Mathematical study of BLUES function method for KdV Burgers’ and BBM-Burgers’ equations

We have previously developed a model-based method to compensate for the crosstalk in simultaneous acquisition of Tc-99m stress and Tl-201 rest myocardial perfusion SPECT. The purpose of this study is to evaluate the performance of this method in terms of a defect detection task using a mathematical Channelized Hoteling Observer (CHO) study. In this study we also optimized the iteration number in reconstruction of Tl distributions. A population of male and female NCAT phantoms were used to realistically model variation in patients. Both defect-free and defect-present data of Tc and Tl were simulated using the SimSET/PHG codes and our newly developed and validated angular response function (ARF) method to mimic simultaneous acquisition and separate acquisition. Poisson noise was modeled at clinically realistic levels. The Tl data were reconstructed using filtered backprojection (FBP) and ordered subset expectation maximization (OSEM) algorithms for up to 20 iterations with and without the model-based crosstalk compensation (MBC). CHO methodology and receiver operating characteristic (ROC) analysis were applied to short axis Tl images to obtain ROC curves and area under ROC curves (AUC). The AUC values were compared with those from separately acquired data reconstructed using FBP and OSEM algorithms. The results show that a relatively small number of iteration (/spl sim/3) is optimal for the postreconstruction filtering cutoff frequency of 0.16 pixel/sup -1/ used in this study. Also, the AUC values obtained with the MBC were significantly better than those without crosstalk compensation and those with the FBP reconstruction method applied to the separately acquired data.

In this research, we study the exact solutions of the Rosenau–Hyman equation, the coupled KdV system and the Burgers–Huxley equation using modified transformed rational function method. In this paper, the simplest equation is the Bernoulli equation. We are not only obtain the exact solutions of the aforementioned equations and system but also give some geometric descriptions of obtained solutions. All can be illustrated vividly by the given graphs.

defined for x > 0, u > 0. A saddle point of (1.2) is defined to be a point (x*, u*), x* > Q, u* > 0 such that +(x, u*) < +(x*, u*) _ +(x*, u) for all x _ 0, u ? 0. One of the Kuhn-Tucker results is that a saddle point of(1.2) provides a solution to (1.1). Under cer-eain additional regularity assumptions the equivalence of the saddle point problem and the program (1.1) has been shown [1], [10]. In particular, if the feasible set in (1.1) has an interior point (a nonnegative x such that g(x) < b),3 and if the objective function is concave and the constraint functions are convex, then x* is a solution to (1.1) if and only if there is a nonnegative u* such that (x*, u*) is a saddle point of (1.2). This is the so-called Kuhn-Tucker equivalence theorem of nonlinear programming. In this paper Lagrange multipliers are generalized from the usual constants to (possibly nonlinear) multiplier functions. This leads to the statement of several general equivalence results under quite weak assumptions. From a somewhat different point of view, Everett [4] drops differentiability assumptions and discusses a procedure for solving nonlinear programs in terms of

Composite finite elements for rigid-plastic analysis

About a rock thermochronologycal model: Laslett's law study and time equivalent method

About a rock thermochronologycal model: Laslett's law study andBtime equivalent method

This paper aims to develop an analytical study of heat propagation in biological tissues for constant and variable heat flux at the skin surface correlated with Hyperthermia treatment. In the present research work we have attempted to impose two unique kind of oscillating boundary condition relevant to practical aspect of the biomedical engineering while the initial condition is constructed as spatially dependent according to a real life situation. We have implemented Laplace’s Transform method (LTM) and Green Function (GFs) method to solve single phase lag (SPL) thermal wave model of bioheat equation (TWMBHE). This research work strongly focuses upon the non-invasive therapy by employing oscillating heat flux. The heat flux at the skin surface is considered as constant, sinusoidal, and cosine forms. A comparative study of the impact of different kinds of heat flux on the temperature field in living tissue explored that sinusoidal heat flux will be more effective if the time of therapeutic heating is high. Cosine heating is also applicable in Hyperthermia treatment due to its precision in thermal waveform. The result also emphasizes that accurate observation must be required for the selection of phase angle and frequency of oscillating heat flux. By possible comparison with the published experimental research work and published mathematical study we have experienced a difference in temperature distribution as 5.33% and 4.73%, respectively. A parametric analysis has been devoted to suggest an appropriate procedure of the selection of important design variables in viewpoint of an effective heating in hyperthermia treatment.

This work examines the fractional Sawada–Kotera and Korteweg–de Vries (KdV)–Burgers equations, which are essential models of nonlinear wave phenomena in many scientific domains. The homotopy perturbation transform method (HPTM) and the Yang transform decomposition method (YTDM) are two sophisticated techniques employed to derive analytical solutions. The proposed methods are novel and remarkable hybrid integral transform schemes that effectively incorporate the Adomian decomposition method, homotopy perturbation method, and Yang transform method. They efficiently yield rapidly convergent series-type solutions through an iterative process that requires fewer computations. The Caputo operator, used to express the fractional derivatives in the equations, provides a robust framework for analyzing the behavior of non-integer-order systems. To validate the accuracy and reliability of the obtained solutions, numerical simulations and graphical representations are presented. Furthermore, the results are compared with exact solutions using various tables and graphs, illustrating the effectiveness and ease of implementation of the proposed approaches for various fractional partial differential equations. The influence of the non-integer parameter on the solutions behavior is specifically examined, highlighting its function in regulating wave propagation and diffusion. In addition, a comparison with the natural transform iterative method and optimal auxiliary function method demonstrates that the proposed methods are more accurate than these alternative approaches. The results highlight the potential of YTDM and HPTM as reliable tools for solving nonlinear fractional differential equations and affirm their relevance in wave mechanics, fluid dynamics, and other fields where fractional-order models are applied.

The Burgers–Korteweg-de Vries (KdV) equation had been used as nonlinear modes for acoustic shock waves in dusty plasmas and so on. The variable transformation and the Jacobi elliptic function method was introduced to find the exact solution. In this paper, we will research into the saddle-node bifurcation and its control of the forced Burgers–KdV. By the transformation, PDEs are reduced to ODEs. Analyzing the frequency response function and its unstable region of the trivial steady state, we know that the saddle-node bifurcation which leads to jump and hysteresis may appear in the resonance response. Controllers for bifurcation modification purpose are designed in order to remove or delay the occurrence of jump and hysteresis phenomena. By means of numerical simulations we compare the uncontrolled system with the controlled system and clarify that controllers are adequate for the saddle-node bifurcation control of the forced Burgers–KdV equation.

We consider fractional-in-space analogues of Burgers equation and Korteweg-de Vries-Burgers equation on bounded domains. Namely, we establish sufficient conditions for finite-time blow-up of solutions to the mentioned equations. The obtained conditions depend on the initial value and the boundary conditions. Some examples are provided to illustrate our obtained results. In the proofs of our main results, we make use of the test function method and some integral inequalities.

Hyperbolic white noise functional solutions of Wick-type stochastic compound KdV–Burgers equations

The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations

The compound KdV–Burgers equation and combined KdV–mKdV equation are real physical models concerning many branches in physics. In this paper, applying the improved trigonometric function method to these equations, rich explicit and exact travelling wave solutions, which contain solitary-wave solutions, periodic solutions, and combined formal solitary-wave solutions, are obtained.

Mathematical study of fractal-fractional leptospirosis disease in human and rodent populations dynamical transmission

On the behavior of r- and ϑ-cracks in composite materials under thermal and mechanical loading