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Statistical event reconstruction techniques can give better results for gamma cameras than the traditional centroid method. However, implementation of such techniques requires detailed knowledge of the PMT light response functions. Here we…
This paper is devoted to a simple and short proof on the sharp upper bound of lifespan of classical solutions to wave equations with the critical power nonlinearities of spatial derivatives of the unknown function. Such a proof is so-called…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and…
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…
Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…
wave solutions to nonlinear partial differential equations. We simplify the so called (G'/G)-expansion method and apply two of those methods to simple physical problems.
Iterative learning to infer approaches have become popular solvers for inverse problems. However, their memory requirements during training grow linearly with model depth, limiting in practice model expressiveness. In this work, we propose…
In this Perspective, we highlight several recent studies that illustrate how inverse strategies using appropriate physical models and computational methods can address complex materials design questions.
We present a general scheme for the construction of new eficient generalized Schultz iterative methods for computing the inverse matrix. These methods have the form $$ X_{k+1} = X_k(a_0^{(k)}I+a_1^{(k)}AX_k),\quad k\in\mathbb{N}, $$ where…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…
Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term numerical emphasizes that a numerical solution is computed. The method consists in replacing the right hand…
We propose and test an iterative technique for improving the temporal focusing of a time reversal mirror. A single amplification parameter is introduced to tune the convergence of the iteration. The tunable iterative technique is validated…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Iterated loop algebras are by definition obtained by repeatedly applying the loop construction, familiar from the theory of affine Kac-Moody Lie algebras, to a given base algebra. Our interest in this iterated construction is motivated by…
A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation…
This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…