OPTIMIZATION ON ?n BY COGGINS-FIBONACCI METHOD

A   computational   procedure   called   Coggins-Fibonacci   method   for   the   optimization   of   unconstrained                     ?n        functions in       is developed. The method is found to be more efficient and converges faster than        either of the conventional Coggins or Fibonacci search methods.&nbsp

Existence and Uniqueness of Solution of an HIV/AIDS Model Considering Counseling, Vaccination and Antiretroviral Therapy (ART)

The control of HIV/AIDS is not yet over. Recently, the main method of control is the use of counseling and antiretroviral therapy (ART). In this study, a mathematical model of HIV/AIDS transmission dynamics considering counseling, vaccination and ART is formulated and the existence of its unique solution is investigated.Key words: HIV/AIDS, Mathematical Model, Existence and Uniqueness of Solution, Counselling, Vaccination, Antiretroviral Therap

A Class of Three Stage Implicit Rational Runge-Kutta Schemes for Approximation of Second Order Ordinary Differential Equations

In this paper, 3 – stage Implicit Rational Runge – Kutta methods are derived using Taylor and Binomial series expansion for the direct solution of general second order initial value problems of ordinary differential equations with constant step length. The basic properties of the developed method were investigated and found to be consistent and convergent. The efficiency of the method were tested on some numerical examples and found to give better approximations than the existing methods. Keywords: Java Programming Language, Implicit Rational Runge Kutta scheme, Second order equations

Ancient role of vasopressin/oxytocin-type neuropeptides as regulators of feeding revealed in an echinoderm.

BACKGROUND: Vasopressin/oxytocin (VP/OT)-type neuropeptides are well known for their roles as regulators of diuresis, reproductive physiology and social behaviour. However, our knowledge of their functions is largely based on findings from studies on vertebrates and selected protostomian invertebrates. Little is known about the roles of VP/OT-type neuropeptides in deuterostomian invertebrates, which are more closely related to vertebrates than protostomes. RESULTS: Here, we have identified and functionally characterised a VP/OT-type signalling system comprising the neuropeptide asterotocin and its cognate G-protein coupled receptor in the starfish (sea star) Asterias rubens, a deuterostomian invertebrate belonging to the phylum Echinodermata. Analysis of the distribution of asterotocin and the asterotocin receptor in A. rubens using mRNA in situ hybridisation and immunohistochemistry revealed expression in the central nervous system (radial nerve cords and circumoral nerve ring), the digestive system (including the cardiac stomach) and the body wall and associated appendages. Informed by the anatomy of asterotocin signalling, in vitro pharmacological experiments revealed that asterotocin acts as a muscle relaxant in starfish, contrasting with the myotropic actions of VP/OT-type neuropeptides in vertebrates. Furthermore, in vivo injection of asterotocin had a striking effect on starfish behaviour-triggering fictive feeding where eversion of the cardiac stomach and changes in body posture resemble the unusual extra-oral feeding behaviour of starfish. CONCLUSIONS: We provide a comprehensive characterisation of VP/OT-type signalling in an echinoderm, including a detailed anatomical analysis of the expression of both the VP/OT-type neuropeptide asterotocin and its cognate receptor. Our discovery that asterotocin triggers fictive feeding in starfish provides important new evidence of an evolutionarily ancient role of VP/OT-type neuropeptides as regulators of feeding in animals

Robust decision making for a climate-resilient development of the agricultural sector in Nigeria.

Adaptation options that work reasonably well across an entire range of potential outcomes are shown to be preferable in a context of deep uncertainty. This is because robust practices that are expected to perform satisfactorily across the full range of possible future conditions, are preferable to those that are the best ones, but just in one specific scenario. Thus, using a Robust Decision Making Approach in Nigerian agriculture may increase resilience to climate change. To illustrate, the expansion of irrigation might be considered as a complementary strategy to conservation techniques and a shift in sowing/planting dates to enhance resilience of agriculture. However, given large capital expenditures, irrigation must consider climate trends and variability. Using historical climate records is insufficient to size capacity and can result in "regrets" when the investment is undersized/oversized, if the climate turns out to be drier/wetter than expected. Rather utilizing multiple climate outcomes to make decisions will decrease "regrets." This chapter summarizes the main results from a study titled "Toward climate-resilient development in Nigeria" funded by the Word Bank (See Cervigni et al. 2013)

Patterns and Perceptions of Climate Change in a Biodiversity Conservation Hotspot

Quantifying local people's perceptions to climate change, and their assessments of which changes matter, is fundamental to addressing the dual challenge of land conservation and poverty alleviation in densely populated tropical regions To develop appropriate policies and responses, it will be important not only to anticipate the nature of expected changes, but also how they are perceived, interpreted and adapted to by local residents. The Albertine Rift region in East Africa is one of the world's most threatened biodiversity hotspots due to dense smallholder agriculture, high levels of land and resource pressures, and habitat loss and conversion. Results of three separate household surveys conducted in the vicinity of Kibale National Park during the late 2000s indicate that farmers are concerned with variable precipitation. Many survey respondents reported that conditions are drier and rainfall timing is becoming less predictable. Analysis of daily rainfall data for the climate normal period 1981 to 2010 indicates that total rainfall both within and across seasons has not changed significantly, although the timing and transitions of seasons has been highly variable. Results of rainfall data analysis also indicate significant changes in the intra-seasonal rainfall distribution, including longer dry periods within rainy seasons, which may contribute to the perceived decrease in rainfall and can compromise food security. Our results highlight the need for fine-scale climate information to assist agro-ecological communities in developing effective adaptive management

Two-step rational cononical function in the numerical integration of initial value problems in ordinary differential equation

This work concerns the approximation of the numerical solution of Value Problem (IVP) by rational interpolants. Cononical polynomials were used as the rational interpolants. By collocation, an explicit nonlinerar two-step scheme is obtained. Numerical examples are provided to demonstrate the performance of the scheme. The results obtained were found to be quite comparable with those by existing schemes. Key Words: Collocation two-step scheme. [Global Jnl Mathematical Sci Vol.2(1) 2003: 1-8

A New Numerical Integrator for the Solution of Initial Value Problems in Ordinary Differential Equations. The Pacific

ABSTRACT This research paper presents the development, analysis, and implementation of a new numerical integrator capable of solving first order initial value problems in ordinary differential equations. The algorithm developed is based on a local representation of the theoretical solution ( ) y x to the initial value problem by a nonlinear interpolating function (comprising of the combination of polynomial, exponential and cyclometric functions). The integrator is further applied on sampled problems to generate numerical results. From the results obtained, the new numerical integrator can be said to be computationally reliable and ingenious

Bifurcation Analysis of a Mathematical Model for Tuberculosis Transmission

The total population of the model is divided into five mutually exclusive classes: Vaccinated V ( t), susceptible S ( t), latent Lt(t)infected It (t ) and Recovery Rt(t ). Invariant region of the model were obtained and the result shows that whenever, NT > ^/N , the population reduces asymptotically to the carrying capacity and whenever NT  <= ^/N , every solution with initial condition inohms remains in that region for t > 0, so the model is well posed in ohms. We obtained positivity of Solution, it shows that all the solutions of the system are all positive for all t > 0; disease free and endemic equilibrium of the model were obtained, more, also the model threshold parameter (Reproduction Number) was examined using next-generation operator method. The model result shows that diseases free equilibrium is local asymptotically stable at R0 < 1 and unstable at R0 > 1. we also tested to know if the system will exhibits a backward bifurcation and the result show that ^T = 0 correspond to disease free equilibrium point (PDE) and ^T > 0 correspond to a situation when the disease persists (endemic), then we applied transcriptical bifurcation and the result show that a > 0 and b > 0 hence backward bifurcation; we also obtained Hopf Bifurcation for the system and the result show that B = B(complement) and dT/dB != 0 which means that the susceptible, latent and Recovery have to be control or else the endemic will occur and finally sensitivity analysis of ROT with respect to the model parameters were carried out