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Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…

We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using…

In this paper, we propose a tensor type of discretization and optimization process for solving high dimensional partial differential equations. First, we design the tensor type of trial function for the high dimensional partial differential…

It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpler structural form, but it is well known that this goal may imply an increase in the dimension of the system. This is what happens if in this…

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…

The present work deals with the search of useful physical applications of some generalized groups of metric transformations. We put forward different proposals and focus our attention on the implementation of one of them. Particularly, the…

The circular coordinates algorithm, a key tool in topological data analysis, relies on a theoretically unvalidated lifting step to convert cocycles from a prime field to integer coefficients. We provide a rigorous analysis of this…

Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expressed as the projection of a much simpler set in higher…

The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important…

Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have…

Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way.…

A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the…

The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…

We develop a general framework for working with structured lifting problems, establishing closure and uniqueness properties of their solutions. In a subsequent paper, we apply these results to axiomatize computation rules of cubical type…

A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the…

A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the…

We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie…

This paper describes the notion of \sigma -symmetry, which extends the one of \lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider…

High-dimensional quantum information processing has become a mature field of research with several different approaches being adopted for the encoding of $D$-dimensional quantum systems. Such progress has fueled the search of reliable…