Diagonally Implicit Block Backward Differentiation Formulas for Solving Ordinary Differential Equations 1.0 Introduction In mathematics‚ if y is a function of x‚ then an equation that involves x‚ y and one or more derivatives of y with respect to x is called an ordinary differential equation (ODE). The ODEs which do not have additive solutions are non-linear‚ and finding the solutions is much more sophisticated because it is rarely possible to represent them by elementary function in close
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Band broadening theory (Van Deemter equation) It is well recognized now that column band broadening originates from three main sources: 1. multiple path of an analyte through the column packing; 2. molecular diffusion; 3. effect of mass transfer between phases. In 1956 J.J. Van Deemter introduced the equation which combined all three sources and represented them as the dependence of the theoretical plate height (HETP) on the mobile phase linear velocity. Originally‚ it was introduced for gas
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CHEMICAL PARAMETERS OF FRESHWATERS Objectives At the end of this section‚ students should be able to 1. Distinguish between freshwaters and seawater in terms of ionic composition. 2. Describe the variation of ionic composition in natural freshwaters and other inland waters. 3. Explain the factors that contribute to such variation. 4. Describe Gibbs’ model that explains the major factors contributing to variation in chemical composition of inland waters. 5. Explain
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Three things are usually required for a chemical explosion: a chemical reaction that occurs very rapidly‚ a large increase in gas pressure‚ and a confined-reaction vessel in which the pressure of the gaseous products can increase to a point that the gases break violently out of the container. In this chemistry and physics science fair project‚ you will use the combustion of ethanol to provide energy for a small explosion. The chemical equation that describes the combustion of ethanol is shown below
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MOMENTS OF A RANDOM VARIABLE Definition: Let X be a rv with the range space Rx and let c be any known constant. Then the kth moment of X about the constant c is defined as Mk (X) = E[ (X c)k ]. (12) In the field of statistics only 2 values of c are of interest: c = 0 and c = . Moments about c = 0 are called origin moments and are denoted by k‚ i.e.‚ k = E(Xk )‚ where c = 0 has been inserted into equation (12). Moments about the population
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Coefficient of Linear Expansion Introduction With few exceptions materials expand somewhat when heated through a temperature range that does not produce a change in phase (i.e. melting‚ freezing‚ boiling etc.). The added heat increases the average amplitude of vibration of the atoms in the material‚ which increases the average separation between the atoms. Although this effect is small‚ it is very important in any application that involves using different materials in an environment where they
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Patterns within systems of Linear Equations HL Type 1 Maths Coursework Maryam Allana 12 Brook The aim of my report is to discover and examine the patterns found within the constants of the linear equations supplied. After acquiring the patterns I will solve the equations and graph the solutions to establish my analysis. Said analysis will further be reiterated through the creation of numerous similar systems‚ with certain patterns‚ which will aid in finding a conjecture. The hypothesis
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– The Constant Gardener In the article “The Constant Gardener: What the Movie Missed” by Sonia Shah‚ she talks about the issues and concerns of new drugs being tested on people in developing countries such as Latin America‚ Eastern Europe‚ Asia and Africa. In Shah’s essay she brings up two convincing arguments against these experiments. One argument Shah speaks on is that in the movie The Constant Gardener the seriousness of the possible danger in these experiments is not well depicted. She argues
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Global Variables This writing assignment will focus on global variables. A global variable is a variable every module in a program can see‚ meaning that the entire program is its scope (Gaddis‚ 2010). There are both advantages and disadvantages to using global variables and it is my intention to explore some of them here‚ starting with the disadvantages. There seems to be a lot to be said about the disadvantages of using global variables. First and foremost the scope itself can be a disadvantage
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2/20/2014 Frequently Used Equations - The Physics Hypertextbook Frequently Used Equations Mechanics velocity Δ s v= Δ t ds v= dt acceleration Δ v a= Δ t dv a= dt equations of motion v = 0+at v x =x0+v 0 +½ 2 t at weight W =m g momentum p =m v dry friction ƒ μ =N centrip. accel. v2 ac = r 2 ac =−ω r impulse J =F Δ t impulse–momentum F Δ= Δ t m v J =⌠ dt F ⌠ dt =Δ F p ⌡ kinetic energy potential energy ⌡ K =½ mv
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