Russell developed his type theory to be more precise than naive set theory. In Russell’s theory of types, each "term" has a "type" and operations are restricted to terms of a specific type. In Principia Mathematica, published in 1910, Russell and Whitehead attempt to avoid Russell’s paradox by asserting a hierarchy of types, after which each entity (mathematical or other) is assigned a type. In this way, Russell created his ramified theory of types compounded with an axiom of reducibility. As his work progressed Russell relied on the axiom of reducibility, a hierarchy of predicates, as an answer to the impredicative definitions that arose when he first introduced his ramified theory.
Introduction: Most of the engineering problems are nonlinear and therefore some of them are solved using numerical methods and some are solved using the different analytic methods. One of semi-exact methods which does not need linearization or discretization is Adomian Decomposition Method (ADM) [see Bellman and Adomian ;Adomian(1994)]. .The objective of the decomposition method is to make physically realistic solutions of complex systems without the usual modeling and solution compromises to achieve tractability. This method is a powerful technique, which provides an efficient algorithm for analytic approximate solutions and numeric simulations for real-world applications in the applied science and engineering, particularly in the practical solution of the linear or nonlinear and deterministic or stochastic operator equations, including ordinary and partial differential equation, integral equations, integro-differential equations, etc. Adomian decomposition method has been employed by Gejji and Jafari  to obtain solutions of a system of fractional differential equations and also discussed the convergence of the method.
Ivan Pavlov theorized classical conditioning where in an experiment dogs associated food with the arrival of the laboratory assistant through learned behaviour through an external stimulus. BF Skinner coined the term ‘Radical Behaviourism’ which theorizes that all action is predetermined and not
There are one and two dimensional cutting stock problems. Based on the literature studies, the Russian economist, Kantorovich(1960) has given the first formulation of cutting stock problem. Next, Gilmore(1961) and Gomory(1963) described their delayed pattern generation technique for solving the one dimensional minimization problem using linear programming. BASIC MATHEMATICAL
One of the most widely used supply models has been the Nerlovean response model based on adaptive expectations hypothesis. The model was developed by Nerlove in 1958. The model endeavours to analyse the speed and adjustment level of actual acreage towards the desired level. The short and long-run elasticities of supply response with respect to changes in expected prices is estimated by the model. According to Nerlove (1958) as cited by Tchereni and Tchereni (2013) the model argues that producers respond to expected prices as opposed to actual prices and acreage response follows a partial adjustment hypothesis which means that full adjustment to desired cultivated area may not be possible in the short-run such that actual adjustment to area
2.2. Adsorption Kietics Much adsorption kinetic models have been approved to characterize the manner of batch biosorption processes in various experimental conditions. Kinetics of adsorption is one of the major characteristics defining the efficiency of adsorption. 2.2.1 Pseudo first order model The Lagergren rate equation can have been the first rate equation for the sorption in liquid /solid systems depending on solid efficiency. The Lagergren rate equation is the most excessively utilized rate equation for sorption of a solute from a liquid solution (Ho and Mckay,2000).
Logistic regression model has been widely used for researching issues in many industries, especially in predicting probability of bankruptcy and default risks of corporations and clients (in banking field). Among those researches, the work Ohlson (1980) could be considered to be outstanding. In his paper, Ohlson used logistic regression model to quantitatively measure and predict the probability of bankruptcy. His trend of work was later studied and upgraded by Zavgren (1985) and Zmijewski (1984). Although the multivariate discriminant analysis (MDA) was the dominating method in studying such fields, regression model arose with many advantages compared to the MDA.
In such cases distributed lag model may be suitable for measuring the farmer’s response behaviour. In the Nerlovian framework the long-run equilibrium supply Y_t^* is assumed to be a linear function of the expected price P_t^* Y_t^*=a+bP_t^*+U_t --------------------- (1) The expected price P_t^* is adjusted in each time period by a proportion
Literature Review In 1973, Fisher Black, Robert Merton, and Myron Scholes developed The Black Scholes model, which is one of the most important concepts in today’s financial works. The key idea of this model is to help investors to buy and sell the underlying asset in the right time with no risk. This model has some more assumptions aside from follow the normal distribution, they are no dividends are paid out during the life of the option, efficient markets, no commission, risk-free rate and volatility are
Forrester (1961) developed four steps to create a system dynamics model. The first step is the articulation of the problem: defining the purpose of modeling and identifying the entities, interactions and behaviors to highlight. The second step is to describe the causal relationships between these entities, by building the causal (or influence) diagram. The third step corresponds to the introduction of stock variables and flow in the system by building a stock flow diagram. The fourth step is to formulate simulation