Abstract: In this paper, we study the semilocal convergence of
a fifth order iterative method using recurrence relation under the
assumption that first order Fréchet derivative satisfies the Hölder
condition. Also, we calculate the R-order of convergence and provide
some a priori error bounds. Based on this, we give existence and
uniqueness region of the solution for a nonlinear Hammerstein
integral equation of the second kind.
Abstract: The aim of this paper is to introduce the concepts of the (λ, μ)-intuitionistic fuzzy subgroups and (λ, μ)-intuitionistic fuzzy normal subgroups of groups with operators, and to investigate their properties and characterizations based on M-group homomorphism.
Abstract: We formulate and analyze a mathematical model
describing dynamics of the hypothalamus-pituitary-thyroid
homoeostatic mechanism in endocrine system. We introduce
to this system two types of couplings and delay. In our model,
feedback controls the secretion of thyroid hormones and delay
reflects time lags required for transportation of the hormones. The
influence of delayed feedback on the stability behaviour of the
system is discussed. Analytical results are illustrated by numerical
examples of the model dynamics. This system of equations describes
normal activity of the thyroid and also a couple of types of
malfunctions (e.g. hyperthyroidism).
Abstract: A relative efficiency is defined as Ridge Estimate in the general linear model. The relative efficiency is based on the Mean square error. In this paper, we put forward a parameter of Ridge Estimate and discussions are made on the relative efficiency between the ridge estimation and the General Ridge Estimate. Eventually, this paper proves that the estimation is better than the general ridge estimate, which is based on the MSE.
Abstract: Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.
Abstract: Modelling realized volatility with high-frequency returns is popular as it is an unbiased and efficient estimator of return volatility. A computationally simple model is fitting the logarithms of the realized volatilities with a fractionally integrated long-memory Gaussian process. The Gaussianity assumption simplifies the parameter estimation using the Whittle approximation. Nonetheless, this assumption may not be met in the finite samples and there may be a need to normalize the financial series. Based on the empirical indices S&P500 and DAX, this paper examines the performance of the linear volatility model pre-treated with normalization compared to its existing counterpart. The empirical results show that by including normalization as a pre-treatment procedure, the forecast performance outperforms the existing model in terms of statistical and economic evaluations.
Abstract: A loading factor performance is necessary for the modeling of centrifugal compressor gas dynamic performance curve. Measured loading factors are linear function of a flow coefficient at an impeller exit. The performance does not depend on the compressibility criterion. To simulate loading factor performances, the authors present two parameters: a loading factor at zero flow rate and an angle between an ordinate and performance line. The calculated loading factor performances of non-viscous are linear too and close to experimental performances. Loading factor performances of several dozens of impellers with different blade exit angles, blade thickness and number, ratio of blade exit/inlet height, and two different type of blade mean line configuration. There are some trends of influence, which are evident – comparatively small blade thickness influence, and influence of geometry parameters is more for impellers with bigger blade exit angles, etc. Approximating equations for both parameters are suggested. The next phase of work will be simulating of experimental performances with the suggested approximation equations as a base.
Abstract: In this paper, we extend the fuzzy subrings with operators to the (λ, μ)-fuzzy subrings with operators. And the concepts of the (λ, μ)-fuzzy subring with operators and (λ, μ)-fuzzy quotient ring with operators are gived, while their elementary properties are discussed.
Abstract: In this article, experimental situations are considered
where a main effects plan is to be used to study m two-level factors
using n runs which are partitioned into b blocks, not necessarily
of same size. Assuming the block sizes to be even for all blocks,
for the case n ≡ 2 (mod 4), optimal designs are obtained with
respect to type 1 and type 2 optimality criteria in the class of designs
providing estimation of all main effects orthogonal to the block
effects. In practice, such orthogonal estimation of main effects is
often a desirable condition. In the wider class of all available m two
level even sized blocked main effects plans, where the factors do not
occur at high and low levels equally often in each block, E-optimal
designs are also characterized. Simple construction methods based on
Hadamard matrices and Kronecker product for these optimal designs
are presented.
Abstract: This study optimized the design parameters of a cone loudspeaker as an example of high flexibility of the product design. We developed an acoustic analysis software program that considers the impact of damping caused by air viscosity. In sound reproduction, it is difficult to optimize each parameter of the loudspeaker design. To overcome the limitation of the design problem in practice, this study presents an acoustic analysis algorithm to optimize the design parameters of the loudspeaker. The material character of cone paper and the loudspeaker edge were the design parameters, and the vibration displacement of the cone paper was the objective function. The results of the analysis showed that the design had high accuracy as compared to the predicted value. These results suggested that although the parameter design is difficult, with experience and intuition, the design can be performed easily using the optimized design found with the acoustic analysis software.
Abstract: The aim of this work is to modelize the occlusion of a
person with temporomandibular disorders as an evolutionary equation
and approach its solution by the construction and characterizing
of discrete variational splines. To formulate the problem, certain
boundary conditions have been considered. After showing the
existence and the uniqueness of the solution of such a problem, a
convergence result of a discrete variational evolutionary spline is
shown. A stress analysis of the occlusion of a human jaw with
temporomandibular disorders by finite elements is carried out in
FreeFem++ in order to prove the validity of the presented method.
Abstract: We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).
Abstract: The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l10, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.
Abstract: In this paper, the definitions of the quaternion measure
and the quaternion vector measure are introduced. The relation
between the quaternion measure and the complex vector measure
as well as the relation between the quaternion linear functional and
the complex linear functional are discussed respectively. By using
these relations, the necessary and sufficient condition to determine
the quaternion vector measure is given.
Abstract: This paper is concerned with the development of a
fully implicit and purely Eulerian fluid-structure interaction method
tailored for the modeling of the large deformations of elastic
membranes in a surrounding Newtonian fluid. We consider a
simplified model for the mechanical properties of the membrane, in
which the surface strain energy depends on the membrane stretching.
The fully Eulerian description is based on the advection of a modified
surface tension tensor, and the deformations of the membrane are
tracked using a level set strategy. The resulting nonlinear problem
is solved by a Newton-Raphson method, featuring a quadratic
convergence behavior. A monolithic solver is implemented, and we
report several numerical experiments aimed at model validation and
illustrating the accuracy of the presented method. We show that
stability is maintained for significantly larger time steps.
Abstract: Calibration of Optical Time Domain Reflectometer (OTDR) has a crucial role for the accurate determination of fault locations and the accurate calculation of loss budget of long-haul optical fibre links during installation and repair. A comparison has been made between the Egyptian National Institute for Standards (NIS-Egypt) and the National Metrology institute of South Africa (NMISA-South Africa) for the calibration of an OTDR. The distance and the attenuation scales of a transfer OTDR have been calibrated by both institutes using their standards according to the standard IEC 61746-1 (2009). The results of this comparison have been compiled in this report.
Abstract: We present in this paper a fully implicit finite element
method tailored for the numerical modeling of inextensible fluidic
membranes in a surrounding Newtonian fluid. We consider a highly
simplified version of the Canham-Helfrich model for phospholipid
membranes, in which the bending force and spontaneous curvature
are disregarded. The coupled problem is formulated in a fully
Eulerian framework and the membrane motion is tracked using
the level set method. The resulting nonlinear problem is solved
by a Newton-Raphson strategy, featuring a quadratic convergence
behavior. A monolithic solver is implemented, and we report several
numerical experiments aimed at model validation and illustrating
the accuracy of the proposed method. We show that stability is
maintained for significantly larger time steps with respect to an
explicit decoupling method.
Abstract: This research is aimed to study a two-step iteration
process defined over a finite family of σ-asymptotically
quasi-nonexpansive nonself-mappings. The strong convergence
is guaranteed under the framework of Banach spaces with some
additional structural properties including strict and uniform
convexity, reflexivity, and smoothness assumptions. With similar
projection technique for nonself-mapping in Hilbert spaces, we
hereby use the generalized projection to construct a point within
the corresponding domain. Moreover, we have to introduce the use
of duality mapping and its inverse to overcome the unavailability
of duality representation that is exploit by Hilbert space theorists.
We then apply our results for σ-asymptotically quasi-nonexpansive
nonself-mappings to solve for ideal efficiency of vector optimization
problems composed of finitely many objective functions. We also
showed that the obtained solution from our process is the closest to
the origin. Moreover, we also give an illustrative numerical example
to support our results.
Abstract: This article considers the problem of evaluating
infinite-time (or finite-time) ruin probability under a given compound
Poisson surplus process by approximating the claim size distribution
by a finite mixture exponential, say Hyperexponential, distribution. It
restates the infinite-time (or finite-time) ruin probability as a solvable
ordinary differential equation (or a partial differential equation).
Application of our findings has been given through a simulation study.
Abstract: This paper analyzes fundamental ideas and concepts related to neural networks, which provide the reader a theoretical explanation of Long Short-Term Memory (LSTM) networks operation classified as Deep Learning Systems, and to explicitly present the mathematical development of Backward Pass equations of the LSTM network model. This mathematical modeling associated with software development will provide the necessary tools to develop an intelligent system capable of predicting the behavior of licensed users in wireless cognitive radio networks.