Open Access

Article

Article ID: 2901

The new Generalized Schwarzschild-spacetimes trivial Ricci solitons and the new smooth metric space

by Orchidea Maria Lecian

Journal of AppliedMath, Vol.3, No.4, 2025;

The Ricci flow of the Generalized-Schwarzschild spacetimes is newly studied. The soliton configurations are newly stated as trivial Ricci soliton of (Generalized)-Schwarzschild spacetimes. The new smooth metric space is written; the majorization theorem for the distance is given. The application of harmonic maps is presented. The definition of topological soliton as a Schwarzschild soliton of complete Riemannian manifold is newly provided with. New theorems about Generalized-Schwarzschild solitons which are extended from those about the Kaehler solitons are proven; the new theorems are given, which allow one to establish the differences with respect to Kaehler solitons. The new properties of the Generalized Schwarzschild metric are studied. As results, smooth metric spaces are newly exposed as ones endowed with bounded Bakry-Emery curvature; the initial conditions are newly studied: the weight function is majorized as consisting of a polynomial function of the distance(s) (from the initial condition) at most.The Generalized-Schwarzschild metric is now newly proven to be descending from a smooth function. The initial conditions are newly studied to depend only on the spherical neighborhood of the point. The trivial expanding Ricci Kaehler soliton is newly proven to be a Generalized-Schwarzschild soliton; accordingly, this soliton is newly proven to have only one end.

Open Access

Article

Article ID: 2992

Model validation based on value-of-information theory

by George Hazelrigg

Journal of AppliedMath, Vol.3, No.4, 2025;

The modeling and simulation community has devoted considerable attention to the question of model validity as a condition for the use of a model in an engineering decision-making process. Their work has focused on the concept of “accuracy”, loosely defined as the difference between a model-computed result and a real-world result. The objective of this paper is to introduce an alternative approach, based on classical decision theory, that focuses on the value of the information that a model provides to the decision-making process. This is a significant departure from the current approach to model validation, and it derives from the preference, “I want the best outcome that I can get”. Use is made of an example case that results in a paradox to illustrate weaknesses in the accuracy-focused approach. Instead of advocating the use of a model based on its accuracy, this work advocates using a model if it adds value to the overall application, thus relating validation directly to system performance. The approach fills significant gaps in the current theory, notably providing a clearly defined validity metric and a mathematically rigorous rationale for the use of this metric.

Open Access

Article

Article ID: 3040

On wavelet type Chlodovsky Bézier operators

by Harun Karsli

Journal of AppliedMath, Vol.3, No.4, 2025;

This paper mainly deals with Chlodovsky Bézier variants constructed via compactly supported Daubechies wavelets. We estimate the convergence rate of the aforementioned operators at a fixed point x₀ > 0 at which the one-sided limits exist of the target function f. It is evident that the class of operators under consideration encompasses at least the classical version of the Chlodovsky operators along with their B ézier and Kantorovich variants. Therefore, our findings broaden and build upon previous results on Chlodovsky, Chlodovsky Bézier, Chlodovsky-Kantorovich Bézier operators presented in the literature.

Open Access

Review

Article ID: 3011

A new quantum computational set-up for algebraic topology via simplicial sets

by Roberto Zucchini

Journal of AppliedMath, Vol.3, No.4, 2025;

In this paper, a quantum computational framework for algebraic topology based on simplicial set theory is presented. This extends previous work, which was limited to simplicial complexes and aimed mostly at topological data analysis. The proposed set-up applies to any parafinite simplicial set and proceeds by associating with it a finite dimensional simplicial Hilbert space, whose simplicial operator structure is studied in some depth. It is shown in particular how the problem of determining the simplicial set’s homology can be solved within the simplicial Hilbert framework. Further, the conditions under which simplicial set theoretic algorithms can be implemented in a quantum computational setting with finite resources are examined. Finally a quantum algorithmic scheme capable of computing the simplicial homology spaces and Betti numbers of a simplicial set combining a number of basic quantum algorithms is outlined.

Open Access

Article

Article ID: 2837

Mathematical modeling of the process of hydrotreating diesel fuel from organosulfur impurities

by Naum A. Samoilov

Journal of AppliedMath, Vol.3, No.3, 2025;

Hydrotreating of diesel fuel is a major catalytic process for motor fuel production. This process aims to reduce the organosulfur content in the fuel to 10 parts per million (ppm) in order to meet environmental standards. However, this deep purification of diesel fuel requires the use of an expensive catalyst at hydrotreating plants, which have giant reactors with a capacity of 200–600 cubic meters. Such a volume of reactors is associated with the use of methods of classical kinetics of chemical reactions, when all the raw materials of the process are in the reactor until the required conversion depth is reached, while hydrotreating has its own specific features. All known mathematical models for diesel fuel hydrotreating take into account different nuances of the process, but they all have one common disadvantage: they use approximate, often crude, ideas about the composition of multicomponent raw materials, such as diesel oil fractions, which contain several dozen different organosulfur compounds with varying activity in hydrogenation reactions. Most often, these raw materials are represented in a mathematical model as a combination of two to six pseudo-components, or lumps, that combine sulfo-organic impurities from one or more homologous groups. Such a theoretical framework allows us to model the current state of hydrotreating technology, but it does not advance it. We propose a new approach to mathematical modeling of diesel fuel hydrotreatment, which better takes into account the actual features of the process. The structure of the mathematical model considers the composition of the raw material as a set of 10–20 narrow fractions. In each fraction, the set of hydrogenated organosulfur impurities is treated as a single pseudo-component. Another feature of the model is the use of different rate constants for different organosulfur impurities in the raw material, represented as a continuous kinetic characteristic that changes over time. This allows us to integrate the system of differential equations in the model and adapt the rate constant to the concentration of the hydrogenated organosulfur impurity at any given time during the process. The developed model has also made it possible to propose a new technology, hydrotreatment: separating the feedstock into two or three wide fractions, combining the corresponding narrow fractions, and then subjecting them to separate hydrogenation processes. This differential hydrotreatment technique will allow for a reduction of the catalyst load in the hydrotreatment unit by almost 50% while maintaining its efficiency or for doubling the efficiency while maintaining the same catalyst load with traditional technology.

Open Access

Article

Article ID: 2609

On galaxies of sequences of matrix Pythagorean triples and completely Pythagorean maps

by Joachim Moussounda Mouanda, Jean Raoul Tsiba, Kinvi Kangni

Journal of AppliedMath, Vol.3, No.3, 2025;

We develop an algorithm that allows us to construct the sequences of matrix Pythagorean triples of any size. We prove that there exists an infinite number of galaxies of sequences of matrix Pythagorean triples. We construct the semiring of sequences of matrix Pythagorean triples called the astral body of the set Mm(ℕ) associated to a galaxy. We show that every galaxy of sequences of matrix Pythagorean triples is associated with a semiring, and every semiring is associated with a homomorphism of semirings. We construct the astral body of the set of complex polynomials over the unit disk D. We construct the semiring of astral bodies of the set Mm(ℕ) associated with several galaxies. We also introduce the sequences of completely Pythagorean maps over N³.