The h-Integrability and the Weak Laws of Large Numbers for Arrays

In this paper, the concept of weak laws of large numbers for arrays (WLLNFA) is studied, and a new notion of uniform integrability referred to as h-integrability is introduced as a condition for WLLNFA in obtaining the main results

On a Survey of Uniform Integrability of Sequences of Random Variables

This paper presents explicitly a survey of uniformly integrable sequences of random variables. We also study extensively several cases and conditions required for uniform integrability, with the establishment of some new conditions needed for the generalization of the earlier results obtained by many scholars and researchers, noting the links between uniform integrability and pointwise convergence of a class of polynomial functions on conditional based

Analytic and Numerical Solutions of Time-Fractional Linear Schrödinger Equation

Fractional Schrödinger equation is a basic equation in fractional quantum mechanics. In this paper, we consider both analytic and numerical solutions of time-fractional linear Schrödinger Equations. This is done via a proposed semi-analytical method upon the modification of the classical Differential Transformation Method (DTM). Some illustrative examples are used; the results obtained converge faster to their exact forms. This shows that this modified version is very efficient, and reliable; as less computational work is involved, even without given up accuracy. Therefore, it is strongly recommended for both linear and nonlinear time-fractional partial differential equations (PDEs) with applications in other areas of applied sciences, management, and finance

Development of a Proactive Fault Diagnosis for Critical System

Large-scale network environments, such as the Internet, are characterized by the presence of various devices connected at various remote locations. There is a scenario of main office connected to different branch offices in another town and cities, with the presence of central administrative system at the main office. Any problem at branches is reported to the main office, due to availability of enough resources there. However, few support tools have been developed to allow the administrators at the central office to remotely control and monitor the computers at the branches. Even, in local area network environment, diagnosing the computers on the network is always a big problem for the administrator, as he/she moves from one computer to another, running the diagnostic program and collecting report for each machine tested. This is strenuous and time consuming. To help address these problems, I have employed the concept of mobile agent to design an architecture that can remotely perform various checks and tests on computers on network, and report its findings to the server administrator as central location. This architecture was implemented with Java, using Jini lookup service to establish communication between the computers. The agent tasks were implemented in C programming language. The result of this research work shows that the use of mobile agent for remote maintenance of computers on network was found to provide an improved, efficient, and dynamic diagnostic management system. All the same, it has proven to be a substantive contributor to efficient network management

Gas Chromatography-Mass Spectrometric (GC-MS) Analysis of Ethanolic Extract of the Peel of Dioscorea bulbifera Linn (Air Potatoe)

The bioactive chemical compounds in the ethanolic extracts of the peel of Dioscorea bulbifera Linn, native to Nigeria was investigated and characterized using gas chromatography-mass spectrometric (GC-MS) analysis. The relatively high concentration of the phytochemicals in the peel of this tuber; saponin (32.28mg/g), terpenoid (22.90mg/g), cardiac glycoside (15.90mg/g), flavonoid (9.17mg/g), tannin (4.79mg/g) and phlobatannin (1.87mg/g), was the most attractive factors that triggered the present study. The GC-MS analysis of the ethanolic extract of the peel of D. bulbifera shows 4 prominent peaks as R-(-)-1,2-Propanediol (C3H8O2) with retention time of 6.103min and the highest peak area of 86.05%; 1-Methylhexylhydroperoxide (C7H16O2) with retention time of 42.567min and peak area of 5.57%; Cis-3-hexenyllactate (C9H16O3) with retention time of 45.395min and peak area of 5.01%; and Pyrrole (C4H5N) showed peak of 3.37% with retention time of 45.508min. Other less prominent peaks at other retention times included; 2-Nitro-Dimethylnitromethane (C3H7NO2) with retention time of 37.355min, Ethylenimine (C2H5N) with retention time of 42.665min, N-Formyl-N-Methyl-formamide (C3H5NO2) with retention time of 44.225min, and Guanidine (CH5N3) with retention 44.225min. This work which is the first-time report on the bioactive compounds in the organic crude extracts of Dioscorea bulbifera native to Nigeria, using the GC-MS, has however established the presence of quite number of chemical compounds in the peel of the tuber, to which their pharmacological activities could be attributed. The presence of these secondary metabolites in the peel of Dioscorea bulbifera, is hence, the major contributing factors behind its antimicrobial potential. Keywords: GC-MS, Dioscorea bulbifera, antimicrobial properties, bioactive compounds, ethanolic extrac

A Table Mounted Device for Cracking Dika Nut (Irvingia gabonensis)

A simply designed machine for cracking dika nut was fabricated. The nut is fed by hand inbetween a toggle mechanism comprising of the slider and a fixed block. Fracture mechanism was based on the deformation characteristics of dried dika nut under uni-axial compression. When actuated, the slider compresses the nutshell to failure along its line of symmetry. The experimental machine gave 100% cracking efficiency but with 24% kernel breakage in cracking sun-dried dika nut at 6.6% moisture content (w.b). The machine provides a viable and effective technique for safe dika kernel extraction

A table mounted device for cracking dika nut (Irvingia gabonensis)

A simply designed machine for cracking dika nut was fabricated. The nut is fed by hand inbetween a toggle mechanism comprising of the slider and a fixed block. Fracture mechanism was based on the deformation characteristics of dried dika nut under uni-axial compression. When actuated, the slider compresses the nutshell to failure along its line of symmetry. The experimental machine gave 100% cracking efficiency but with 24% kernel breakage in cracking sun-dried dika nut at 6.6% moisture content (w.b). The machine provides a viable and effective technique for safe dika kernel extraction

A Semi-Analytical Method for Solutions of a Certain Class of Second Order Ordinary Differential Equations

This paper presents the theory and applications of a new computational technique referred to as Differential Transform Method (DTM) for solving second order linear ordinary differential equations, for both homogeneous and nonhomogeneous cases. For the robustness and efficiency of the method, four examples are considered. The results indicate that the DTM is reliable and accurate when compared to the exact solutions of the solved problems

Some Methods of Numerical Solutions of Singular System of Transistor Circuits

In this paper, observer design in generalized state space also known as singular system of transistor circuits is solved using the Differential transform method (DTM) and the Picard iterative technique (PIT). The numerical results obtained via these methods converge rapidly to their associated exact solutions upon comparison. It is obvious that these results are in excellent agreement with those already in literature via other numerical methods. However, the DTM reveals the ease of application and fewer computations compared to other numerical methods. Whereas, the PIT requires the Lipschitzian continuity condition to be satisfied

The effect of spent engine oil on some vegetative parameters of Eichhornia crassipes

The effect of spent engine oil pollution on some vegetative parameters of Eichhornia crassipes was studied in a greenhouse for eight (8) weeks to evaluate the level of tolerance of E. crassipes to spent engine oil pollution, and to make recommendations on the use of E. crassipes for phytoremediation of spilled engine oil. Three levels of spent engine oil: 5 ml, 15 ml and 45 ml were applied to pollute the water culture container. A plant grown in an unpolluted medium served as the control. Results showed that there were significant (p<0.05) reductions in plant height, width of lamina, leaf area and petiole length of all the plants in polluted media compared with the control. Among the treatments, 15 ml treatment had minimal pollution effect on plant growth and produced the highest percentage flowering whereas 45 ml treatment gave the highest pollution effect on the plant, resulting in low percentage flowering. The growth of the vegetative parameters of plants cultured in both polluted and unpolluted water was enhanced by the application of fertilizer. It is recommended that E. crassipes be employed in phytoremediation trial experiments since the vegetative parameters studied were not adversely affected by spent engine oil when supplied with nutrients like NPK fertilizer