Abstract: A code has been developed in Mathematica using
Direct Simulation Monte Carlo (DSMC) technique. The code was
tested for 2-D air flow around a circular cylinder. Same geometry
and flow properties were used in FLUENT 6.2 for comparison. The
results obtained from Mathematica simulation indicated significant
agreement with FLUENT calculations, hence providing insight into
particle nature of fluid flows.
Abstract: Fractional Fourier Transform is a powerful tool,
which is a generalization of the classical Fourier Transform. This
paper provides a mathematical relation relating the span in Fractional
Fourier domain with the amplitude and phase functions of the signal,
which is further used to study the variation of quality factor with
different values of the transform order. It is seen that with the
increase in the number of transients in the signal, the deviation of
average Fractional Fourier span from the frequency bandwidth
increases. Also, with the increase in the transient nature of the signal,
the optimum value of transform order can be estimated based on the
quality factor variation, and this value is found to be very close to
that for which one can obtain the most compact representation. With
the entire mathematical analysis and experimentation, we consolidate
the fact that Fractional Fourier Transform gives more optimal
representations for a number of transform orders than Fourier
transform.
Abstract: The paper describes the futures trading and aims to
design the speculators trading strategy. The problem is formulated as
the decision making task and such as is solved. The solution of the
task leads to complex mathematical problems and the approximations
of the decision making is demanded. Two kind of approximation are
used in the paper: Monte Carlo for the multi-step prediction and
iteration spread in time for the optimization. The solution is applied to the real-market data and the results of the off-line experiments are
presented.
Abstract: The objective of the paper is to develop the forecast
model for the HW flows. The methodology of the research included
6 modules: historical data, assumptions, choose of indicators, data
processing, and data analysis with STATGRAPHICS, and forecast
models. The proposed methodology was validated for the case study
for Latvia. Hypothesis on the changes in HW for time period of
2010-2020 have been developed and mathematically described with
confidence level of 95.0% and 50.0%. Sensitivity analysis for the
analyzed scenarios was done. The results show that the growth of
GDP affects the total amount of HW in the country. The total amount
of the HW is projected to be within the corridor of – 27.7% in the
optimistic scenario up to +87.8% in the pessimistic scenario with
confidence level of 50.0% for period of 2010-2020. The optimistic
scenario has shown to be the least flexible to the changes in the GDP
growth.
Abstract: The upgrading of low quality crude natural gas (NG) is attracting interest due to high demand of pipeline-grade gas in recent years. Membrane processes are commercially proven technology for the removal of impurities like carbon dioxide from NG. In this work, cross flow mathematical model has been suggested to be incorporated with ASPEN HYSYS as a user defined unit operation in order to design the membrane system for CO2/CH4 separation. The effect of operating conditions (such as feed composition and pressure) and membrane selectivity on the design parameters (methane recovery and total membrane area required for the separation) has been studied for different design configurations. These configurations include single stage (with and without recycle) and double stage membrane systems (with and without permeate or retentate recycle). It is shown that methane recovery can be improved by recycling permeate or retentate stream as well as by using double stage membrane systems. The ASPEN HYSYS user defined unit operation proposed in the study has potential to be applied for complex membrane system design and optimization.
Abstract: In this paper two mathematical models for definition of gas accidental escape localization in the gas pipelines are suggested. The first model was created for leak localization in the horizontal branched pipeline and second one for leak detection in inclined section of the main gas pipeline. The algorithm of leak localization in the branched pipeline did not demand on knowledge of corresponding initial hydraulic parameters at entrance and ending points of each sections of pipeline. For detection of the damaged section and then leak localization in this section special functions and equations have been constructed. Some results of calculations for compound pipelines having two, four and five sections are presented. Also a method and formula for the leak localization in the simple inclined section of the main gas pipeline are suggested. Some results of numerical calculations defining localization of gas escape for the inclined pipeline are presented.
Abstract: Interaction effects of xanthan gum (XG), carboxymethyl
cellulose (CMC), and locust bean gum (LBG) on the flow properties
of oil-in-water emulsions were investigated by a mixture design
experiment. Blends of XG, CMC and LBG were prepared according
to an augmented simplex-centroid mixture design (10 points) and used
at 0.5% (wt/wt) in the emulsion formulations. An appropriate
mathematical model was fitted to express each response as a function
of the proportions of the blend components that are able to
empirically predict the response to any blend of combination of the
components. The synergistic interaction effect of the ternary
XG:CMC:LBG blends at approximately 33-67% XG levels was
shown to be much stronger than that of the binary XG:LBG blend at
50% XG level (p < 0.05). Nevertheless, an antagonistic interaction
effect became significant as CMC level in blends was more than 33%
(p < 0.05). Yield stress and apparent viscosity (at 10 s-1) responses
were successfully fitted with a special quartic model while flow
behaviour index and consistency coefficient were fitted with a full
quartic model (R2
adjusted ≥ 0.90). This study found that a mixture
design approach could serve as a valuable tool in better elucidating
and predicting the interaction effects beyond the conventional twocomponent
blends.
Abstract: Implicit equations play a crucial role in Engineering.
Based on this importance, several techniques have been applied to
solve this particular class of equations. When it comes to practical
applications, in general, iterative procedures are taken into account.
On the other hand, with the improvement of computers, other
numerical methods have been developed to provide a more
straightforward methodology of solution. Analytical exact approaches
seem to have been continuously neglected due to the difficulty
inherent in their application; notwithstanding, they are indispensable
to validate numerical routines. Lagrange-s Inversion Theorem is a
simple mathematical tool which has proved to be widely applicable to
engineering problems. In short, it provides the solution to implicit
equations by means of an infinite series. To show the validity of this
method, the tree-parameter infiltration equation is, for the first time,
analytically and exactly solved. After manipulating these series,
closed-form solutions are presented as H-functions.
Abstract: –In this paper the damage in clamped-free, clampedclamped and free-free beam are analyzed considering samples
without and with structural modifications. The damage location is
investigated by the use of the bispectrum and wavelet analysis. The
mathematical models are obtained using 2D elasticity theory and the
Finite Element Method (FEM). The numerical and experimental data
are approximated using the Particle Swarm Optimizer (PSO) method
and this way is possible to adjust the localization and the severity of
the damage. The experimental data are obtained through
accelerometers placed along the sample. The system is excited using
impact hammer.
Abstract: In this paper, Novel method, Particle Swarm Optimization (PSO) algorithm, based technique is proposed to estimate and analyze the steady state performance of self-excited induction generator (SEIG). In this novel method the tedious job of deriving the complex coefficients of a polynomial equation and solving it, as in previous methods, is not required. By comparing the simulation results obtained by the proposed method with those obtained by the well known mathematical methods, a good agreement between these results is obtained. The comparison validates the effectiveness of the proposed technique.
Abstract: Functional imaging procedures for the non-invasive assessment of tissue microcirculation are highly requested, but require a mathematical approach describing the trans- and intercapillary passage of tracer particles. Up to now, two theoretical, for the moment different concepts have been established for tracer kinetic modeling of contrast agent transport in tissues: pharmacokinetic compartment models, which are usually written as coupled differential equations, and the indicator dilution theory, which can be generalized in accordance with the theory of lineartime- invariant (LTI) systems by using a convolution approach. Based on mathematical considerations, it can be shown that also in the case of an open two-compartment model well-known from functional imaging, the concentration-time course in tissue is given by a convolution, which allows a separation of the arterial input function from a system function being the impulse response function, summarizing the available information on tissue microcirculation. Due to this reason, it is possible to integrate the open two-compartment model into the system-theoretic concept of indicator dilution theory (IDT) and thus results known from IDT remain valid for the compartment approach. According to the long number of applications of compartmental analysis, even for a more general context similar solutions of the so-called forward problem can already be found in the extensively available appropriate literature of the seventies and early eighties. Nevertheless, to this day, within the field of biomedical imaging – not from the mathematical point of view – there seems to be a trench between both approaches, which the author would like to get over by exemplary analysis of the well-known model.
Abstract: This paper proposes a meta-heuristic called Ant Colony Optimization to solve multi-objective production problems. The multi-objective function is to minimize lead time and work in process. The problem is related to the decision variables, i.e.; distance and process time. According to decision criteria, the mathematical model is formulated. In order to solve the model an ant colony optimization approach has been developed. The proposed algorithm is parameterized by the number of ant colonies and the number of pheromone trails. One example is given to illustrate the effectiveness of the proposed model. The proposed formulations; Max-Min Ant system are then used to solve the problem and the results evaluate the performance and efficiency of the proposed algorithm using simulation.
Abstract: This paper focuses on cost and profit analysis of
single-server Markovian queuing system with two priority classes. In
this paper, functions of total expected cost, revenue and profit of the
system are constructed and subjected to optimization with respect to
its service rates of lower and higher priority classes. A computing
algorithm has been developed on the basis of fast converging
numerical method to solve the system of non linear equations formed
out of the mathematical analysis. A novel performance measure of
cost and profit analysis in view of its economic interpretation for the
system with priority classes is attempted to discuss in this paper. On
the basis of computed tables observations are also drawn to enlighten
the variational-effect of the model on the parameters involved
therein.
Abstract: The use of the mechanical simulation (in particular the finite element analysis) requires the management of assumptions in order to analyse a real complex system. In finite element analysis (FEA), two modeling steps require assumptions to be able to carry out the computations and to obtain some results: the building of the physical model and the building of the simulation model. The simplification assumptions made on the analysed system in these two steps can generate two kinds of errors: the physical modeling errors (mathematical model, domain simplifications, materials properties, boundary conditions and loads) and the mesh discretization errors. This paper proposes a mesh adaptive method based on the use of an h-adaptive scheme in combination with an error estimator in order to choose the mesh of the simulation model. This method allows us to choose the mesh of the simulation model in order to control the cost and the quality of the finite element analysis.
Abstract: Symbolic Circuit Analysis (SCA) is a technique used
to generate the symbolic expression of a network. It has become a
well-established technique in circuit analysis and design. The
symbolic expression of networks offers excellent way to perform
frequency response analysis, sensitivity computation, stability
measurements, performance optimization, and fault diagnosis. Many
approaches have been proposed in the area of SCA offering different
features and capabilities. Numerical Interpolation methods are very
common in this context, especially by using the Fast Fourier
Transform (FFT). The aim of this paper is to present a method for
SCA that depends on the use of Wavelet Transform (WT) as a
mathematical tool to generate the symbolic expression for large
circuits with minimizing the analysis time by reducing the number of
computations.
Abstract: The study on the tree growth for four species groups of commercial timber in Koh Kong province, Cambodia-s tropical rainforest is described. The simulation for these four groups had been successfully developed in the 5-year interval through year-60. Data were obtained from twenty permanent sample plots in the duration of thirteen years. The aim for this study was to develop stand table simulation system of tree growth by the species group. There were five steps involved in the development of the tree growth simulation: aggregate the tree species into meaningful groups by using cluster analysis; allocate the trees in the diameter classes by the species group; observe the diameter movement of the species group. The diameter growth rate, mortality rate and recruitment rate were calculated by using some mathematical formula. Simulation equation had been created by combining those parameters. Result showed the dissimilarity of the diameter growth among species groups.
Abstract: Avoiding learning failures in mathematics e-learning environments caused by emotional problems in students with autism has become an important topic for combining of special education with information and communications technology. This study presents an adaptive emotional adjustment model in mathematics e-learning for students with autism, emphasizing the lack of emotional perception in mathematics e-learning systems. In addition, an emotion classification for students with autism was developed by inducing emotions in mathematical learning environments to record changes in the physiological signals and facial expressions of students. Using these methods, 58 emotional features were obtained. These features were then processed using one-way ANOVA and information gain (IG). After reducing the feature dimension, methods of support vector machines (SVM), k-nearest neighbors (KNN), and classification and regression trees (CART) were used to classify four emotional categories: baseline, happy, angry, and anxious. After testing and comparisons, in a situation without feature selection, the accuracy rate of the SVM classification can reach as high as 79.3-%. After using IG to reduce the feature dimension, with only 28 features remaining, SVM still has a classification accuracy of 78.2-%. The results of this research could enhance the effectiveness of eLearning in special education.
Abstract: Buyer coalition with a combination of items is a group of buyers joining together to purchase a combination of items with a larger discount. The primary aim of existing buyer coalition with a combination of items research is to generate a large total discount. However, the aim is hard to achieve because this research is based on the assumption that each buyer completely knows other buyers- information or at least one buyer knows other buyers- information in a coalition by exchange of information. These assumption contrast with the real world environment where buyers join a coalition with incomplete information, i.e., they concerned only with their expected discounts. Therefore, this paper proposes a new buyer community coalition formation with a combination of items scheme, called the Community Compromised Combinatorial Coalition scheme, under such an environment of incomplete information. In order to generate a larger total discount, after buyers who want to join a coalition propose their minimum required saving, a coalition structure that gives a maximum total retail prices is formed. Then, the total discount division of the coalition is divided among buyers in the coalition depending on their minimum required saving and is a Pareto optimal. In mathematical analysis, we compare concepts of this scheme with concepts of the existing buyer coalition scheme. Our mathematical analysis results show that the total discount of the coalition in this scheme is larger than that in the existing buyer coalition scheme.
Abstract: The modern queueing theory is one of the powerful
tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. The paper is designated to the analysis of queueing
systems, arising in the networks theory and communications theory
(called open queueing network). The authors of this research in the
sphere of queueing theory present the theorem about the law of the iterated logarithm (LIL) for the queue length of a customers in open
queueing network and its application to the mathematical model of
the open message switching system.
Abstract: Recent articles have addressed the problem to construct the confidence intervals for the mean of a normal distribution where the parameter space is restricted, see for example Wang [Confidence intervals for the mean of a normal distribution with restricted parameter space. Journal of Statistical Computation and Simulation, Vol. 78, No. 9, 2008, 829–841.], we derived, in this paper, analytic expressions of the coverage probability and the expected length of confidence interval for the normal mean when the whole parameter space is bounded. We also construct the confidence interval for the normal variance with restricted parameter for the first time and its coverage probability and expected length are also mathematically derived. As a result, one can use these criteria to assess the confidence interval for the normal mean and variance when the parameter space is restricted without the back up from simulation experiments.