Mathematical modelling is the process of formulating an abstract model
in terms of mathematical language to describe the complex behaviour of
a real system. Mathematical models are quantitative models and often
expressed in terms of ordinary differential equations and partial differential
equations. Mathematical models can also be statistical models,
fuzzy logic models and empirical relationships. In fact, any model description
using mathematical language can be called a mathematical
Mathematical Modeling I – preliminary is designed for undergraduate students. Two other followup
books, Mathematical Modeling II – advanced and Mathematical Modeling III – case studies in biology,
will be published. II and III will be designed for both graduate students and undergraduate students.
All the three books are independent and useful for study and application of mathematical modeling in
Knowing that the plant parameters can vary within their lower and upper bounds, this
parametric uncertainty is formulated as an additive perturbation in the transfer function
matrix. It is important to note that the controller be designed with respect to worst case
uncertainty for each λij. This can be achieved by performing an optimization procedure
given by (61) for 200 frequencies. Here an element by element uncertainty bound model is
used for the characterization of upper bound of the uncertainty matrix. Then wij , which
satisfies (62) for each λij is given in matrix form as,...
The modelling of mechanical systems provides engineers and students with the methods to model and understand mechanical systems by using both mathematical and computer-based tools. Written by an eminent authority in the field, this is the second of four volumes which provide engineers with a comprehensive resource on this cornerstone mechanical engineering subject.
Dealing with continuous systems, this book covers solid mechanics, beams, plates and shells.
The discrete wavelet transform (DWT) algorithms have a firm position in processing
of signals in several areas of research and industry. As DWT provides both octavescale
frequency and spatial timing of the analyzed signal, it is constantly used to solve
and treat more and more advanced problems. The DWT algorithms were initially
based on the compactly supported conjugate quadrature filters (CQFs). However, a
drawback in CQFs is due to the nonlinear phase effects such as spatial dislocations in
Single period market models are the most elementary market models.
Only a single period is considered. The beginning of the period is usually
denoted by the time t = 0 and the end of the period by time t = 1.
At time t = 0 stock prices, bond prices,possibly prices of other financial
assets or specific financial values are recorded and the financial agent
can choose his investment, often a portfolio of stocks and bond. At time
t = 1 prices are recorded again and the financial agent obtains a payoff
corresponding to the value of his portfolio at time t = 1....
With rapid advancements in computing power, computer modeling and simulations
have become an important complement to experimentations in many areas of research
as well as industrial applications. The Discrete Event Simulation (DES) method has
received widespread attention and acceptance by both researchers and practitioners in
recent years. The range of application of DES spans across many different disciplines
and research fields.
Road traffic microsimulations based on the individual motion of all the involved vehicles are now recognized as an important tool to describe, understand, and manage road traffic. Cellular automata (CA) are very efficient way to implement vehicle motion. CA is a methodology that uses a discrete space to represent the state of each element of a domain, and this state can be changed according to a transition rule.
A mathemalical model is presented that describes heat and moisture transfer during the holpressing of MDF. The model includes conduction of heat between the press platens and the central layer of the mattress, phase change of water from the adsorbed to the vapor state and the convective heat and mass transfer through the edges of the mattress. This approach results in a three-dimensional unsleady-state problem in which the properties of the wood fibers, water and the wood-water system are dependent on temperature, mattress moisture content and steam pressure.
Introduction to hydrodynamic modelling and
The present text introduces hydrodynamic modelling principles in the context of batch wet
granulation and coating systems and it reviews the latest achievements and proposals in the
scientific literature in this field. The text concerns primarily the Eulerian and the Lagrangian
modelling technique. In accordance with some of the latest published Ph.d. thesis in the field of
hydrodynamics modelling, the Lagrangian technique is divided into a soft-particle and a hardsphere
What is the relationship between syntax, prosody and phonetics? This paper argues for a declarative constraint-based theory, in which each step in a derivation adds diverse constraints to a pool. Some of these describe well formed objects in the feature structure domain, in terms of both syntactic and prosodic features. Some characterise the relative prominence of constituents as a partial order over some discrete domain (playing the role of metrical grid). Some are simultaneous equations in the reals, whose solutions represent the pitch level of phonetic objects - high and low tones....