This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms.

We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of anisotropic diffusion. By incorporating edges found at multiple scales via an adaptive edge detector-based indicator function, the proposed scheme removes noise while respecting salient boundaries. We create a smooth transition region around probable edges found and reduce the diffusion rate near it by a gradient-based diffusion coefficient. In contrast to the previous anisotropic diffusion schemes, we prove the well-posedness of our scheme in the space of bounded variation. The proposed scheme is general in the sense that it can be used with any of the existing diffusion equations. Numerical simulations on noisy images show the advantages of our scheme when compared to other related schemes.

The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameter $\epsilon $, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.

We study several criteria for the (non)linearity of Costas permutations, with or without the imposition of additional algebraic structure in the domain and the range of the permutation, aiming to find one that successfully identifies Costas permutations as more nonlinear than randomly chosen permutations of the same order.

We propose a new definition of a fractional-order Sumudu transform for fractional differentiable functions. In the development of the definition we use fractional analysis based on the modified Riemann-Liouville derivative that we name the fractional Sumudu transform. We also established a relationship between fractional Laplace and Sumudu duality with complex inversion formula for fractional Sumudu transform and apply new definition to solve fractional differential equations.

In recent years, many researchers have studied vibration suppression of fluttering plates using piezoelectric actuators. Lots of these researchers have focused on optimal placement of piezoelectric patches to obtain maximum controllability. Although mass and stiffness characteristics of bonded patches can alter aeroelastic behavior of fluttering plates, few of them considered the effect of the mentioned parameters in optimization process. This paper investigates effect of a bonded patch on aeroelastic behavior of cantilevered plates in supersonic flow. For this purpose, critical dynamic pressure and limit-cycle oscillations of the system are studied. Von Karman plate theory along with first order piston theory is employed for mathematical simulation of the system. Obtained results reveal that a bonded patch with a small mass ratio can change the system critical dynamic pressure significantly, where the main part of the variations is resulted from the added mass of the bonded patch. The maximum raise of dynamic pressure is acquired when the patch is placed on the plate’s leading edge. The results show that mass and stiffness characteristics of bonded piezoelectric patches can have a great impact on aeroelastic performance of fluttering plates. Therefore, these parameters must be considered as effective factors for optimal placement of piezo-actuators.

This paper proposes a simple surface interpolation attaining tangent-plane continuity. It is a natural extension of the local quadratic ${C}^{0}$ interpolator developed by the author (2005) in one of his works, which has already been applied successfully to diverse engineering problems. The methodology presented in this paper inherits most of the advantages possessed by the ${C}^{0}$ scheme. That is, (i) The algorithm is efficient and completely local requiring only the position vectors and normals given at the nodes of a patch, and hence it is suitable for parallel processing. (ii) It converges rapidly to the given surface with the increase in the number of nodes. (iii) Singular points (apexes, sharp edges, etc.) and nonmanifolds can be treated quite easily. (iv) Because of the minimization criteria assigned to the surface coefficients, it is rather robust and amenable to computational analyses. Validity and effectiveness of the proposed technique are demonstrated through numerical examples.

We consider the Bresse system with frictional dissipative terms acting in all the equations. We show the exponential decay of the solution by using a method developed by Z. Liu and S. Zheng and their collaborators in past years. The numerical computations were made by using the finite difference method to prove the theoretical results. In particular, the finite difference method in our case is locking free.

As a diffusion distance, we propose to use a metric (closely related to cosine similarity) which is defined as the ${L}^{2}$ distance between two ${L}^{2}$-normalized vectors. We provide a mathematical explanation as to why the normalization makes diffusion distances more meaningful. Our proposal is in contrast to that made some years ago by R. Coifman which finds the ${L}^{2}$ distance between certain ${L}^{1}$ unit vectors. In the second part of the paper, we give two proofs that an extension of mean first passage time to mean first passage cost satisfies the triangle inequality; we do not assume that the underlying Markov matrix is diagonalizable. We conclude by exhibiting an interesting connection between the (normalized) mean first passage time and the discretized solution of a certain Dirichlet-Poisson problem and verify our result numerically for the simple case of the unit circle.

This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation $c\left(x\right){\partial }_{t}^{2}u-\Delta u=0$ in a bounded smooth domain in ${ℝ}^{d}$ from partial (on part of the boundary) dynamic boundary measurements. In this paper, we prove that the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subset $\Gamma $ of the boundary determines explicitly the coefficient $c$ provided that $c$ is known outside a bounded domain. Then, through construction of appropriate test functions by a geometrical control method, we derive a formula for calculating the coefficient $c$ from the knowledge of the difference between the local Dirichlet-to-Neumann maps.

The paper describes a new method for numerical monitoring of discrepancies in natural gas supply to consumers, who receive gas from gas distribution loops. This method serves to resolve the vital problem of commercial natural gas accounting under the conditions of deficient field measurements of gas supply volumes. Numerical monitoring makes it possible to obtain computational estimates of actual gas deliveries over given time spans and to estimate their difference from corresponding values reported by gas consumers. Such estimation is performed using a computational fluid dynamics simulator of gas flows in the gas distribution system of interest. Numerical monitoring of the discrepancy is based on a statement and numerical solution of identification problem of a physically proved gas dynamics mode of natural gas transmission through specified gas distribution networks. The identified mode parameters should have a minimum discrepancy with field measurements of gas transport at specified reference points of the simulated pipeline network.

Neutral stochastic functional differential equations (NSFDEs) have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper is to remove the linear growth condition and establish a Khasminskii-type test for nonlinear NSFDEs. New criteria not only cover a wide class of highly nonlinear NSFDEs but they can also be verified much more easily than the classical criteria. Finally, several examples are given to illustrate main results.

The complex relationships of a crop with the pest, its natural enemies, and the climate factors exist in all the ecosystems, but the mathematic models has studied only some components to know the relation cause-effect. The most studied system has been concerned with the relationship pest-natural enemies such as prey-predator or host-parasitoid. The present paper shows a dynamical system for studying the relationship host-parasitoid (Diaphorina citri, Tamarixia radiata) and shows that a nonlinear model permits the estimation of the parasite nymphs using nymphs healthy as the known variable. The model showed the functional answer of the parasitoid, in which a point arrives that its density is not augmented although the number host increases, and it becomes necessary to intervene in the ecosystem. A simple algorithm is used to estimate the parasitoids level using the priori relationship between the host and the climate factors and then the nonlinear model.

The random perturbation of generalized reduced gradient method for optimization under nonlinear differentiable constraints is proposed. Generally speaking, a particular iteration of this method proceeds in two phases. In the Restoration Phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, a generally nonlinear system of equations. In the Optimization Phase, optimality is improved by means of the consideration of the objective function, on the tangent subspace to the constraints. In this paper, optimal assumptions are stated on the Restoration Phase and the Optimization Phase that establish the global convergence of the algorithm. Some numerical examples are also given by mixture problem and octagon problem.

We present a constructive approach to the functional quantization problem of stochastic processes, with an emphasis on Gaussian processes. The approach is constructive, since we reduce the infinite-dimensional functional quantization problem to a finite-dimensional quantization problem that can be solved numerically. Our approach achieves the sharp rate of the minimal quantization error and can be used to quantize the path space for Gaussian processes and also, for example, Lévy processes.

An interfacial area transport equation (IATE), proposed to dynamically describe the interfacial structure evolution of two-phase flows, could help improve the predictive capability of the two-fluid model. The present study aims to investigate the well-posedness issue of a one-dimensional two-fluid model with the IATE (named “two-fluid-IATE model” hereafter) using a characteristic analysis. The momentum flux parameters, which take into account the coupling of the volumetric fraction of phase and velocity distributions over the cross-section of a flow passage, are employed. A necessary condition for the system to achieve hyperbolicity under an adiabatic flow condition is identified. A case study is performed for an adiabatic liquid-liquid slug flow, which shows that the hyperbolicity of the two-fluid-IATE model is guaranteed if appropriate correlations of the momentum flux parameters are applied in the two-fluid-IATE model.

Image analysis by topological gradient approach is a technique based upon the historic application of the topological asymptotic expansion to crack localization problem from boundary measurements. This paper aims at reviewing this methodology through various applications in image processing; in particular image restoration with edge detection, classification and segmentation problems for both grey level and color images is presented in this work. The numerical experiments show the efficiency of the topological gradient approach for modelling and solving different image analysis problems. However, the topological gradient approach presents a major drawback: the identified edges are not connected and then the results obtained particularly for the segmentation problem can be degraded. To overcome this inconvenience, we propose an alternative solution by combining the topological gradient approach with the watershed technique. The numerical results obtained using the coupled method are very interesting.

3D solutions of the dynamical equations in the presence of external forces are derived for a homogeneous, prestressed medium. 2D plane waves solutions are obtained from general solutions and show that there exist two types of plane waves, namely, quasi-P waves and quasi-SV waves. Expressions for slowness surfaces and apparent velocities for these waves are derived analytically as well as numerically and represented graphically.

The covariance structure of spatial Gaussian predictors (aka Kriging predictors) is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood of spatial Gaussian predictor models as a function of its hyperparameters is investigated theoretically. Asymptotic sandwich bounds for the maximum likelihood function in terms of the condition number of the associated covariance matrix are established. As a consequence, the main result is obtained: optimally trained nondegenerate spatial Gaussian processes cannot feature arbitrary ill-conditioned correlation matrices. The implication of this theorem on Kriging hyperparameter optimization is exposed. A nonartificial example is presented, where maximum likelihood-based Kriging model training is necessarily bound to fail.

Optimization problems with second-order cone constraints (SOCs) can be solved efficiently by interior point methods. In order for some of these methods to get started or to converge faster, it is important to have an initial feasible point or near-feasible point. In this paper, we study and apply Chinneck's Original constraint consensus method and DBmax constraint consensus method to find near-feasible points for systems of SOCs. We also develop and implement a new backtracking-like line search technique on these methods that attempts to increase the length of the consensus vector, at each iteration, with the goal of finding interior feasible points. Our numerical results indicate that the new methods are effective in finding interior feasible points for SOCs.