Abstract: The paper is devoted to stochastic analysis of finite
dimensional difference equation with dependent on ergodic Markov
chain increments, which are proportional to small parameter ". A
point-form solution of this difference equation may be represented
as vertexes of a time-dependent continuous broken line given on the
segment [0,1] with "-dependent scaling of intervals between vertexes.
Tending " to zero one may apply stochastic averaging and diffusion
approximation procedures and construct continuous approximation of
the initial stochastic iterations as an ordinary or stochastic Ito differential
equation. The paper proves that for sufficiently small " these
equations may be successfully applied not only to approximate finite
number of iterations but also for asymptotic analysis of iterations,
when number of iterations tends to infinity.
Abstract: Modeling of a heterogeneous industrial fixed bed
reactor for selective dehydrogenation of heavy paraffin with Pt-Sn-
Al2O3 catalyst has been the subject of current study. By applying
mass balance, momentum balance for appropriate element of reactor
and using pressure drop, rate and deactivation equations, a detailed
model of the reactor has been obtained. Mass balance equations have
been written for five different components. In order to estimate
reactor production by the passage of time, the reactor model which is
a set of partial differential equations, ordinary differential equations
and algebraic equations has been solved numerically.
Paraffins, olefins, dienes, aromatics and hydrogen mole percent as
a function of time and reactor radius have been found by numerical
solution of the model. Results of model have been compared with
industrial reactor data at different operation times. The comparison
successfully confirms validity of proposed model.
Abstract: As days go by, we hear more and more about HIV,
Ebola, Bird Flu and other dreadful viruses which were unknown a
few decades ago. In both detecting and fighting viral diseases
ordinary methods have come across some basic and important
difficulties. Vaccination is by a sense introduction of the virus to the
immune system before the occurrence of the real case infection. It is
very successful against some viruses (e.g. Poliomyelitis), while
totally ineffective against some others (e.g. HIV or Hepatitis-C). On
the other hand, Anti-virus drugs are mostly some tools to control and
not to cure a viral disease. This could be a good motivation to try
alternative treatments. In this study, some key features of possible
physical-based alternative treatments for viral diseases are presented.
Electrification of body parts or fluids (especially blood) with micro
electric signals with adjusted current or frequency is also studied. The
main approach of this study is to find a suitable energy field, with
appropriate parameters that are able to kill or deactivate viruses. This
would be a lengthy, multi-disciplinary research which needs the
contribution of virology, physics, and signal processing experts. It
should be mentioned that all the claims made by alternative cures
researchers must be tested carefully and are not advisable at the time
being.
Abstract: The knowledge base of welding defect recognition is
essentially incomplete. This characteristic determines that the recognition results do not reflect the actual situation. It also has a further influence on the classification of welding quality. This paper is
concerned with the study of a rough set based method to reduce the influence and improve the classification accuracy. At first, a rough set
model of welding quality intelligent classification has been built. Both condition and decision attributes have been specified. Later on, groups
of the representative multiple compound defects have been chosen
from the defect library and then classified correctly to form the
decision table. Finally, the redundant information of the decision table has been reducted and the optimal decision rules have been reached. By this method, we are able to reclassify the misclassified defects to
the right quality level. Compared with the ordinary ones, this method
has higher accuracy and better robustness.
Abstract: Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.
Abstract: In the article the historical formation of interethnic and
interconfessional agreement policy in Kazakhstan and their
developing features at present time will be analyzed.
The successfully pursued by Kazakhstan at the present in the
direction of ethnic and confessional policy is regarded as a major
factor in promoting stability for the country.
Abstract: Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.
Abstract: We propose a reduced-ordermodel for the instantaneous
hydrodynamic force on a cylinder. The model consists of a system of
two ordinary differential equations (ODEs), which can be integrated
in time to yield very accurate histories of the resultant force and
its direction. In contrast to several existing models, the proposed
model considers the actual (total) hydrodynamic force rather than its
perpendicular or parallel projection (the lift and drag), and captures
the complete force rather than the oscillatory part only. We study
and provide descriptions of the relationship between the model
parameters, evaluated utilizing results from numerical simulations,
and the Reynolds number so that the model can be used at any
arbitrary value within the considered range of 100 to 500 to provide
accurate representation of the force without the need to perform timeconsuming
simulations and solving the partial differential equations
(PDEs) governing the flow field.
Abstract: Fluid flow and heat transfer of vertical full cone
embedded in porous media is studied in this paper. Nonlinear
differential equation arising from similarity solution of inverted cone
(subjected to wall temperature boundary conditions) embedded in
porous medium is solved using a hybrid neural network- particle
swarm optimization method.
To aim this purpose, a trial solution of the differential equation is
defined as sum of two parts. The first part satisfies the initial/
boundary conditions and does contain an adjustable parameter and
the second part which is constructed so as not to affect the
initial/boundary conditions and involves adjustable parameters (the
weights and biases) for a multi-layer perceptron neural network.
Particle swarm optimization (PSO) is applied to find adjustable
parameters of trial solution (in first and second part). The obtained
solution in comparison with the numerical ones represents a
remarkable accuracy.
Abstract: In the present study, a procedure was developed to
determine the optimum reaction rate constants in generalized
Arrhenius form and optimized through the Nelder-Mead method. For
this purpose, a comprehensive mathematical model of a fixed bed
reactor for dehydrogenation of heavy paraffins over Pt–Sn/Al2O3
catalyst was developed. Utilizing appropriate kinetic rate expressions
for the main dehydrogenation reaction as well as side reactions and
catalyst deactivation, a detailed model for the radial flow reactor was
obtained. The reactor model composed of a set of partial differential
equations (PDE), ordinary differential equations (ODE) as well as
algebraic equations all of which were solved numerically to
determine variations in components- concentrations in term of mole
percents as a function of time and reactor radius. It was demonstrated
that most significant variations observed at the entrance of the bed
and the initial olefin production obtained was rather high. The
aforementioned method utilized a direct-search optimization
algorithm along with the numerical solution of the governing
differential equations. The usefulness and validity of the method was
demonstrated by comparing the predicted values of the kinetic
constants using the proposed method with a series of experimental
values reported in the literature for different systems.
Abstract: The possibilities of mobile technology generate new
demands for vocational teacher trainers to transform their approach
to work and to incorporate its usage into their ordinary educational
practice. This paper presents findings of a focus discussion group
(FDG) session on the usage of iPads within a school of vocational
teacher education (SoVTE). It aims to clarify how the teacher
trainers are using iPads and what has changed in their work during
the usage of iPads. The analytical framework bases on content
analysis and expansive learning cycle. It was not only found what
kind of a role iPads played in their daily practices but it brought also
into attention how a cultural change regarding the usage of social
media and mobile technology was desperately needed in the whole
work community. Thus, the FGD was abducted for developing the
knowledge practices of the community of the SoVTE.
Abstract: Current spectrums of a high power induction machine was calculated for the cases of full symmetry, static and dynamic eccentricity. The calculations involve integration of 93 electrical plus four mechanical ordinary differential equations. Electrical equations account for variable inductances affected by slotting and eccentricities. The calculations were followed by Fourier analysis of the stator currents in steady state operation. The paper presents the stator current spectrums in full symmetry, static and dynamic eccentricity cases, and demonstrates the harmonics present in each case. The effect of dynamic eccentricity is demonstrating via comparing the current spectrums related to dynamic eccentricity cases with the full symmetry one. The paper includes one case study, refers to dynamic eccentricity, to present the spectrum of the measured current and demonstrate the existence of the harmonics related to dynamic eccentricity. The zooms of current spectrums around the main slot harmonic zone are included to simplify the comparison and prove the existence of the dynamic eccentricity harmonics in both calculated and measured current spectrums.
Abstract: The present contribution deals with the
thermophoretic deposition of nanoparticles over a rapidly rotating
permeable disk in the presence of partial slip, magnetic field, thermal
radiation, thermal-diffusion, and diffusion-thermo effects. The
governing nonlinear partial differential equations such as continuity,
momentum, energy and concentration are transformed into nonlinear
ordinary differential equations using similarity analysis, and the
solutions are obtained through the very efficient computer algebra
software MATLAB. Graphical results for non-dimensional
concentration and temperature profiles including thermophoretic
deposition velocity and Stanton number (thermophoretic deposition
flux) in tabular forms are presented for a range of values of the
parameters characterizing the flow field. It is observed that slip
mechanism, thermal-diffusion, diffusion-thermo, magnetic field and
radiation significantly control the thermophoretic particles deposition
rate. The obtained results may be useful to many industrial and
engineering applications.
Abstract: The concentrations of As, Hg, Co, Cr and Cd were
tested for each soil sample, and their spatial patterns were analyzed
by the semivariogram approach of geostatistics and geographical
information system technology. Multivariate statistic approaches
(principal component analysis and cluster analysis) were used to
identify heavy metal sources and their spatial pattern. Principal
component analysis coupled with correlation between heavy metals
showed that primary inputs of As, Hg and Cd were due to
anthropogenic while, Co, and Cr were associated with pedogenic
factors. Ordinary kriging was carried out to map the spatial patters of
heavy metals. The high pollution sources evaluated was related with
usage of urban and industrial wastewater. The results of this study
helpful for risk assessment of environmental pollution for decision
making for industrial adjustment and remedy soil pollution.
Abstract: In this paper, linear multistep technique using power
series as the basis function is used to develop the block methods
which are suitable for generating direct solution of the special second
order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some
grids and off – grid points to obtain two different three discrete
schemes, each of order (4,4,4)T, which were used in block form for
parallel or sequential solutions of the problems. The computational
burden and computer time wastage involved in the usual reduction of
second order problem into system of first order equations are avoided
by this approach. Furthermore, a stability analysis and efficiency of
the block method are tested on linear and non-linear ordinary
differential equations whose solutions are oscillatory or nearly
periodic in nature, and the results obtained compared favourably with
the exact solution.
Abstract: A steady two-dimensional magnetohydrodynamics
flow and heat transfer over a stretching vertical sheet influenced by
radiation and porosity is studied. The governing boundary layer
equations of partial differential equations are reduced to a system of
ordinary differential equations using similarity transformation. The
system is solved numerically by using a finite difference scheme
known as the Keller-box method for some values of parameters,
namely the radiation parameter N, magnetic parameter M, buoyancy
parameter l , Prandtl number Pr and permeability parameter K. The
effects of the parameters on the heat transfer characteristics are
analyzed and discussed. It is found that both the skin friction
coefficient and the local Nusselt number decrease as the magnetic
parameter M and permeability parameter K increase. Heat transfer
rate at the surface decreases as the radiation parameter increases.
Abstract: Due to growing environmental concerns of the cement
industry, alternative cement technologies have become an area of
increasing interest. It is now believed that new binders are
indispensable for enhanced environmental and durability
performance. Self-compacting Geopolymer concrete is an innovative
method and improved way of concreting operation that does not
require vibration for placing it and is produced by complete
elimination of ordinary Portland cement.
This paper documents the assessment of the compressive strength
and workability characteristics of low-calcium fly ash based selfcompacting
geopolymer concrete. The essential workability
properties of the freshly prepared Self-compacting Geopolymer
concrete such as filling ability, passing ability and segregation
resistance were evaluated by using Slump flow, V-funnel, L-box and
J-ring test methods. The fundamental requirements of high
flowability and segregation resistance as specified by guidelines on
Self Compacting Concrete by EFNARC were satisfied. In addition,
compressive strength was determined and the test results are included
here. This paper also reports the effect of extra water, curing time and
curing temperature on the compressive strength of self-compacting
geopolymer concrete. The test results show that extra water in the
concrete mix plays a significant role. Also, longer curing time and
curing the concrete specimens at higher temperatures will result in
higher compressive strength.
Abstract: In this paper, Steam Assisted Gravity Drainage
(SAGD) is introduced and its advantages over ordinary steam
injection is demonstrated. A simple simulation model is built and
three scenarios of natural production, ordinary steam injection, and
SAGD are compared in terms of their cumulative oil production and
cumulative oil steam ratio. The results show that SAGD can
significantly enhance oil production in quite a short period of time.
However, since the distance between injection and production wells
is short, the oil to steam ratio decreases gradually through time.
Abstract: Dengue, a disease found in most tropical and
subtropical areas of the world. It has become the most common
arboviral disease of humans. This disease is caused by any of four
serotypes of dengue virus (DEN1-DEN4). In many endemic
countries, the average age of getting dengue infection is shifting
upwards, dengue in pregnancy and infancy are likely to be
encountered more frequently. The dynamics of the disease is studied
by a compartmental model involving ordinary differential equations
for the pregnant, infant human and the vector populations. The
stability of each equilibrium point is given. The epidemic dynamic is
discussed. Moreover, the numerical results are shown for difference
values of dengue antibody.
Abstract: In this paper, parallelism in the solution of Ordinary
Differential Equations (ODEs) to increase the computational speed is
studied. The focus is the development of parallel algorithm of the two
point Block Backward Differentiation Formulas (PBBDF) that can
take advantage of the parallel architecture in computer technology.
Parallelism is obtained by using Message Passing Interface (MPI).
Numerical results are given to validate the efficiency of the PBBDF
implementation as compared to the sequential implementation.