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Motivated by investigations of the tridiagonal pairs of linear transformations, we introduce the augmented tridiagonal algebra ${\mathcal T}_q$. This is an infinite-dimensional associative ${\mathbb C}$-algebra with 1. We classify the…
Ordinary electric woodworking tools are integrated into a multiple-object-aware augmented framework to assist operators in fabrication tasks. This study presents an advanced evaluation of the developed open-source fabrication software…
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
Additive utility function models are widely used in multiple criteria decision analysis. In such models, a numerical value is associated to each alternative involved in the decision problem. It is computed by aggregating the scores of the…
The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…
This article provides an introduction to and review of the field of computer-aided molecular design (CAMD). It is intended to be approachable for the absolute beginner as well as useful to the seasoned CAMD practitioner. We begin by…
The focus on locally refined spline spaces has grown rapidly in recent years due to the need in Isogeoemtric analysis (IgA) of spline spaces with local adaptivity: a property not offered by the strict regular structure of tensor product…
This paper begins by reviewing numerous theoretical advancements in the field of multivariate splines, primarily contributed by Professor Larry L. Schumaker. These foundational results have paved the way for a wide range of applications and…
Industrial X-ray computed tomography (XCT) is a powerful tool for non-destructive characterization of materials and manufactured components. XCT commonly accompanied by advanced image analysis and computer vision algorithms to extract…
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…
Integrating topology optimization and additive manufacturing (AM) technology can facilitate innovative product development. However, laser powder bed fusion, which is the predominant method in metal AM, can lead to issues such as residual…
Ising machines are specialized computers for finding the lowest energy states of Ising spin models, onto which many practical combinatorial optimization problems can be mapped. Simulated bifurcation (SB) is a quantum-inspired parallelizable…
Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear…
Hybrid manufacturing (HM) technologies combine additive and subtractive manufacturing (AM/SM) capabilities in multi-modal process plans that leverage the strengths of each. Despite the growing interest in HM technologies, software tools for…
As a quantum-inspired, non-traditional analog solver architecture, the analog Ising machine (AIM) has emerged as a distinctive computational paradigm to address the rapidly growing demand for computational power. However, the mathematical…
Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. While most of these methods are in principle directly extendable to non-additive surface models, they…
There is an increasing interest in the fabrication of cement-based materials via additive manufacturing (AM) techniques. However, the processing-induced heterogeneities and interfaces represent a major challenge. The role of processing in…
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…
Conformal Geometric Algebra (CGA) is a framework that allows the representation of objects, such as points, planes and spheres, and deformations, such as translations, rotations and dilations as uniform vectors, called multivectors. In this…