Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations
Issue:
Volume 3, Issue 5, October 2014
Pages:
95-98
Received:
28 August 2014
Accepted:
13 September 2014
Published:
20 September 2014
Abstract: Oscillation criteria for a class of second order neutral delay differential equations of the form [c(t)((x(t)+p(t)x(t-τ))^' )^α ]^'+q(t)f(x(t-σ) )=0,t≥t_0 is studied. By using first and second mean value theorem of integrals, the new sufficient condition is obtained and the corresponding result what was already obtained is generalized by the result in this paper.
Abstract: Oscillation criteria for a class of second order neutral delay differential equations of the form [c(t)((x(t)+p(t)x(t-τ))^' )^α ]^'+q(t)f(x(t-σ) )=0,t≥t_0 is studied. By using first and second mean value theorem of integrals, the new sufficient condition is obtained and the corresponding result what was already obtained is generalized by the result...
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On Differential Growth Equation to Stochastic Growth Model Using Hyperbolic Sine Function in Height/Diameter Modeling of Pines
Oyamakin Samuel Oluwafemi,
Chukwu Angela Unna
Issue:
Volume 3, Issue 5, October 2014
Pages:
99-104
Received:
15 September 2014
Accepted:
30 September 2014
Published:
10 October 2014
Abstract: Richrads growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richards growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richards growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richards nonlinear growth models better than the classical Richards growth model.
Abstract: Richrads growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richards growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction ...
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A Study on Compactness in Metric Spaces and Topological Spaces
Rabeya Akter,
Nour Mohammed Chowdhury,
Mohammad Safi Ullah
Issue:
Volume 3, Issue 5, October 2014
Pages:
105-112
Received:
16 September 2014
Accepted:
27 September 2014
Published:
20 October 2014
Abstract: Topology may be considered as an abstract study of the limit point concept. As such, it stems in part from recognition of the fact that many important mathematical topics depend entirely upon the properties of limit points. This study shows that compactness implies limit point compactness but not conversely and every compact space is locally compact but not conversely. This study also shows that compactness, limit point compactness and sequentially compactness are equivalent in metrizable spaces and the product of finitely many compact spaces is a locally compact space. This study introduce it here as an interesting application of the Tychonoff theorem.
Abstract: Topology may be considered as an abstract study of the limit point concept. As such, it stems in part from recognition of the fact that many important mathematical topics depend entirely upon the properties of limit points. This study shows that compactness implies limit point compactness but not conversely and every compact space is locally compac...
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