APPLICATION OF LEAST ABSOLUTE SUM (LAS) DEFORMATION DETECTION METHOD USING COORDINATE DIFFERENCES FROM DIFFERENT OBSERVATIONAL CAMPAIGNS

Omogunloye O.G., Shittu O.G., Ipadeola A.O. and Ojegbile B.M

Department of Surveying and Geoinformatics Engineering

University of Lagos, Akoka-Lagos, Nigeria

E-mail:- gabolushohan@yahoo.com,

ABSTRACT

Deformation study is one of the main research fields in geodesy. Deformation study comprises measurement, processing and analysis phases, Measurement techniques can be divided into geotechnical, structural and geodetic methods. Geotechnical and structural methods uses equipment such as tiltmeters, Pseodolites, Laser scanners e.t.c to measure changes in length, inclination, relative height, strains e.t.c.  The geodetic methods are of two basic types, the reference and relative methods. This study focuses on the deformation analysis using the geodetic method known as the Least Absolute Sum Method. The method consists mainly of the independent adjustment of each of two epoch data, compatibility test on their a posteriori variances, followed by determination of Trend of movements for all the common points in the monitoring network. A triangulation network was designed (carefully selected) consisting of  45  YTT series second order control  points within the study area (Lagos State) resulting in  a total of  63 triangles,189 observations and 90 unknown parameters with 99 degrees of freedom. The network adjustment was done using the method of least squares observation equations. The estimated variance factors for the 2D (horizontal) network were 7.82989325645394e-08 and 7.7207636996395e-08 while 0.03944 and 0.052339 represent the estimated variance factors for the 1D (height) for the first and second epochs networks respectively. The compatibility of the two epoch data was tested with the variance ratio and compatibility test criteria. Actual displacement vectors were computed and transformed into the same computational base using S-transformation by Least Absolute Sum (LAS), stable and unstable points within the monitoring network were determined using Single Point displacement test, the displacement vector magnitude was computed for the two methods, represented graphically to indicate possible trend of movements that might have occurred. This study finds applications in studying the deformation of large engineering structures such as high rise buildings, bridges, dams, oil exploration zones, mining sites and land slide monitoring.

Keywords: Deformation, Analysis, Least Absolute Sum (LAS).

Table of Contents

Numerical Simulations on the Effect of Recycle and Time

Delayon the Cubic Autocatalytic Reaction Model

Yakubu, A. A., Yatim, M. Y.                                                                          1-12

Structural, Optical Absorbance and Transmittance Properties

of Silar Deposited Iron Lead Sulphide(Pbsfe) and

Ironcopper Sulphide(Cusfe)  Thin Films

Udeajah, V.N.  and Onah, D.U                                                                    13-33

The Role of Mathematics in the Development of Science &

Technology in Nigeria in the 21^st Century

Orngudwem, Terfa Iyorshe, Atindiga, Simon Terhemen and Kper,

Bartholomew Torkuma                                                                                34-46

Application of Least Absolute Sum (Las) Deformation Detection Method

Using Coordinate Differences From Different Observational Campaigns

Omogunloye O.G., Shittu O.G., Ipadeola A.O. and Ojegbile B.M                      47-78

STRUCTURAL, OPTICAL ABSORBANCE AND TRANSMITTANCE PROPERTIES OF SILAR DEPOSITED IRON LEAD SULPHIDE(PbSFe) AND IRONCOPPER SULPHIDE(CuSFe) THIN FILMS

Udeajah, V.N.  and Onah, D.U

Department of Industrial Physics

Ebonyi State University, Abakaliki

Email: vakadujah45 @ gmail.com, d_onah @yahoo.co.uk

ABSTRACT

The influence of iron on lead sulphide(PbS)  and Copper Sulphide (CuS) thin films deposited on glass substrates via successive ionic layer adsorption (SILAR) Technique using lead acetate,Pb(CH ₃ COO) ₂, Cupric Acetate Cu(CH ₃ COO) ₂,   thioacetamide ( S ₂ H ₅ NS),  Iron (II) Chloride dehydrate(Fe Cl ₂. 2H ₂ O), ethanol and ammonia by  in alkaline medium annealed between  283K and 500K was investigated.   The structural and morphological studies were performed by X-ray diffraction (XRD) Analysis and  scanning electron microscopy(SEM) respectively. The Uv-visible studies were done using spectrometer in the Technical University, Ibadan.   The XRD showed  films of cubic  crystalline   PbS thin films, cubic and face-centred crystalline  PbSFe thin films, cubic CuS thin film, hexagonal Cu ₂ S thin films and cubic and hexagonal crystalline natured CuSFe thin films with the preferential (111),(002)(004) (311) orientations.

THE ROLE OF MATHEMATICS IN THE DEVELOPMENT OF SCIENCE & TECHNOLOGY IN NIGERIA IN THE 21ST CENTURY

Omogunloye O.G., Shittu O.G., Ipadeola A.O. and Ojegbile B.M

Department of Surveying and Geoinformatics Engineering

University of Lagos, Akoka-Lagos, Nigeria

E-mail:- gabolushohan@yahoo.com,

ABSTRACT

Deformation study is one of the main research fields in geodesy. Deformation study comprises measurement, processing and analysis phases, Measurement techniques can be divided into geotechnical, structural and geodetic methods. Geotechnical and structural methods uses equipment such as tiltmeters, Pseodolites, Laser scanners e.t.c to measure changes in length, inclination, relative height, strains e.t.c.  The geodetic methods are of two basic types, the reference and relative methods. This study focuses on the deformation analysis using the geodetic method known as the Least Absolute Sum Method. The method consists mainly of the independent adjustment of each of two epoch data, compatibility test on their a posteriori variances, followed by determination of Trend of movements for all the common points in the monitoring network. A triangulation network was designed (carefully selected) consisting of  45  YTT series second order control  points within the study area (Lagos State) resulting in  a total of  63 triangles,189 observations and 90 unknown parameters with 99 degrees of freedom. The network adjustment was done using the method of least squares observation equations. The estimated variance factors for the 2D (horizontal) network were 7.82989325645394e-08 and 7.7207636996395e-08 while 0.03944 and 0.052339 represent the estimated variance factors for the 1D (height) for the first and second epochs networks respectively. The compatibility of the two epoch data was tested with the variance ratio and compatibility test criteria. Actual displacement vectors were computed and transformed into the same computational base using S-transformation by Least Absolute Sum (LAS), stable and unstable points within the monitoring network were determined using Single Point displacement test, the displacement vector magnitude was computed for the two methods, represented graphically to indicate possible trend of movements that might have occurred. This study finds applications in studying the deformation of large engineering structures such as high rise buildings, bridges, dams, oil exploration zones, mining sites and land slide monitoring.

Keywords: Deformation, Analysis, Least Absolute Sum (LAS).

NUMERICAL SIMULATIONS ON THE EFFECT OF RECYCLE AND TIME DELAYON THE CUBIC AUTOCATALYTIC REACTION MODEL

Yakubu, A. A.¹, Yatim, M. Y.²

¹Department of Mathematical Sciences, Ibrahim Badamasi Babangida University, Lapai, Nigeria;

²School of Mathematical Sciences, UniversitiSains Malaysia, P.O.Box 11800, Penang, Malaysia

email: aaishaty@ibbu.edu.ng

ABSTRACT

The effect of recycle and time delay on the cubic autocatalytic reaction model with linear decay in the absence of an autocatalyst in a continuous stirred tank reactor (CSTR) is studied. The model comprises a system of nonlinear ordinary differential equation which describes the autocatalytic behavior of two chemicals (a reactant and an autocatalyst) flowing into the CSTR. When the system is affected by recycle (using different values of ) without time delay , the concentration of the reactant decomposes until it reaches equilibrium while the concentration of the autocatalyst oscillates in an unstable pattern, but with increase in time  . However, when the system is affected by both recycle and time dalay, the concentrations oscillations is quite small and unstable for the autocatalyst.

Keywords: Continuous stirred tank reactor (CSTR),Nonlinear ODE, Recycle and Time delay