A logic element that performs a threshold operation.

Threshold: The starting point for a new state or experience.

Boundary operator: a certain element that permits transition by gradient profiling at boundary plane of a space to either divides of a domain.

Determinant: The characteristic value of a group of variables that ascribes peculiarity and representative attribute to the variables.

Egwunatum I. Samuel

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