The BCA
Bootstrap Confidence Intervals
of the True Correlation Coefficient
MUHAMAD SAFIIH
LOLA and MUSTAFA BIN MAMAT
Mathematics Department Faculty of Science and Technology
University College of Science and Technology
20310 Kuala Terengganu (MALAYSIA)
Abstract:The performances of these two estimates were investigated by
constructing the confidence interval of true correlation coefficient, r.
The BCA (bias corrected and accelerated) bootstrap confidence intervals,
which does not rely on the normality assumptions is used to construct the
interval. The result from the bootstrap technique agreed with the earlier
findings that the robust M-based correlation coefficient is slightly
better than the Pearson’s paper, we use Bootstrap method to obtain the
confidence intervals (C.I) of the population correlation coefficient and
to assess the properties of the Bias Corrected and Accelerated (BCA)
confidence intervals for the M-based and Pearson’s correlation
coefficient in both situations where the data is cleaned and data with an
outlier. In this study, only the robust M-estimator and the BCA bootstrap
confidence has been considered for estimating the value of the
corrtelation coefficient. Furthermore, the BCA bootstrap confidence
interval is used mainly for obtaining the confidence interval and it’s
confidence interval length.
Keywords:
Confidence Intervals, Bootstrap Method, Bias Corrected and Accelerated (BCA),
Pearson Correlation Coefficient, M-estimator, Outliers. |
Optimization
of process control variables with the use of hierarchical genetic fuzzy
control algorithm
S. R. Kannan
Indian Institute of Technology Madras (India)
Email: kannaniitm@mail.com
Abstract: In chemical plants the main components of information are
stored in the form of decision tables. In the functioning of the decision
tables, the output states are largely dependent on the internal states.
The internal states, in general, in most of the chemical plants are too
many and some of them are not compatible enough to give a proper output,
resulting in loss of time, engineering cost, and damage to the very
system. To overcome these problems we use hierarchical genetic fuzzy
control algorithms. Operability study is a method to study the decision
tables in a chemical plant. This method examines the safety of chemical
plants by systematically identifying every conceivable process deviations
and it can reduce the time and the engineering. The tools for the
operability study are guidewords, property words and decision tables.
Decision tables are a main concern in this operability study, because the
decision tables govern property words and guidewords. Component
information is stored in the form of decision tables. We describe HGFCA
method by the use of genetic algorithms to decision tables of operability
study. By using HGFCA, we improve the system performance with minimal
valid conditions in decision tables.
Keywords :
Genetic Algorithms; Fuzzy control; Decision tables; Operability study;
Membership functions. |
Properties
of harmonic convex functions
in the unit disc
S. M. Khairnar
Department of Mathematics, Anuradha College of Engineering,
Chikhli-443 201 Buldana (M.S.) (India)
Abstract: In this paper we introduced a new class KH(b, g)
of Harmonic univalent functions in the unit disc
E = {z; ½z½< 1} on the lines of Jahangiri1 and we have obtain various
properties such as coefficient condition, extreme points, distortion
bounds, Hadamard (convolution) and their related results. For the
functions f = h + /UntiOE13.JPG)
that are harmonic, orientation preserving and univalent in the open unit
disc E with the normalization,
h(z) = z + /UntiOE14.JPG) a
n Z n and g(z) = /UntiOE15.JPG) bn
Zn; ½b1½< 1
Key words :
Harmonic function, Univalent functions, Convex functions, Distortion
bounds. |
A general
method of determining nth root of a given
number - an elaboration
Meena Sharma
Department of Chemistry, University of Jammu, Jammu (India)
Abstract: Besides providing justification for the procedure adopted in
an earlier publication1, the paper presents the general method for
determining higher roots of a given number.
Keywords :
cube root, general method, higher numbers. |
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Heat
transfer in second order fluid flow between two
stationary naturally permeable disks in the presence of a magnetic
field
Dileep Singh Chauhan
and Ritu Ghiya
Department of Mathematics, University of Rajasthan,
Jaipur-302 004 (India)
Abstract: Heat transfer is considered in a second order electrically
conducting non-Newtonian fluid flow between two stationary naturally
permeable disks of very small permeability in the presence of a magnetic
field. Both the disks have been kept at constant but different
temperatures. The effects of nonNewtonian parameters, magnetic field and
the permeability of the porous medium are investigated on the velocity and
temperature fields. |
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Steady
laminar flow between parallel porous
discs when upper disc is rotating moderately
P. R. Sharma and
Seema Chawla
Department of Mathematics, University of Rajasthan
Jaipur-302004 (Raj.) (India)
Abstract: Steady laminar flow of an incompressible viscous fluid
between two parallel porous discs when the upper disc is rotating
moderately and the fluid is injected at uniform rate through both the
discs is investigated. The expressions of radial and transverse velocity
distributions are derived, discussed numerically and shown through Figures
2 and 3, respectively. Also the expressions of pressure coefficient and
skin-friction coefficient at the lower disc are obtained, discussed
numerically and presented through Figures 4 and 5, respectively. The
moment coefficient at the upper rotating disc is also derived and it’s
numerical values for various values of cross-flow Reynolds number and
rotation parameter. It is observed from Table 1 that the moment
coefficient decreases due to increase of rotation of the upper disc or
cross-flow Reynolds number. |
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On the
approximation of Fourier-Laguerre
expansion by (N,p,q) summability method
Shyam Lal and
Prem Narain Singh
Department Of Mathematics, Faculty of Science
University of Allahabad, Allahabad 211002 (India)
Abstract: In this paper on approximation of Fourier-Laguerre’s
expansion by (N,p,q) summability method has been established. This theorem
is generalization of several known result |
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Hydromagnetic
flow through a long vertical channel with transpiration cooling
R. C. Chaudhary and
bhupendra K. Sharma
Department of Mathematics, University of Rajasthan
JAIPUR-302004 (India)
Abstract: The three-dimensional convection MHD flow of a viscous
incompressible fluid confined in a long vertical channel, whose both the
sides are made of permeable plates, is discussed. The fluid is injected
from both the sides with a uniform velocity. A uniform magnetic field is
applied perpendicular to the flat plates. A set of nonlinear ordinary
differential equations results and these are solved analytically.
Expressions for the velocity and heat transfer are obtained. The effect of
magnetic field and injection on the results are reported.
Key Words: MHD,
Incompressible fluid, heat transfer, three dimensional. |
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Single
server poisson queueing model with mixture of exponential service time
distribution
P. Srinivasa Rao, K.
Srinivasa Rao1 and J. Lakshminarayana1
Department of Computer Science and Systems Engineering
1Department of Statistics,
Andhra University, Visakhapatnam-530 003 (India)
Abstract: A single server poison queueing model is developed with
the assumption that the service times follow a mixture of exponential
distribution. Using the imbedded Markov - Chain technique, the system
behaviour is analysed. The system characteristics namely, the average
number of customers in the system, variance of system size, waiting time
distribution etc. are derived. The sensitivity of the model with
respect to the parameters is studied through numerical values. It is
observed that mixing parameter has a tremendous influence on the system
behaviour. These models are much useful in data voice transmission,
computer communication systems, transportation systems etc. This
model also includes the M/M/1: µ model as particular case when the mixing
parameter p = 0 or 1.
Key words :
Mixture of Exponential distribution, Probability generating function, bulk
arrivals, imbedded Markov - Chain technique. |
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Speed Based
Dynamic Soft Handoff Technique in
Mobile Communication
Yogesh Chaba and
Dharminder Kumar1
Lecturer(CSE), GJU Hisar -125001 Haryana (India)
E-Mail : YOGESHCHABA@YAHOO.COM
1Chairman & Reader (CSE), GJU Hisar - 125001 Haryana (INDIA)
E-Mail : KUMAR_DK_O1@YAHOO.COM
Abstract: In this paper,
a new soft handoff priority algorithm is presented and a model is provided
for the analysis of proposed algorithm. Traffic characteristics of
non-priority and proposed dynamic priority method are compared and
analyzed.
In mobile communication,
mobile stations move from cell to cell, so handoff is essential for
seamless communication. There are two types of handoff: hard handoff and
soft handoff. In hard handoff a new channel is setup after the release of
old channel while in soft handoff, a new channel is established before
releasing old channel, which is make-before-break policy. Mobile Stations
in a soft handoff region use multiple radio channels and receive their
signal from multiple base stations simultaneously.
Handoff management is an
important aspect in the performance of cellular communication system
because user would not like to get his call terminated when he passes over
from one cell to another. Hence properly designed handoff procedures are
essential in maintaining the quality of a call in progress thus keeping
forced terminating probability as low as possible.
In our proposed soft
handoff scheme, it is assumed that speed and location of any mobile can be
estimated by either Global Positioning System, Beacons, Fast fading or
microsensors. On the basis of above information time left for forcible
termination of mobile in handoff region incoming toward any cell can be
calculated. Let we take this as Permissible waiting time Tp defined as the
time left within which the channel allocated to mobile from previous cell
will be deallocated due to going out of range. When a mobile enters into
multi-connection area handoff procedure gets initiated. If the handoff
attempt finds all channel in the target cell already allocated we consider
that it can be queued. Similarly all the incoming mobiles approaching a
particular cell which are presently communicating through their respective
source cell are added to the queue of that target cell. When a mobile gets
its services completed a channel become available to serve the next mobile
waiting in the queue. The waiting line model is developed for the
following queue discipline:
i) Non Priority Handoff
Algorithm.
ii) Proposed Priority Queuing Handoff Algorithm without Preemption.
iii) Proposed Dynamic Priority Queuing Handoff Algorithm with Preemption.
In non-priority system
mobiles are selected from the queue on FCFS basis, while in priority
system highest priority is given to mobile whose permissible waiting time
is minimum. With preemptive dynamic priority method the lower priority
mobile being served is preempted (ejected back into the q ueue) whenever a
higher priority mobile enters the queuing system, a channel is thereby
freed to begin serving the highest priority mobile in queue. When it
finish its service the next mobile to begin receiving service is selected
from the queue with next higher priority.
We have considered a system with an
unlimited waiting room having
constant arrival rate(l)
of mobiles incoming towards a particular cell seeking a channel and
interarrival time for each mobile is exponentially distributed with mean
rate of 1/l. The system provides for a maximum of c channels in any cell.
The time spent by each channel in serving the call is exponentially
distributed with mean service rate 1/µ. This is within the reach of
Birth-Death formulation for M/M/c model. The condition for ergodicity is :
l / cµ < l.
The normalized waiting time is calculated
mathematically for all the three models described above. To determine the
improvement in efficiency of the system, normalized waiting time is
compared for non-priority method and method proposed. Result shows that
proposed method can reduce waiting time and hence forced termination
probability. Results are improved further in dynamic preemptive priority
method. |
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Similarity
flows behind strong self-gravitating magneto-radiative cylindrical shock
waves in an inhomogeneous rotating atmosphere with an
exponential density distribution
Ashok Ganguly and
Shilpa Shinde
Department of Applied Mathematics and Computational Sciences
Shri G. S. Institute of Technology and Science 23, Park Road,
Indore-452003 (India)
Abstract: Similarity solutions describing the flow of a perfect gas
behind strong cylindrical shock waves propagating in a self-gravitating
magneto-radiative rotating atmosphere with an exponential density
distribution in both the direction of increasing and decreasing density
are investigated. The shock velocity and the total energy of the waves are
assumed to be variable and Planck’s diffusion approximation is taken
into account in the present problem. The influence of gravitational field
on the flow parameters have been studied with the help of graphs.
Key words :
self gravitating magneto-radiative rotating atmosphere, similarity flow,
Planck’s diffusion approximation, shock waves. |
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Bianchi
VI0 string cosmology with a scalar field
R. Bhattacharjee
and K. K. Baruah1
Department of Mathematics Gauhati University, Guwahati-781014 (India)
1Department of Mathematics North Gauhati College, Guwahati-781031(India)
Abstract: We shall study the anisotropic model of Bianchi VI0 universe
containing a self interacting scalar field with an exponential potential
of the form V(f) = eKf in the context of cosmic strings. Physical features
of this model are briefly discussed. |
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Dual
and Strong convergence theorems for nonexpansive mappings
B. K. Sharma amd
P. K. Mehta
School of Studies in Mathematics, Pt. Ravishankar Shukla
University, Raipur-492010 (India)
Abstract: The concept of almost-convergence is due to Loventz1: a
sequence (xn) in a Banach space X is almost convergent to a point xÎX if
and only if
/UntiOE16.JPG)
uniformly in i = 0,1,2,... .
.We also say that (tn)
in l¥ is said to be almost convergent if all of its Banach lmits agree. |
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An inventory
model with non-linear stock-dependent
consumption rate
Ashok Ganguly and
Manjusha Panwar
Department of Applied Mathematics
Shri G.S. Institute of Technology & Science, Indore - 3 (India)
Abstract: This note is concerned with an inventory model with
instantaneous stock replenishment and non-linear stock-dependent
consumption rate. This model is illustrated with a numerical example. |
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Stability
in the perturbed solutions of the restricted three body problem
A. K. Choudhary and
A. K. Sharma*
Department of Mathematics
A.P.S.M., College, Barauni L.N.M.U., Darbhanga, Bihar (India)
*Resrarch Scholar
Abstract: In this paper, the stability in the perturbed solution of
the restricted three body problem is examined by the solution obtained in
the variational equation of the generating system. |
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