Abstract: In this study integral form and new recursive formulas
for Favard constants and some connected with them numeric and
Fourier series are obtained. The method is based on preliminary
integration of Fourier series which allows for establishing finite
recursive representations for the summation. It is shown that the
derived recursive representations are numerically more effective than
known representations of the considered objects.
Abstract: In this paper, self-starting block hybrid method of
order (5,5,5,5)T is proposed for the solution of the special second
order ordinary differential equations with associated initial or
boundary conditions. The continuous hybrid formulations enable us
to differentiate and evaluate at some grids and off – grid points to
obtain four discrete schemes, 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 stiff ordinary differential equations,
and the results obtained compared favorably with the exact solution.
Abstract: In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.
Abstract: A block backward differentiation formula of uniform
order eight is proposed for solving first order stiff initial value
problems (IVPs). The conventional 8-step Backward Differentiation
Formula (BDF) and additional methods are obtained from the same
continuous scheme and assembled into a block matrix equation which
is applied to provide the solutions of IVPs on non-overlapping
intervals. The stability analysis of the method indicates that the
method is L0-stable. Numerical results obtained using the proposed
new block form show that it is attractive for solutions of stiff problems
and compares favourably with existing ones.
Abstract: Strict stability can present the rate of decay of the
solution, so more and more investigators are beginning to study the
topic and some results have been obtained. However, there are few
results about strict stability of stochastic differential equations. In
this paper, using Lyapunov functions and Razumikhin technique, we
have gotten some criteria for the strict stability of impulsive stochastic
functional differential equations with markovian switching.
Abstract: We used mathematical model to study the
transmission of dengue disease. The model is developed in which
the human population is separated into two populations, pregnant and
non-pregnant humans. The dynamical analysis method is used for
analyzing this modified model. Two equilibrium states are found and
the conditions for stability of theses two equilibrium states are
established. Numerical results are shown for each equilibrium state.
The basic reproduction numbers are found and they are compared by
using numerical simulations.
Abstract: In this paper we introduce some subspaces of fuzzy entire sequence space. Some general properties of these sequence spaces are discussed. Also some inclusion relation involving the spaces are obtained. Mathematics Subject Classification: 40A05, 40D25.
Abstract: Motivated by the recent work of Herbert, Hayen, Macaskill and Walter [Interval estimation for the difference of two independent variances. Communications in Statistics, Simulation and Computation, 40: 744-758, 2011.], we investigate, in this paper, new confidence intervals for the difference between two normal population variances based on the generalized confidence interval of Weerahandi [Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423): 899-905, 1993.] and the closed form method of variance estimation of Zou, Huo and Taleban [Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics 20: 172-180, 2009]. Monte Carlo simulation results indicate that our proposed confidence intervals give a better coverage probability than that of the existing confidence interval. Also two new confidence intervals perform similarly based on their coverage probabilities and their average length widths.
Abstract: The radius-of-curvature (ROC) defines the degree of
curvature along the centerline of a roadway whereby a travelling
vehicle must follow. Roadway designs must encompass ROC in
mitigating the cost of earthwork associated with construction while
also allowing vehicles to travel at maximum allowable design speeds.
Thus, a road will tend to follow natural topography where possible,
but curvature must also be optimized to permit fast, but safe vehicle
speeds. The more severe the curvature of the road, the slower the
permissible vehicle speed. For route planning, whether for urban
settings, emergency operations, or even parcel delivery, ROC is a
necessary attribute of road arcs for computing travel time.
It is extremely rare for a geo-spatial database to contain ROC. This
paper will present a procedure and mathematical algorithm to
calculate and assign ROC to a segment pair and/or polyline.
Abstract: A graph G is fractional k-covered if for each edge e of
G, there exists a fractional k-factor h, such that h(e) = 1. If k = 2,
then a fractional k-covered graph is called a fractional 2-covered
graph. The binding number bind(G) is defined as follows,
bind(G) = min{|NG(X)|
|X|
: ├ÿ = X Ôèå V (G),NG(X) = V (G)}.
In this paper, it is proved that G is fractional 2-covered if δ(G) ≥ 4
and bind(G) > 5
3 .
Abstract: In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.
Abstract: In this paper, we present some new upper bounds for
the spectral radius of iterative matrices based on the concept of
doubly α diagonally dominant matrix. And subsequently, we give
two examples to show that our results are better than the earlier ones.
Abstract: This paper studies the effect of time delay on stability
of mutualism population model with limited resources for both
species. First, the stability of the model without time delay is
analyzed. The model is then improved by considering a time delay in
the mechanism of the growth rate of the population. We analyze the
effect of time delay on the stability of the stable equilibrium point.
Result showed that the time delay can induce instability of the stable
equilibrium point, bifurcation and stability switches.
Abstract: This paper has, as its point of departure, the foundational
axiomatic theory of E. De Giorgi (1996, Scuola Normale
Superiore di Pisa, Preprints di Matematica 26, 1), based on two
primitive notions of quality and relation. With the introduction of
a unary relation, we develop a system totally based on the sole
primitive notion of relation. Such a modification enables a definition
of the concept of dynamic unary relation. In this way we construct a
simple language capable to express other well known theories such
as Robinson-s arithmetic or a piece of a theory of concatenation. A
key role in this system plays an abstract relation designated by “( )",
which can be interpreted in different ways, but in this paper we will
focus on the case when we can perform computations and obtain
results.
Abstract: This paper presents an algorithm for reconstructing phase and magnitude responses of the impulse response when only the output data are available. The system is driven by a zero-mean independent identically distributed (i.i.d) non-Gaussian sequence that is not observed. The additive noise is assumed to be Gaussian. This is an important and essential problem in many practical applications of various science and engineering areas such as biomedical, seismic, and speech processing signals. The method is based on evaluating the bicepstrum of the third-order statistics of the observed output data. Simulations results are presented that demonstrate the performance of this method.
Abstract: Let Xi be a Lacunary System, we established large
deviations inequality for Lacunary System. Furthermore, we gained
Marcinkiewicz Larger Number Law with dependent random variables
sequences.
Abstract: We propose a phenomenological model for the
process of polymer desorption. In so doing, we omit the usual
theoretical approach of incorporating a fictitious viscoelastic
stress term into the flux equation. As a result, we obtain a
model that captures the essence of the phenomenon of trapping
skinning, while preserving the integrity of the experimentally
verified Fickian law for diffusion. An appropriate asymptotic
analysis is carried out, and a parameter is introduced to represent
the speed of the desorption front. Numerical simulations are
performed to illustrate the desorption dynamics of the model.
Recommendations are made for future modifications of the
model, and provisions are made for the inclusion of experimentally
determined frontal speeds.
Abstract: In this article, we are dealing with a model consisting of a classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. The major problem is analyzed. The regular dynamics of the system is considered using analytical methods. In this case, we provide an approximate solution for this system using parameter-expansion method. Also, we find approximate values for frequencies of the system. In parameter-expansion method the solution and unknown frequency of oscillation are expanded in a series by a bookkeeping parameter. By imposing the non-secularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation. One iteration step provides an approximate solution which is valid for the whole solution domain.
Abstract: The mathematical equation for Separation of the
binary aqueous solution is developed by using the Spiegler- Kedem
theory. The characteristics of a B-9 hollow fibre module of Du Pont
are determined by using these equations and their results are
compared with the experimental results of Ohya et al. The agreement
between these results is found to be excellent.
Abstract: A gradient learning method to regulate the trajectories
of some nonlinear chaotic systems is proposed. The method is
motivated by the gradient descent learning algorithms for neural
networks. It is based on two systems: dynamic optimization system
and system for finding sensitivities. Numerical results of several
examples are presented, which convincingly illustrate the efficiency
of the method.