First time, an analytical two-dimensional (2D) elasticity solution for arbitrarily supported axially functionally graded (FG) beam is developed. Linear gradation of the material property along the axis of the beam is considered. Using the strain displacement and constitutive relations, governing partial differential equations (PDEs) is obtained by employing Ressiner mixed var...

We propose an approach to solving two-dimensional linear and nonlinear boundary-value problems of statics for shallow shells based on the generalized method finite integral transformations Newton– Kantorovich–Raphson linearization. In case, application is reduced construction two with respect different variables in analyzed domain under assumption that kernels one transformation are transforms ...

We propose a new algorithm to solve the unbalanced and partial L1-Monge– Kantorovich problems. The proposed method is a first-order primal-dual method that is scalable and parallel. The method’s iterations are conceptually simple, computationally cheap, and easy to parallelize. We provide several numerical examples solved on a CUDA GPU, which demonstrate the method’s practical effectiveness.

We revisit a one-step intermediate Newton iterative scheme that was used by Uko and Velásquez in [17] for the constructive solution of nonlinear equations of the type f(u) + g(u) = 0 . By utilizing weaker hypotheses of the Zabrejko-Nguen kind and a modified majorizing sequence we perform a semilocal convergence analysis which yields finer error bounds and more precise information on the locatio...

We recall the history of the transportation (Kantorovich) metric and the Monge–Kantorovich problem. We also describe several little-known applications: the first one concerns the theory of decreasing sequences of partitions (tower of measures and iterated metric), the second one relates to Ornstein's theory of Bernoulli automorphisms (¯ d-metric), and the third one is the formulation of the str...

We propose a constructive approach to solve the Monge-Kantorovich problem for chains of infinite order on a finite alphabet with an additive cost function. From this constructive description of the Kantorovich coupling we obtain, for any ǫ > 0, a perfect simulation algorithm for sampling from an ǫ-approximating coupling which assigns to the cost function an expectation which is ǫ-close to the m...

Calculation schemes for numerical solution of elliptic boundary-value problems for Schrödinger-type equations based on Kantorovich method that reduces the initial problem to a set of boundary-value problems for a system of ordinary second-order differential equations are presented. The reduced boundaryvalue problems are discretized using the high-accuracy finite element method and implemented i...

In this paper, we present some applications of the multivariate sampling Kantorovich operators Sw to seismic engineering. The mathematical theory of these operators, both in the space of continuous functions and in Orlicz spaces, show how it is possible to approximate/reconstruct multivariate signals, such as images. In particular, to obtain applications for thermographic images a mathematical ...