Abstract: Breast skin-line estimation and breast segmentation is an important pre-process in mammogram image processing and computer-aided diagnosis of breast cancer. Limiting the area to be processed into a specific target region in an image would increase the accuracy and efficiency of processing algorithms. In this paper we are presenting a new algorithm for estimating skin-line and breast segmentation using fast marching algorithm. Fast marching is a partial-differential equation based numerical technique to track evolution of interfaces. We have introduced some modifications to the traditional fast marching method, specifically to improve the accuracy of skin-line estimation and breast tissue segmentation. Proposed modifications ensure that the evolving front stops near the desired boundary. We have evaluated the performance of the algorithm by using 100 mammogram images taken from mini-MIAS database. The results obtained from the experimental evaluation indicate that this algorithm explains 98.6% of the ground truth breast region and accuracy of the segmentation is 99.1%. Also this algorithm is capable of partially-extracting nipple when it is available in the profile.
Abstract: The modeling of sound radiation is of fundamental importance for understanding the propagation of acoustic waves and, consequently, develop mechanisms for reducing acoustic noise. The propagation of acoustic waves, are involved in various phenomena such as radiation, absorption, transmission and reflection. The radiation is studied through the linear equation of the acoustic wave that is obtained through the equation for the Conservation of Momentum, equation of State and Continuity. From these equations, is the Helmholtz differential equation that describes the problem of acoustic radiation. In this paper we obtained the solution of the Helmholtz differential equation for an infinite cylinder in a pulsating through free and homogeneous. The analytical solution is implemented and the results are compared with the literature. A numerical formulation for this problem is obtained using the Boundary Element Method (BEM). This method has great power for solving certain acoustical problems in open field, compared to differential methods. BEM reduces the size of the problem, thereby simplifying the input data to be worked and reducing the computational time used.
Abstract: Avalanche release of snow has been modeled in the present studies. Snow is assumed to be represented by semi-solid and the governing equations have been studied from the concept of continuum approach. The dynamical equations have been solved for two different zones [starting zone and track zone] by using appropriate initial and boundary conditions. Effect of density (ρ), Eddy viscosity (η), Slope angle (θ), Slab depth (R) on the flow parameters have been observed in the present studies. Numerical methods have been employed for computing the non linear differential equations. One of the most interesting and fundamental innovation in the present studies is getting initial condition for the computation of velocity by numerical approach. This information of the velocity has obtained through the concept of fracture mechanics applicable to snow. The results on the flow parameters have found to be in qualitative agreement with the published results.
Abstract: In this paper, the criteria of Ψ-eventual stability have been established for generalized impulsive differential systems of multiple dependent variables. The sufficient conditions have been obtained using piecewise continuous Lyapunov function. An example is given to support our theoretical result.
Abstract: The Goursat partial differential equation arises in
linear and non linear partial differential equations with mixed
derivatives. This equation is a second order hyperbolic partial
differential equation which occurs in various fields of study such as
in engineering, physics, and applied mathematics. There are many
approaches that have been suggested to approximate the solution of
the Goursat partial differential equation. However, all of the
suggested methods traditionally focused on numerical differentiation
approaches including forward and central differences in deriving the
scheme. An innovation has been done in deriving the Goursat partial
differential equation scheme which involves numerical integration
techniques. In this paper we have developed a new scheme to solve
the Goursat partial differential equation based on the Adomian
decomposition (ADM) and associated with Boole-s integration rule to
approximate the integration terms. The new scheme can easily be
applied to many linear and non linear Goursat partial differential
equations and is capable to reduce the size of computational work.
The accuracy of the results reveals the advantage of this new scheme
over existing numerical method.
Abstract: By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g t, 0 −τ x(t + s) dα(s) + e(t), some criteria to guarantee the existence of periodic solutions are obtained.
Abstract: This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a distributed piezoelectric actuators. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations.
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: In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.
Abstract: Nonlinear propagation of ion-acoustic waves in a selfgravitating
dusty plasma consisting of warm positive ions,
isothermal two-temperature electrons and negatively charged dust
particles having charge fluctuations is studied using the reductive
perturbation method. It is shown that the nonlinear propagation of
ion-acoustic waves in such plasma can be described by an uncoupled
third order partial differential equation which is a modified form of
the usual Korteweg-deVries (KdV) equation. From this nonlinear
equation, a new type of solution for the ion-acoustic wave is
obtained. The effects of two-temperature electrons, gravity and dust
charge fluctuations on the ion-acoustic solitary waves are discussed
with possible applications.
Abstract: In this paper the Differential Quadrature Method (DQM) is employed to study the coupled lateral-torsional free vibration behavior of the laminated composite beams. In such structures due to the fiber orientations in various layers, the lateral displacement leads to a twisting moment. The coupling of lateral and torsional vibrations is modeled by the bending-twisting material coupling rigidity. In the present study, in addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies of the beam. The governing differential equations of motion which form a system of three coupled PDEs are solved numerically using DQ procedure under different boundary conditions consist of the combinations of simply, clamped, free and other end conditions. The resulting natural frequencies and mode shapes for cantilever beam are compared with similar results in the literature and good agreement is achieved.
Abstract: The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.
Abstract: In this paper, a self starting two step continuous block
hybrid formulae (CBHF) with four Off-step points is developed using
collocation and interpolation procedures. The CBHF is then used to
produce multiple numerical integrators which are of uniform order
and are assembled into a single block matrix equation. These
equations are simultaneously applied to provide the approximate
solution for the stiff ordinary differential equations. The order of
accuracy and stability of the block method is discussed and its
accuracy is established numerically.
Abstract: This paper considers the development of a two-point
predictor-corrector block method for solving delay differential
equations. The formulae are represented in divided difference form
and the algorithm is implemented in variable stepsize variable order
technique. The block method produces two new values at a single
integration step. Numerical results are compared with existing
methods and it is evident that the block method performs very well.
Stability regions of the block method are also investigated.
Abstract: In this paper we present discretization and decomposition methods for a multi-component transport model of a chemical vapor deposition (CVD) process. CVD processes are used to manufacture deposition layers or bulk materials. In our transport model we simulate the deposition of thin layers. The microscopic model is based on the heavy particles, which are derived by approximately solving a linearized multicomponent Boltzmann equation. For the drift-process of the particles we propose diffusionreaction equations as well as for the effects of heat conduction. We concentrate on solving the diffusion-reaction equation with analytical and numerical methods. For the chemical processes, modelled with reaction equations, we propose decomposition methods and decouple the multi-component models to simpler systems of differential equations. In the numerical experiments we present the computational results of our proposed models.
Abstract: In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parameters for improved noise characteristics of the differential amplifier.
Abstract: Solutions are proposed for the central problem of estimating the reaction rate coefficients in homogeneous kinetics. The first is based upon the fact that the right hand side of a kinetic differential equation is linear in the rate constants, whereas the second one uses the technique of neural networks. This second one is discussed deeply and its advantages, disadvantages and conditions of applicability are analyzed in the mirror of the first one. Numerical analysis carried out on practical models using simulated data, and our programs written in Mathematica.
Abstract: The RK5GL3 method is a numerical method for solving
initial value problems in ordinary differential equations, and is
based on a combination of a fifth-order Runge-Kutta method and
3-point Gauss-Legendre quadrature. In this paper we describe an
effective local error control algorithm for RK5GL3, which uses local
extrapolation with an eighth-order Runge-Kutta method in tandem
with RK5GL3, and a Hermite interpolating polynomial for solution
estimation at the Gauss-Legendre quadrature nodes.
Abstract: In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.
Abstract: This paper analyses the unsteady, two-dimensional
stagnation point flow of an incompressible viscous fluid over a flat
sheet when the flow is started impulsively from rest and at the same
time, the sheet is suddenly stretched in its own plane with a velocity
proportional to the distance from the stagnation point. The partial
differential equations governing the laminar boundary layer forced
convection flow are non-dimensionalised using semi-similar
transformations and then solved numerically using an implicit finitedifference
scheme known as the Keller-box method. Results
pertaining to the flow and heat transfer characteristics are computed
for all dimensionless time, uniformly valid in the whole spatial region
without any numerical difficulties. Analytical solutions are also
obtained for both small and large times, respectively representing the
initial unsteady and final steady state flow and heat transfer.
Numerical results indicate that the velocity ratio parameter is found
to have a significant effect on skin friction and heat transfer rate at
the surface. Furthermore, it is exposed that there is a smooth
transition from the initial unsteady state flow (small time solution) to
the final steady state (large time solution).